%PDF-1.4 % 5 0 obj << /Length 15044 /LC /QQAP >> stream q BT /F53 17.9328 Tf 81.917 707.187 Td [(Example\255driven)-278(Design)-278(of)-278(Ef\002cient)-278(Recor)20(d)-278(Matc)10(hing)]TJ 189.549 -19.925 Td [(Queries)]TJ/F54 11.9552 Tf -191.626 -40.598 Td [(Sur)10(ajit)-278(Chaudhur)-15(i)-2780(Bee\255Chung)-278(Chen)]TJ/F36 8.9664 Tf 218.015 8.966 Td [(\003)]TJ/F54 11.9552 Tf 31.196 -8.966 Td [(V)80(enkatesh)-278(Ganti)-2224(Ragha)20(v)-278(Kaushik)]TJ -254.493 -11.877 Td [(Microsoft)-278(Research)-3336(UW)40(\255Madison)-3058(Microsoft)-278(Research)-834(Microsoft)-278(Research)]TJ/F36 8.9664 Tf 52.676 -11.878 Td [(f)]TJ/F54 11.9552 Tf 4.608 0 Td [(sur)10(ajitc)15(,vganti,skaushi)]TJ/F36 8.9664 Tf 116.634 0 Td [(g)]TJ/F54 11.9552 Tf 4.608 0 Td [(@microsoft.com)-1390(beechung@cs)15(.wisc.edu)]TJ/F55 11.9552 Tf -199.286 -47.098 Td [(ABSTRA)55(CT)]TJ/F56 8.9664 Tf 0 -14.446 Td [(Record)-389(matching)-389(is)-390(the)-389(task)-389(of)-389(identifying)-390(records)-389(that)-389(match)-389(the)]TJ 0 -10.461 Td [(same)-341(real)-342(w)10(orld)-341(entity)65(.)-584(This)-341(is)-341(a)-341(problem)-342(of)-341(great)-341(signi\002cance)-341(for)]TJ 0 -10.461 Td [(a)-341(v)25(ariety)-342(of)-341(b)20(usiness)-341(intelligence)-341(applications.)-584(Implementations)-341(of)]TJ 0 -10.46 Td [(record)-297(matching)-296(rely)-297(on)-296(e)15(xact)-297(as)-296(well)-297(as)-296(approximate)-297(string)-296(match-)]TJ 0 -10.461 Td [(ing)-307(\050e.g.,)-320(edit)-307(distances\051)-306(and)-307(use)-306(of)-307(e)15(xternal)-306(reference)-307(data)-306(sources.)]TJ 0 -10.461 Td [(Record)-280(matching)-281(can)-280(be)-280(vie)25(wed)-281(as)-280(a)-281(query)-280(composed)-280(of)-281(a)-280(small)-280(set)]TJ 0 -10.461 Td [(of)-299(primiti)25(v)15(e)-299(operators.)-456(Ho)25(we)25(v)15(er)40(,)-311(formulating)-299(such)-299(record)-298(matching)]TJ 0 -10.461 Td [(queries)-290(is)-291(dif)25(\002cult)-290(and)-290(depends)-290(on)-291(the)-290(speci\002c)-290(application)-290(scenario.)]TJ 0 -10.46 Td [(Speci\002cally)65(,)-282(the)-275(number)-276(of)-275(options)-275(both)-276(in)-275(terms)-276(of)-275(string)-275(matching)]TJ 0 -10.461 Td [(operations)-366(as)-365(well)-366(as)-366(the)-365(choice)-366(of)-366(e)15(xternal)-365(sources)-366(can)-366(be)-365(daunt-)]TJ 0 -10.461 Td [(ing.)-308(In)-245(this)-245(paper)40(,)-246(we)-245(e)15(xploit)-245(the)-245(a)20(v)25(ailability)-245(of)-245(positi)25(v)15(e)-244(and)-245(ne)15(g)5(ati)25(v)15(e)]TJ 0 -10.461 Td [(e)15(xamples)-319(to)-318(search)-319(through)-319(this)-318(space)-319(and)-318(suggest)-319(an)-319(initial)-318(record)]TJ 0 -10.46 Td [(matching)-306(query)65(.)-479(Such)-307(queries)-306(can)-306(be)-306(subsequently)-307(modi\002ed)-306(by)-306(the)]TJ 0 -10.461 Td [(programmer)-283(as)-283(needed.)-408(W)80(e)-283(ensure)-283(that)-283(the)-283(record)-283(matching)-282(queries)]TJ 0 -10.461 Td [(our)-283(approach)-282(produces)-283(are)-282(\0501\051)-283(ef)25(\002cient:)-375(these)-282(queries)-283(can)-282(be)-283(run)-282(on)]TJ 0 -10.461 Td [(lar)18(ge)-390(datasets)-390(by)-390(le)25(v)15(eraging)-390(operations)-390(that)-390(are)-389(well-supported)-390(by)]TJ 0 -10.461 Td [(RDBMSs,)-249(and)-249(\0502\051)-248(e)15(xplainable:)-310(the)-248(queries)-249(are)-248(easy)-249(to)-249(understand)-248(so)]TJ 0 -10.46 Td [(that)-242(the)15(y)-241(may)-242(be)-242(modi\002e)1(d)-242(by)-242(the)-241(programmer)-242(with)-242(relati)25(v)15(e)-241(ease.)-307(W)80(e)]TJ 0 -10.461 Td [(demonstrate)-286(the)-287(ef)25(fecti)25(v)15(eness)-286(of)-286(our)-287(a)1(pproach)-287(on)-286(se)25(v)15(eral)-286(real-w)10(orld)]TJ 0 -10.461 Td [(datasets.)]TJ/F55 11.9552 Tf 0 -26.247 Td [(1.)-1000(INTR)30(ODUCTION)]TJ/F56 8.9664 Tf 8.967 -12.952 Td [(Data)-336(cleaning)-335(is)-336(a)-335(critical)-336(element)-336(for)-335(de)25(v)15(eloping)-336(ef)25(fecti)25(v)15(e)-335(b)20(usi-)]TJ -8.967 -10.46 Td [(ness)-358(intelligence)-358(applications.)-635(The)-358(inability)-358(to)-358(ensure)-358(data)-358(quality)]TJ 0 -10.461 Td [(can)-365(ne)15(g)5(ati)25(v)15(ely)-365(af)25(fect)-364(do)25(wnstream)-365(data)-365(analysis)-365(and)-365(ultimately)-364(k)10(e)15(y)]TJ 0 -10.461 Td [(b)20(usiness)-278(decisions.)-395(A)-279(v)15(ery)-278(important)-278(data)-278(cleaning)-279(operation)-278(is)-278(that)]TJ 0 -10.461 Td [(of)-315(identifying)-316(records)-315(which)-315(match)-316(the)-315(same)-316(real)-315(w)10(orld)-315(entity)65(.)-506(F)15(or)]TJ 0 -10.46 Td [(e)15(xample,)-341(o)25(wing)-323(to)-322(v)25(arious)-323(errors)-323(in)-323(data)-322(and)-323(to)-323(dif)25(ferences)-323(in)-322(con-)]TJ 0 -10.461 Td [(v)15(entions)-360(of)-361(representing)-360(data,)-388(product)-360(names)-360(in)-361(sales)-360(records)-360(may)]TJ 0 -10.461 Td [(not)-305(match)-304(e)15(xactly)-305(with)-304(records)-305(in)-304(master)-305(product)-304(catalog)-305(tables.)-473(In)]TJ 0 -10.461 Td [(these)-206(situations,)-216(it)-206(w)10(ould)-207(be)-206(desirable)-207(to)]TJ/F57 8.9664 Tf 143.202 0 Td [(matc)15(h)-207(s)1(imilar)-207(r)37(ecor)37(ds)]TJ/F56 8.9664 Tf 79.473 0 Td [(across)]TJ -222.675 -10.461 Td [(relations.)-303(This)-230(problem)-230(of)-230(matching)-230(similar)-230(records)-230(has)-230(be)1(en)-230(studied)]TJ 0 -10.46 Td [(in)-261(the)-260(conte)15(xt)-261(of)-260(record)-261(linkage)-260(\050e.g.)-261([16,)-263(21,)-263(13]\051)-260(and)-261(of)-260(identifying)]TJ 0 -10.461 Td [(approximate)-250(duplicate)-250(entities)-250(in)-250(databases)-250(\050e.g.,)-250([15,)-250(23,)-250(25]\051.)]TJ 8.967 -10.461 Td [(Gi)25(v)15(en)-322(tw)10(o)-321(relations)]TJ/F34 8.9664 Tf 74.447 0 Td [(R)]TJ/F56 8.9664 Tf 9.919 0 Td [(and)]TJ/F34 8.9664 Tf 15.832 0 Td [(S)]TJ/F56 8.9664 Tf 6.139 0 Td [(,)-340(the)-321(record)-322(matching)-322(probl)1(em)-322(is)-322(to)]TJ ET q 1 0 0 1 53.798 188.324 cm []0 d 0 J 0.398 w 0 0 m 98.031 0 l S Q BT /F36 8.9664 Tf 53.798 181.363 Td [(\003)]TJ/F56 8.9664 Tf 4.608 -3.985 Td [(W)80(ork)-250(done)-250(when)-250(this)-250(author)-250(w)10(as)-250(visiting)-250(Microsoft)-250(Research.)]TJ/F56 7.9701 Tf -1.619 -33.149 Td [(Permission)-186(to)-186(cop)10(y)-186(without)-186(fee)-186(all)-186(or)-185(part)-186(of)-186(this)-186(material)-186(is)-186(granted)-186(pro)15(vided)]TJ 0 -8.966 Td [(that)-229(the)-230(copies)-229(are)-230(not)-229(made)-230(or)-229(distrib)20(uted)-230(for)-229(direct)-230(commercial)-229(adv)25(antage,)]TJ 0 -8.967 Td [(the)-160(VLDB)-160(cop)10(yright)-160(notice)-161(and)-160(the)-160(title)-160(of)-160(the)-160(publication)-161(and)-160(its)-160(date)-160(appear)40(,)]TJ 0 -8.966 Td [(and)-335(notice)-334(is)-335(gi)25(v)15(en)-334(that)-335(cop)10(ying)-335(is)-334(by)-335(permission)-335(of)-334(the)-335(V)111(ery)-334(Lar)18(ge)-335(Data)]TJ 0 -8.966 Td [(Base)-338(Endo)25(wment.)-625(T)80(o)-338(cop)10(y)-338(otherwise,)-361(or)-338(to)-338(republish,)-360(to)-338(post)-338(on)-338(serv)15(ers)]TJ 0 -8.967 Td [(or)-286(to)-286(redistrib)20(ute)-286(to)-286(lists,)-295(requires)-286(a)-286(fee)-286(and/or)-286(special)-286(permission)-286(from)-286(the)]TJ 0 -8.966 Td [(publisher)40(,)-250(A)40(CM.)]TJ/F57 7.9701 Tf 0 -8.966 Td [(VLDB)-250(`07,)]TJ/F56 7.9701 Tf 36.527 0 Td [(September)-250(23\25528,)-250(2007,)-250(V)60(ienna,)-250(Austria.)]TJ -36.527 -8.967 Td [(Cop)10(yright)-250(2007)-250(VLDB)-250(Endo)25(wment,)-250(A)40(CM)-250(978\2551\25559593\255649\2553/07/09.)]TJ/F56 8.9664 Tf 254.047 503.313 Td [(identify)-201(pairs)-202(of)-201(records)-202(in)]TJ/F34 8.9664 Tf 95.19 0 Td [(R)]TJ/F36 8.9664 Tf 7.428 0 Td [(\002)]TJ/F34 8.9664 Tf 7.56 0 Td [(S)]TJ/F56 8.9664 Tf 7.946 0 Td [(that)-201(\223represent\224)-202(the)-201(same)-202(real)-201(w)10(orld)]TJ -118.124 -10.461 Td [(entity)65(.)-571(Consider)-337(the)-337(scenario)-337(that)-337(arose)-337(after)-337(the)-336(hurricane)-337(Katrina)]TJ 0 -10.461 Td [(hit)-311(the)-311(gulf)-311(coast.)-493(While)-311(af)25(fected)-311(people)-311(were)-311(re)15(gistered)-311(into)-311(e)25(v)25(ac-)]TJ 0 -10.461 Td [(uee)-333(camps,)-354(relati)25(v)15(es)-333(and)-334(friends)-333(across)-333(the)-333(country)-333(were)-333(enquiring)]TJ 0 -10.46 Td [(for)-357(their)-358(safety)65(.)-632(Figure)-357(1)-358(sho)25(ws)-357(a)-357(fe)25(w)-358(e)15(xample)-357(records)-358(in)-357(tw)10(o)-357(re-)]TJ 0 -10.461 Td [(lations,)]TJ/F57 8.9664 Tf 28.797 0 Td [(Evacuees)]TJ/F56 8.9664 Tf 36.418 0 Td [(\050af)25(fected)-286(people)-285(re)15(gistered)-286(at)-286(e)25(v)25(acuee)-285(camps\051)-286(and)]TJ/F57 8.9664 Tf -65.215 -10.461 Td [(Enquiries)]TJ/F56 8.9664 Tf 38.33 0 Td [(\050requests)-386(for)-386(whereabouts)-386(of)-385(e)25(v)25(acuees\051.)]TJ/F56 5.9776 Tf 146.585 3.809 Td [(1)]TJ/F56 8.9664 Tf 9.922 -3.809 Td [(As)-386(seen)-386(from)]TJ -194.837 -10.461 Td [(the)-306(e)15(xample,)-320(both)-306(relations)-307(are)-306(quite)-306(unclean)-306(with)-306(lots)-306(of)-306(incorrect,)]TJ 0 -10.46 Td [(abbre)25(viated,)-407(and)-376(missing)-376(v)25(alues,)-407(and)-375(therefore)-376(the)-376(task)-376(of)-375(design-)]TJ 0 -10.461 Td [(ing)-253(a)-254(program)-253(for)-254(accurately)-253(matching)-253(enquiry)-254(records)-253(with)-253(e)25(v)25(acuee)]TJ 0 -10.461 Td [(records)-381(is)-382(quite)-381(challenging.)-704(Such)-382(challenges)-381(also)-382(arise)-381(in)-381(record)]TJ 0 -10.461 Td [(matching)-243(scenarios)-243(across)-244(a)-243(v)25(ariety)-243(of)-243(other)-244(domains:)-306(matching)-243(cus-)]TJ 0 -10.461 Td [(tomers)-336(across)-336(tw)10(o)-336(sales)-336(databases,)-358(matching)-336(patient)-336(records)-336(across)]TJ 0 -10.46 Td [(tw)10(o)-350(databases)-349(in)-350(a)-350(lar)18(ge)-350(hospital,)-374(matching)-350(product)-350(records)-349(across)]TJ 0 -10.461 Td [(tw)10(o)-311(catalogs,)-326(etc.)-493(In)-311(all)-311(these)-311(scenarios,)-326(a)-311(primary)-311(requirement)-311(be-)]TJ 0 -10.461 Td [(sides)-332(accurac)15(y)-333(is)-332(that)-332(record)-332(matching)-333(programs)-332(be)-332(also)-332(ef)25(\002ciently)]TJ 0 -10.461 Td [(e)15(x)15(ecutable)-250(o)15(v)15(er)-250(v)15(ery)-250(lar)18(ge)-250(relations.)]TJ/F57 8.9664 Tf 8.967 -13.487 Td [(Pr)45(o)10(gr)15(amming)-343(Primitives)]TJ/F56 8.9664 Tf 89.616 0 Td [(:)-496(One)-343(of)-342(our)-343(primary)-343(design)-343(goals)-343(is)-343(to)]TJ -98.583 -10.46 Td [(ensure)-313(that)-314(record)-313(matching)-313(programs)-314(be)-313(e)15(x)15(ecutable)-313(ef)25(\002ciently)-313(and)]TJ 0 -10.461 Td [(scalably)-272(o)15(v)15(er)-273(lar)18(ge)-272(input)-273(relations.)-377(T)80(o)25(w)10(ards)-272(that)-273(goal,)-278(we)-272(model)-272(the)]TJ 0 -10.461 Td [(record)-300(matching)-300(task)-300(as)-300(that)-300(of)-300(designing)-300(an)]TJ/F57 8.9664 Tf 163.962 0 Td [(oper)15(ator)-300(tr)37(ee)]TJ/F56 8.9664 Tf 50.239 0 Td [(obtained)]TJ -214.201 -10.461 Td [(by)-250(composing)-250(a)-250(fe)25(w)-250(primiti)25(v)15(e)-250(operators.)]TJ 8.967 -10.46 Td [(A)-273(v)25(ariety)-273(of)-273(string)-273(similarity)-273(functions)-273(ha)20(v)15(e)-273(been)-273(widely)-273(used)-273(for)]TJ -8.967 -10.461 Td [(declaring)-326(record)-326(pairs)-327(with)-326(high)-326(similarities)-326(to)-327(be)-326(matches)-326([21,)-345(25,)]TJ 0 -10.461 Td [(22,)-455(15,)-455(23,)-454(13].)-802(Ho)25(we)25(v)15(er)40(,)-455(no)-413(single)-414(string)-414(similarity)-414(function)-413(is)]TJ 0 -10.461 Td [(kno)25(wn)-250(to)-250(be)-250(the)-250(o)15(v)15(erall)-250(best)-250([24,)-250(34].)]TJ 8.967 -10.461 Td [(More)-300(comple)15(x)-301(functions)-300(may)-301(be)-300(b)20(uilt)-301(upon)-300(these)-301(basic)-300(functions)]TJ -8.967 -10.46 Td [(in)-342(order)-342(to)-342(impro)15(v)15(e)-342(accurac)15(y)65(.)-587(In)-342(the)-342(e)15(xample)-342(of)-342(Figure)-342(1,)-365(f)10(ather')55(s)]TJ 0 -10.461 Td [(name)-331(may)-331(only)-331(be)-331(used)-331(if)-331(it)-331(is)-332(not)-331(null.)-553(Or)40(,)-351(one)-331(may)-331(use)-331(edit)-331(dis-)]TJ 0 -10.461 Td [(tance)-282(on)-283(the)-282(\050Name,)-290(F)15(ather')55(s)-282(Name\051)-283(columns)-282(and)-282(jaccard)-282(similarity)]TJ 0 -10.461 Td [(on)-279(the)-280(\050Name,)-287(Address\051)-279(columns,)-287(and)-279(\223combine\224)-280(the)-279(similarity)-279(v)25(al-)]TJ 0 -10.46 Td [(ues)-309(in)-309(order)-309(to)-309(arri)25(v)15(e)-309(at)-309(an)-309(accurate)-309(record)-309(matching)-309(progra)1(m.)-487(The)]TJ/F57 8.9664 Tf 0 -10.461 Td [(similarity)-295(join)]TJ/F56 8.9664 Tf 53.622 0 Td [(operator)-295(implements)-295(this)-296(int)1(uition)-296(\050see)-295(tutorial)-295([28]\051.)]TJ -53.622 -10.461 Td [(Informally)65(,)-270(a)-265(similarity)-266(join)-265(between)-266(tw)10(o)-265(relations)]TJ/F34 8.9664 Tf 183.138 0 Td [(R)]TJ/F56 8.9664 Tf 9.417 0 Td [(and)]TJ/F34 8.9664 Tf 15.329 0 Td [(S)]TJ/F56 8.9664 Tf 8.521 0 Td [(is)-266(a)-265(join)]TJ -216.405 -10.461 Td [(where)-329(the)-328(join)-329(predicate)-329(is)-328(a)-329(conjunction)-329(of)-328(one)-329(or)-329(more)-328(similarity)]TJ 0 -10.461 Td [(function)-374(predicates)-374(each)-374(requiring)-374(that)-374(similarities)-373(between)-374(record)]TJ 0 -10.46 Td [(pairs)-323(be)-322(greater)-323(than)-323(a)-322(threshold.)-528(Similarity)-323(joins)-322(for)-323(a)-323(broad)-322(class)]TJ 0 -10.461 Td [(of)-291(similarity)-291(functions)-291(ha)20(v)15(e)-291(been)-291(sho)25(wn)-291(to)-291(be)-291(ef)25(\002ciently)-291(e)15(x)15(ecutable)]TJ 0 -10.461 Td [(\050e.g.,)-250([23,)-250(27,)-250(14,)-250(2],)-250(tutorial)-250([28]\051,)-250(and)-250(thus)-250(\002t)-250(our)-250(design)-250(goals.)]TJ 8.967 -10.461 Td [(Often,)-333(domain)-317(information)-316(such)-317(as)-316(US)-317(postal)-316(service)-317(address)-316(ta-)]TJ -8.967 -10.46 Td [(bles,)-538(and)-481(soft)-481(functional)-480(dependencies)-481(\050zipcode)-481(determines)-480(city\051)]TJ 0 -10.461 Td [(which)-244(are)-244(v)25(alid)-244(for)-244(a)-243(lar)18(ge)-244(subset)-244(of)-244(the)-244(data)-244(are)-244(also)-243(a)20(v)25(ailable.)-308(Such)]TJ 0 -10.461 Td [(information)-258(can)-257(be)-258(ef)25(fecti)25(v)15(ely)-257(used)-258(for)-257(transforming)-258(attrib)20(ute)-257(v)25(alues)]TJ 0 -10.461 Td [(in)-242(order)-243(to)-242(correct)-243(errors)-242(or)-242(\002ll)-243(in)-242(missing)-243(v)25(alues.)-307(Therefore,)-244(we)-242(also)]TJ 0 -10.461 Td [(consider)-386(a)-386(broad)-387(class)-386(of)-386(\050ef)25(\002cient\051)-386(attrib)20(ute)-386(v)25(alue)]TJ/F57 8.9664 Tf 191.409 0 Td [(tr)15(ansformation)]TJ/F56 8.9664 Tf -191.409 -10.46 Td [(operators)-250(\050discussed)-250(in)-250(Section)-250(6\051.)]TJ ET q 1 0 0 1 310.834 94.331 cm []0 d 0 J 0.398 w 0 0 m 98.031 0 l S Q BT /F56 5.9776 Tf 311.831 87.465 Td [(1)]TJ/F56 8.9664 Tf 3.487 -3.809 Td [(The)-360(\002gure)-360(sho)25(ws)-359(e)15(xample)-360(records)-360(appropriately)-360(modi\002ed)-359(to)-360(pre-)]TJ -4.484 -8.966 Td [(serv)15(e)-250(pri)25(v)25(ac)15(y)65(.)]TJ ET Q 1 0 0 1 295.992 36 cm 0 Tr /QQAPFce02551e 12 Tf 0 0 0 rg 100 Tz 0 Ts 0 Tw 0 Tc BT 1 0 0 1 0 0 Tm (327)Tj ET 1 0 0 1 0 0 cm 1 0 0 1 -295.992 -36 cm endstream endobj 4 0 obj << /Type /Page /Resources 3 0 R /MediaBox [ 0 0 612 792 ] /Parent 13 0 R /Contents [ 5 0 R ] >> endobj 3 0 obj << /Font << /F53 6 0 R /F54 7 0 R /F36 8 0 R /F55 9 0 R /F56 10 0 R /F57 11 0 R /F34 12 0 R /QQAPFce02551e 232 0 R >> /ProcSet [ /PDF /Text ] >> endobj 17 0 obj << /Length 13244 /LC /QQAP >> stream q 1 0 0 1 59.178 612.202 cm q 0.66112 0 0 0.78261 0 0 cm q 1 0 0 1 0 0 cm /Im1 Do Q Q 1 0 0 1 338.716 0 cm q 0.86476 0 0 0.74556 0 0 cm q 1 0 0 1 0 0 cm /Im2 Do Q Q 1 0 0 1 -397.894 -612.202 cm BT /F55 8.9664 Tf 215.723 597.983 Td [(Figur)18(e)-250(1:)-310(A)-250(r)18(ecord)-250(matching)-250(example)-250(&)-250(query)]TJ ET 1 0 0 1 86.334 477.423 cm q 0.75954 0 0 0.90002 0 0 cm q 1 0 0 1 0 0 cm /Im3 Do Q Q 1 0 0 1 -86.334 -477.423 cm BT /F55 8.9664 Tf 102.313 457 Td [(Figur)18(e)-250(2:)-310(Example)-250(queries)-250(&)-250(accuracy)]TJ/F56 8.9664 Tf -39.548 -37.105 Td [(Figure)-312(1)-313(illustrates)-312(an)-313(e)15(xample)-313(operator)-312(tree)-313(in)40(v)20(olving)-312(union,)-328(at-)]TJ -8.967 -10.46 Td [(trib)20(ute)-433(v)25(alue)-433(transformation)-432(operations,)-479(and)-433(similarity)-433(join)-432(predi-)]TJ 0 -10.461 Td [(cates.)-711(This)-383(vie)25(w)-384(of)-384(composing)-383(basic)-384(operators)-383(into)-384(data)-383(cleaning)]TJ 0 -10.461 Td [(programs)-264(has)-264(been)-264(e)15(xplored)-264(in)-265(commerc)1(ial)-265(systems)-264(\050e.g.,)-267(ETL)-264(tools)]TJ 0 -10.461 Td [(such)-244(as)-244(IBM)-244(Ascential\051)-244(and)-244(in)-244(research)-244(initiati)25(v)15(es)-244(such)-244(as)-244(Ajax)-244([22],)]TJ 0 -10.46 Td [(Morpheus)-257([20],)-260(and)-257(Potters)-257(wheel)-257([31].)-332(A)-258(similar)-257(compositional)-257(ap-)]TJ 0 -10.461 Td [(proach)-338(is)-339(also)-338(being)-338(e)15(xplored)-339(in)-338(the)-338(conte)15(xt)-339(of)-338(information)-338(e)15(xtrac-)]TJ 0 -10.461 Td [(tion)-250([19].)-310(In)-250(this)-250(paper)40(,)-250(we)-250(focus)-250(on)-250(the)-250(record)-250(matching)-250(problem.)]TJ/F57 8.9664 Tf 8.967 -10.461 Td [(Challeng)10(es)]TJ/F56 8.9664 Tf 40.258 0 Td [(:)-547(A)-368(programmer)-368(who)-369(designs)-368(a)-369(record)-368(matching)-368(op-)]TJ -49.225 -10.461 Td [(erator)-373(tree)-373(based)-372(on)-373(the)-373(abo)15(v)15(e)-373(primiti)25(v)15(es)-372(is)-373(f)10(aced)-373(with)-373(man)15(y)-372(pos-)]TJ 0 -10.46 Td [(sibilities)-341(and)-342(questions.)-584(A)-341(small)-341(group)-342(of)-341(programmers)-341(\050including)]TJ 0 -10.461 Td [(us\051)-311(at)-312(Microsoft)-311(de)25(v)15(eloped)-312(softw)11(are)-312(to)-311(match)-312(Enquiries)-311(with)-311(Ev)25(ac-)]TJ 0 -10.461 Td [(uees)-195(relation)-196(after)-195(the)-196(hurricane)-195(Katrina)-196([36].)-291(De)25(v)15(eloping)-196(an)-195(accurate)]TJ 0 -10.461 Td [(program)-264(to)-264(match)-264(records)-263(across)-264(the)-264(tw)10(o)-264(relations)-264(w)10(as)-264(hard)-263(because)]TJ 0 -10.46 Td [(the)-257(number)-257(of)-257(possible)-257(matching)-257(predicates)-257(w)10(as)-257(quite)-257(high)-257(and)-257(each)]TJ 0 -10.461 Td [(one)-306(w)10(ould)-306(yield)-305(dif)25(ferent)-306(matching)-306(pairs.)-477(A)-306(priori,)-320(it)-306(w)10(as)-306(not)-305(clear)]TJ 0 -10.461 Td [(which)-231(option)-231(w)10(ould)-231(best)-230(deal)-231(with)-231(the)-231(inaccuracies)-231(in)-231(both)-231(the)-230(Ev)25(ac-)]TJ 0 -10.461 Td [(uees)-242(and)-241(Enquiries)-242(relations.)-307(A)-242(fe)25(w)-242(questions)-241(that)-242(we)-242(had)-242(to)-241(grapple)]TJ 0 -10.461 Td [(with)-308(while)-308(identifying)-308(accurate)-308(operator)-308(trees)-308(are)-308(as)-308(follo)25(ws.)-484(What)]TJ 0 -10.46 Td [(columns)-396(must)-397(we)-396(use)-396(for)-397(measuring)-396(similarities)-396(between)-396(records;)]TJ 0 -10.461 Td [(for)-258(e)15(xample,)-260(do)-258(we)-259(use)-258(mother')55(s)-258(or)-258(f)10(ather')55(s)-258(name,)-260(which)-258(sometimes)]TJ 0 -10.461 Td [(may)-264(be)-265(missing,)-268(or)-264(both)-265(along)-264(with)-264(other)-265(attrib)20(utes?)-353(Which)-264(similar)20(-)]TJ 0 -10.461 Td [(ity)-329(function)-328(\050edit)-329(distance)-329(or)-328(jaccard)-329(similarity\051)-329(do)-328(we)-329(use)-329(to)-328(com-)]TJ 0 -10.46 Td [(pare)-262(records)-263(along)-262(each)-263(or)-262(both)-263(these)-262(attrib)20(utes?)-347(What)-263(is)-262(the)-262(thresh-)]TJ 0 -10.461 Td [(old)-265(\050)]TJ/F31 8.9664 Tf 16.824 0 Td [(0)]TJ/F34 8.9664 Tf 4.608 0 Td [(:)]TJ/F31 8.9664 Tf 2.56 0 Td [(9)]TJ/F56 8.9664 Tf 6.987 0 Td [(or)]TJ/F31 8.9664 Tf 9.848 0 Td [(0)]TJ/F34 8.9664 Tf 4.608 0 Td [(:)]TJ/F31 8.9664 Tf 2.56 0 Td [(85)]TJ/F56 8.9664 Tf 9.215 0 Td [(\051)-265(for)-266(a)-265(chosen)-266(s)1(imilarity)-266(function)-265(v)25(alue)-265(abo)15(v)14(e)-265(which)]TJ -57.21 -10.461 Td [(record)-341(pairs)-341(w)10(ould)-342(be)-341(considered)-341(matches?)-584(F)15(or)-341(instance,)-364(Figure)-341(2)]TJ 0 -10.461 Td [(sho)25(ws)-338(the)]TJ/F57 8.9664 Tf 39.211 0 Td [(r)37(ecall)]TJ/F56 8.9664 Tf 23.618 0 Td [(for)-338(a)-338(fe)25(w)-338(high)]TJ/F57 8.9664 Tf 55.72 0 Td [(pr)37(ecision)]TJ/F56 8.9664 Tf 36.072 0 Td [(\050)]TJ/F34 8.9664 Tf 2.986 0 Td [(>)]TJ/F31 8.9664 Tf 11.23 0 Td [(95%)]TJ/F56 8.9664 Tf 16.895 0 Td [(\051)-338(join)-338(predicates)]TJ -185.732 -10.461 Td [(matching)-389(enquiry)-390(records)-389(with)-390(e)25(v)25(acuee)-389(records.)-729(\050)]TJ/F57 8.9664 Tf 187.124 0 Td [(Pr)37(ecision)]TJ/F56 8.9664 Tf 37.528 0 Td [(is)-389(the)]TJ -224.652 -10.46 Td [(percentage)-234(of)-234(all)-234(pairs)-235(returned)-234(by)-234(a)-234(record)-234(matching)-234(program)-234(which)]TJ 0 -10.461 Td [(are)-279(true)-278(matches,)-286(while)]TJ/F57 8.9664 Tf 86.499 0 Td [(r)37(ecall)]TJ/F56 8.9664 Tf 23.086 0 Td [(is)-279(the)-278(percentage)-279(of)-279(matching)-279(records)]TJ -109.585 -10.461 Td [(that)-341(are)-340(in)-341(the)-340(result.)-582(Accurac)15(y)-340(is)-341(often)-340(measured)-341(in)-340(terms)-341(of)-340(pre-)]TJ 0 -10.461 Td [(cision)-278(and)-277(recall.\051)-393(The)-277(\002rst)-278(ro)25(w)-278(indicates)-277(that)-278(using)-277(a)-278(join)-277(predicate)]TJ 0 -10.46 Td [(based)-218(on)-218(a)-217(single)-218(similarity)-218(function)-218(\050an)15(y)-217(one)-218(among)-218(edit,)-224(jaccard,)-224(or)]TJ 0 -10.461 Td [(generalized)-208(edit)-208(similarity)-208(on)-208(an)15(y)-208(combination)-208(of)-208(attrib)20(ut)1(es\051)-208(to)-208(match)]TJ 257.036 500.773 Td [(enquiry)-241(and)-241(e)25(v)25(acuee)-241(records)-242(w)10(as)-241(not)-241(suf)25(\002cient)-241(to)-241(achie)25(v)15(e)-241(a)-241(non-zero)]TJ 0 -10.461 Td [(recall)-265(at)-265(high)-264(precision.)-355(The)-265(second)-264(and)-265(third)-265(ro)25(ws)-265(indicate)-265(that)-264(dif-)]TJ 0 -10.46 Td [(ferent)-325(queries)-324(may)-325(yield)-325(v)15(ery)-324(dif)25(ferent)-325(accuracies.)-534(Thus,)-343(matching)]TJ 0 -10.461 Td [(predicates)-358(may)-358(ha)20(v)15(e)-358(to)-359(be)-358(f)10(airly)-358(comple)15(x)-358(in)-358(order)-358(to)-358(achie)25(v)15(e)-358(high)]TJ 0 -10.461 Td [(accurac)15(y)65(,)-341(and)-323(the)-322(accurac)15(y)-323(v)25(aries)-322(widely)-323(across)-323(v)25(arious)-322(predicates.)]TJ 0 -10.461 Td [(Thus,)-309(the)-297(right)-297(predicates)-297(ha)20(v)15(e)-297(to)-297(be)-298(used.)-451(The)-297(challenge)-297(no)25(w)-297(is)-297(to)]TJ 0 -10.46 Td [(identify)-250(one)-250(or)-250(a)-250(fe)25(w)-250(such)-250(predicates)-250(to)-250(achie)25(v)15(e)-250(high)-250(accurac)15(y)65(.)]TJ 8.967 -10.461 Td [(In)-264(this)-264(paper)40(,)-267(we)-264(address)-264(the)-264(abo)15(v)15(e)-264(issues)-264(and)-264(de)25(v)15(elop)-264(techniques)]TJ -8.967 -10.461 Td [(to)-271(assist)-270(the)-271(creation)-270(of)-271(ef)25(\002cient)-270(record)-271(matching)-270(operator)-271(trees.)-371(W)80(e)]TJ 0 -10.461 Td [(e)15(xploit)-343(the)-343(a)20(v)25(ailability)-343(of)-343(e)15(xamples)-343(of)-343(matching)-343(and)-343(non-matching)]TJ 0 -10.461 Td [(pairs)-327(for)-328(this)-327(purpose.)-543(It)-327(is)-328(often)-327(much)-328(easier)-327(for)-327(a)-328(programmer)-327(to)]TJ 0 -10.46 Td [(pro)15(vide)-340(a)-341(set)-340(of)-341(e)15(xample)-340(matching)-340(and)-341(non-matching)-340(record)-340(pairs,)]TJ 0 -10.461 Td [(perhaps)-235(based)-236(on)-235(a)-236(sample)-235(of)-236(t)1(he)-236(result)-235(of)-236(an)-235(initial)-236(query)-235(or)-235(through)]TJ 0 -10.461 Td [(manual)-433(e)15(xamination,)-480(than)-433(it)-434(is)-433(to)-434(design)-433(an)-433(accurate)-434(query)-433(from)]TJ 0 -10.461 Td [(scratch)-225(and)-225(w)10(orking)-225(their)-225(w)10(ay)-225(manually)-225(through)-225(the)-225(numerous)-225(range)]TJ 0 -10.46 Td [(of)-250(a)20(v)25(ailable)-250(choices.)]TJ 8.967 -10.461 Td [(Using)-329(e)15(xamples)-330(to)-329(create)-329(models)-330(is)-329(a)-330(standard)-329(machine)-329(learning)]TJ -8.967 -10.461 Td [(practice.)-375(In)-272(f)10(act,)-277(machine)-272(learning)-271(based)-272(approaches)-272(ha)20(v)15(e)-272(also)-271(been)]TJ 0 -10.461 Td [(applied)-323(in)-323(the)-323(conte)15(xt)-324(of)-323(record)-323(matching)-323(for)-323(learning)-323(combination)]TJ 0 -10.461 Td [(functions)-272(o)15(v)15(er)-273(se)25(v)15(eral)-272(similarity)-273(functions,)-278(e.g.,)-272([32,)-278(9,)-278(38,)-278(37].)-377(Our)]TJ 0 -10.46 Td [(approach)-217(dif)25(fers)-218(in)-217(the)-218(follo)25(wing)-217(w)10(ays.)-299(Machine)-218(learning)-217(models)-217(are)]TJ 0 -10.461 Td [(usually)-269(applied)-268(on)-269(indi)25(vidual)-269(records)-269(from)-268(a)-269(single)-269(relation)-268(whereas)]TJ 0 -10.461 Td [(in)-237(the)-238(record)-237(matching)-238(problem,)-239(we)-238(join)-237(records)-238(across)-237(tw)10(o)-237(relations)]TJ/F34 8.9664 Tf 0 -10.461 Td [(R)]TJ/F56 8.9664 Tf 9.438 0 Td [(and)]TJ/F34 8.9664 Tf 15.35 0 Td [(S)]TJ/F56 8.9664 Tf 6.139 0 Td [(.)-364(Therefore,)-272(in)-268(order)-268(to)-268(apply)-268(a)-268(machine)-267(learning)-268(model)-268(we)]TJ -30.927 -10.46 Td [(are)-218(either)-218(forced)-219(to)-218(perform)-218(a)-218(cross)-218(product)-219(and)-218(then)-218(apply)-218(the)-218(model)]TJ 0 -10.461 Td [(or)-311(emplo)10(y)-312(a)-311(method)-311(which)-311(can)-312(push)-311(the)-311(model)-312(into)-311(the)-311(join)-311(opera-)]TJ 0 -10.461 Td [(tion.)-729(F)15(or)-390(e)15(xample,)-425(consider)-390(the)-389(class)-390(of)-390(support)-390(v)15(ector)-389(machines)]TJ 0 -10.461 Td [(\050SVM\051)-304(which)-304(ha)20(v)15(e)-304(been)-303(sho)25(wn)-304(to)-304(result)-304(in)-304(the)-304(most)-304(accurate)-303(mod-)]TJ 0 -10.461 Td [(els)-320(for)-320(record)-320(matching)-319([9].)-520(T)80(o)-320(the)-320(best)-320(of)-319(our)-320(kno)25(wledge,)-338(there)-319(is)]TJ 0 -10.46 Td [(no)-303(method)-303(to)-304(ef)25(\002ciently)-303(perform)-303(a)-303(join)-304(betwe)1(en)-304(tw)10(o)-303(lar)18(ge)-303(input)-303(re-)]TJ 0 -10.461 Td [(lations)-252(when)-252(the)-252(join)-252(predicate)-251(is)-252(an)-252(SVM)-252(model.)-316(\050See)-252(Section)-251(2)-252(for)]TJ 0 -10.461 Td [(further)-250(discussion.\051)]TJ 8.967 -10.461 Td [(Our)-250(contrib)20(utions)-250(are)-250(summarized)-250(belo)25(w)65(.)]TJ 2.241 -21.014 Td [(1.)-500(W)80(e)-295(propose)-296(techniques)-295(for)-295(assisting)-295(a)-296(programmer)-295(in)-295(design-)]TJ 11.208 -10.461 Td [(ing)-331(the)-330(highest)-331(\223quality\224)-331(record)-330(matching)-331(operator)-330(trees.)-552(In-)]TJ 0 -10.461 Td [(formally)65(,)-228(the)]TJ/F57 8.9664 Tf 47.537 0 Td [(quality)]TJ/F56 8.9664 Tf 26.905 0 Td [(of)-223(a)-222(record)-223(matching)-223(operat)1(or)-223(tree)]TJ/F34 8.9664 Tf 123.017 0 Td [(Q)]TJ/F56 8.9664 Tf 9.264 0 Td [(with)]TJ -206.723 -10.461 Td [(respect)-281(to)-281(a)-281(set)-281(of)-281(e)15(xamples)-281(is)-281(the)-281(number)-281(of)-280(matching)-281(e)15(xam-)]TJ 0 -10.46 Td [(ples)-331(included)-330(in)-331(the)-330(result)-331(of)]TJ/F34 8.9664 Tf 108.432 0 Td [(Q)]TJ/F56 8.9664 Tf 10.232 0 Td [(subject)-330(to)-331(the)-331(constraint)-330(that)]TJ -118.664 -10.461 Td [(none)-303(or)-303(v)15(ery)-303(fe)25(w)-303(\050less)-304(than)-303(a)-303(user)20(-speci\002ed)-303(fraction)]TJ/F34 8.9664 Tf 191.736 0 Td [(\014)]TJ/F56 8.9664 Tf 5.661 0 Td [(\051)-303(gi)25(v)15(en)]TJ -197.397 -10.461 Td [(non-matching)-253(e)15(xamples)-253(are)-253(in)-253(the)-252(result)-253(of)]TJ/F34 8.9664 Tf 155.685 0 Td [(Q)]TJ/F56 8.9664 Tf 7.269 0 Td [(.)-319(\050W)80(e)-253(discuss)-252(al-)]TJ -162.954 -10.461 Td [(ternati)25(v)15(e)-344(formulations)-345(within)-344(our)-345(frame)25(w)10(ork)-344(in)-345(Section)-344(6.2.\051)]TJ 0 -10.46 Td [(Because)-269(we)-269(return)-269(operator)-268(trees,)-274(a)-269(programmer)-269(is)-269(easily)-268(able)]TJ 0 -10.461 Td [(to)-250(interpret,)-250(re)25(vie)25(w)65(,)-250(and)-250(modify)-250(the)-250(operator)-250(tree)-250(if)-250(required.)]TJ -11.208 -19.485 Td [(2.)-500(Through)-452(an)-452(e)15(xtensi)25(v)15(e)-453(empirical)-452(e)25(v)25(aluation)-452(on)-452(real)-452(datasets)]TJ 11.208 -10.461 Td [(from)-271(a)-272(v)25(ariety)-271(of)-271(domains,)-277(we)-271(demonstrate)-272(that)-271(operator)-271(trees)]TJ 0 -10.461 Td [(determined)-420(by)-421(our)-420(techniques)-421(compare)-420(f)10(a)20(v)20(orably)-421(in)-420(quality)]TJ 0 -10.46 Td [(with)-299(currently)-298(kno)25(wn)-299(best)-299(SVM)-298(models)-299(for)-299(record)-298(matching,)]TJ ET Q 1 0 0 1 295.992 36 cm 0 Tr /QQAPFce02551e 12 Tf 0 0 0 rg 100 Tz 0 Ts 0 Tw 0 Tc BT 1 0 0 1 0 0 Tm (328)Tj ET 1 0 0 1 0 0 cm 1 0 0 1 -295.992 -36 cm endstream endobj 16 0 obj << /Type /Page /Resources 15 0 R /MediaBox [ 0 0 612 792 ] /Parent 13 0 R /Contents [ 17 0 R ] >> endobj 1 0 obj << /Type /XObject /Subtype /Form /FormType 1 /PTEX.FileName (figures/Eg.pdf) /PTEX.PageNumber 1 /PTEX.InfoDict 19 0 R /BBox [0 0 391 161] /Resources << /ProcSet [ /PDF /Text ] /ExtGState << /R7 20 0 R >>/Font << /R10 21 0 R/R11 22 0 R/R9 23 0 R/R8 24 0 R>> >> /Length 25 0 R /Filter /FlateDecode >> stream x\K ϯ*_3/Ula{Wŕ"%fwmR$Hv7ЖFb#~H?ul]go٫5w<^>;t:kZm.w6d?~ѻ䏿O] $UoSh}#x]/q^N~;$U˜L6h?glp9~ jޟL3* ~L~Oԋm<Ȳގ=怆9$KȎF׃ypdFjsC6FQi9P07b݋6{7s;papY$v .¿[ώ 㪧hfa-lUx?`6<挬hCiua,`=, Cz֦2u 8Z\ ]f̱@s\*nvr.f~VӛW52%@znE,BYWW фOQvDcT=6yK,fGD'uHwTXV%:xXJw=E @C$"쁘E _>|h$_~ $F`31>/9wp`B1%} s ;D{?)FUJ7'nw#~'Tc=ь'afb@8iYZdl>>9pRkCE(qDPRƸ %d&YR&$X (oj㐥`=,WTKRXB('Cj ew Bf8Oy?H4D:> +%&zJ[V}[J|8G0}>0,GcCugB\xS0x߯_: 4oDţO )&8xѥM,'|6Ƹٗ gC䭖 9?Ԓy8<̃tAxPbxP3`SAu65j2ȃEFAM4`IAxPU ^~@^U<ރy+Zo \C7[o[D,f}!^[s(ލԇz[ yqP!-zCX+ݑ/[-y.C0Qba@ >U|O՛Bt~jg)} n] UTTHb^܄ Mg1lp1AHY-,nQl'2ټ4ͰX'_,(χf(;HF΀Anb) ;s|6eIMq=}%F:{xYMRS*z:}Bz0 Lv_7 ͔U+5)%&;^Hk}> u8Ky2/PIGhh͵n j=nY @1b މ3t&,-DE26#CS `!:h2EFzM43zImx[\,YmZ qbis @<ՒTKQ!LԎ!gg {S}!@W,^j nM<3ܖm6Mڝp hn*3%5mũ)m읷_m9}aܓuu*I!G<R{Bc{3J80]8)>eWh;Z:igUMu IjҙXZ:E26tgҧ@u`m(rkdꊌLuh: )Lu,)P&X,S۴|M)0O&UUa8A'Aݩ/=&DC,WǧDq}4IBKUKiq%R2A A|X%`̰J)J}Zj "pyv9ݧB&k肦'\Kl_PٺJ_[\W7v<+{%*դ3{=3HFw`m(rkd~B"& gTߦ-e%'U @87 /bnQv^MΗqRR9w_^7;ջT?C IRui7{guzt$*1ɝ6)q)Ϸh>.H{aɚi>vÜ_Ehυu@S2iy,mQ5L|,-"C$WO EnM| _OWǸ!>E%$3eS}kG'_aWd*\)Nj<rNM.u ŗ2\+eBzVs/ͤrGĂߦE$;s>R-aF:5yy씊H۸To䍜\OɲrF$kUC=|hkP6)"F5SKG\eתwGǴvV,-e˒.;KJuJ\}Ju`.;mf.[2m],Y겳THr]6[ek*}2Z ERl/kr J5"T%h)oZ.'Sj) iGWt9l0OVfwTΕr>yWڼL/ŗ"'ft52E-zұnEV@K*y\+.)[O)[+\ozkY2V$)[+}r5)[kz,VdޚezkEֲdΒR"lRo6+lWrtexh ._x#/e.!Ѳџ!RZ03&-W&)~6Tnc.^d)6T sKgk1z<Z'[=,1pm!lWZb pʇS+rK>BpmXRZ=[]l!&tcΦ>%yJPM3fa7K֖^ku]ŤژնҘ9Ln[قsc{Ò6^mmʶ)oҫy0K}Z{[ك.mW[8ӯ5]`.|X[9, eׅk{¥͗XZ ay*XBni ~Ui]8W׫mZ_Xh`L;Dؽo!@s˥4{,uҙ+fYڼAcXXך6bɏ]:fvOH5qSOd͸'RϒqO`)&H5q=j%㦞HɚqSOdɸHU.L 9~3S{4)kTyIC+NΤ "e+ endstream endobj 19 0 obj << /Producer (AFPL Ghostscript 8.53) /CreationDate (D:20070709195537) /ModDate (D:20070709195537) /Title (Microsoft Word - Eg.doc) /Creator (PScript5.dll Version 5.2.2) >> endobj 20 0 obj << /Type /ExtGState /OPM 1 >> endobj 21 0 obj << /BaseFont /Times-Bold /Type /Font /Subtype /Type1 >> endobj 22 0 obj << /BaseFont /Times-Italic /Type /Font /Subtype /Type1 >> endobj 23 0 obj << /BaseFont /Courier /Type /Font /Subtype /Type1 >> endobj 24 0 obj << /BaseFont /Times-Roman /Type /Font /Encoding 26 0 R /Subtype /Type1 >> endobj 25 0 obj 4268 endobj 26 0 obj << /Type /Encoding /Differences [ 133/ellipsis] >> endobj 2 0 obj << /Type /XObject /Subtype /Form /FormType 1 /PTEX.FileName (figures/Eg-Package-sju.pdf) /PTEX.PageNumber 1 /PTEX.InfoDict 27 0 R /BBox [0 0 199 169] /Resources << /ProcSet [ /PDF /Text ] /ExtGState << /R7 28 0 R >>/Font << /R14 29 0 R/R10 30 0 R/R12 31 0 R/R9 32 0 R/R13 33 0 R/R8 34 0 R>> >> /Length 35 0 R /Filter /FlateDecode >> stream x]K-qϯ891MfE'YYlٙQ"9AzWu;3#q!ME6n\Ӌ/~v?wG<廯~WSsk6Ƽl#]o#ltBV),)H${jWʻ-bd$.2QT1J*R[e.;7"~VZXc&l} w3pR+Re*Uc^҇ qf=,Sz"VED+ ڊjde)[IA۫EV)bHdU~~VQk6=zR-՝ ٧҇&ݴ\j%"EwN@^qZJDmYLSjTԊmD6֬j65iY=+ZV$5 kDK1ĄkX+bXcmq 5] u_QݛWwh|8~HXy:5G/DoyVð 3π*%(DiiUǂ g˫oڄ,*[ԧ>En1j9 _SzO~WTzt,a;0$W LJD)0\AEYT*xt.x"c !dt1J^2ږ|OY/&g~{g~{B }83=|OKk^gۄ~3Uz^qÐ)f$I%t o^v`#8j'_eo68nWwKym4׎c 2_r}WnBlZn1'(^rTO\WZ%iJ^qpN .ʖ|XkayX•B^x {ޢu{z)7 O cW<22+L||.Bf9o٦k㙫gMo47 ^_L`fHS뿚Վ{U# }Ƕ2/.z]n;H*9ʈdQ꿅b7T9[uV(i"BӰ!+_hf VdPCK8kxtحCײ¹^e1NQ]o;wB! ogWD$^;2 _yD%}]O+^Mnik4=qY bԄOxVdzͨfܩmYgr>ӭqϡ7zE32A`9|Nm[ƏƋda MSFkSbv n 6B 6"O>be~9)GDd0hһ`./ip^Jdt6QjXKɮCU=+-%hMֵڳ)a7(?bJh)9{):v~ 8.rb`x) -ƭ*w۩.\a[ %Z%b9]H^=hyO-qˊ@6[J#эlїbOrpdiu$5 R" q.5i!lMO*.wvi5FC'[^yЖ<9.-K.͚Pg-<&DhS=ƘY# 1i( !-/,?cmc>c-MuKOuR^*upPnɑ!f&.61%곅26j|QM=wZ(񏼊bm\.iU ÂVh=#]U j-/y1K4v5.aږ$8\sS _][k̵˙:O{5=F #ayK>S"OCT8M uۤP0t}F 0fFah#T : ٘^FШhaHIᡞΣ»/[PYE%}q >as΍j%;礪;O~C/}^pY AwEV35\ O02lj爱K*{x#Bޑx輂,T+4)̵GМ!|wgL13阙syV;qE6[g7LĕKA e(} cCS̒jrױp,DRpƪG,`WxJf.1o,ѷзˣ,:c ;ۃ?bZ7D^B#eӴEvMU?֬DuxXsi(6M_N5ءljn+k^<ڗKe\ɛD4,',Wj>S /'ۺ5Ӯ/+U߂$Cg-ԙ*hֵX(r+@=]Zҽ bG{JծVėsy PY_@ճ•5b-WY6V[s*%5`jI{@GќCuVHP٥7)Fi"_hk]5, ZyGA3>Cg gl̴S x@ TNF/h2m_rJjR?Qwlmc_>s ^+'Ԋ~uQ'i耐Lwlq)/#[` [ra }At5=3!6 q?}ּpnUj^~#貂CH5C=ŮFzK3i QjM[>*}C:(E-,s4 Ϟ)u$o(F+5vGE^#[m\ۺl"i)M)Ӗ Smڙmq[afVi;-Zhm 7=žEsag^j̓dYxq5zV5|IR#Bߴka0`K,HԞjyC.CX.CT>xgDW`~?=?Pqɿ|I*r) ?QuOҟ;Lb[~uAmxz:ƿp>_A>)WKpƃR+qh9.ƪKXg-)+0F /۔,WcP tQ TyX 9p{nL}`kv:<|;%`]}Ǖk~*\roc>:S1B9jo>IeFHy">QSx^--w1[o_W endstream endobj 27 0 obj << /Producer (AFPL Ghostscript 8.53) /CreationDate (D:20070709195538) /ModDate (D:20070709195538) /Title (Microsoft Word - Eg-Package-SJU.doc) /Creator (PScript5.dll Version 5.2.2) >> endobj 28 0 obj << /Type /ExtGState /OPM 1 >> endobj 29 0 obj << /BaseFont /Times-Italic /Type /Font /Subtype /Type1 >> endobj 30 0 obj << /BaseFont /Times-Bold /Type /Font /Subtype /Type1 >> endobj 31 0 obj << /BaseFont /IILUCS#2BHelvetica-Narrow /FontDescriptor 36 0 R /Type /Font /FirstChar 85 /LastChar 85 /Widths [ 592] /Encoding /WinAnsiEncoding /Subtype /Type1 >> endobj 32 0 obj << /BaseFont /Courier /Type /Font /Subtype /Type1 >> endobj 33 0 obj << /BaseFont /Symbol /Type /Font /Subtype /Type1 >> endobj 34 0 obj << /BaseFont /Times-Roman /Type /Font /Subtype /Type1 >> endobj 35 0 obj 5494 endobj 36 0 obj << /Type /FontDescriptor /FontName /IILUCS#2BHelvetica-Narrow /FontBBox [ 0 -19 528 718] /Flags 4 /Ascent 718 /CapHeight 718 /Descent -19 /ItalicAngle 0 /StemV 79 /MissingWidth 228 /CharSet (/U) /FontFile3 37 0 R >> endobj 37 0 obj << /Filter /FlateDecode /Subtype /Type1C /Length 502 >> stream xAkAghnQ'"i&"ՀMTL=F8БG!rȔ10$>h,x6HC,CKTW(Yՙ?ӊ͆nGl[vhp"ev]!GKъ62]Ja>/Font << /R10 40 0 R/R9 41 0 R/R8 42 0 R>> >> /Length 43 0 R /Filter /FlateDecode >> stream xWn7W%FH3ܗC؀@#!yF%]%T,vȒ/_qu\Q? Ӆ <^!pa|RG7 rQx09q>#1r r*%e_UNlAo&^ib0ɢ́(N%duq:IQZ]|e ͼ|)!;/;ܺ,1*XcL]+PCqqTJLÇavi7UgK0iEYqLTS,E]ЂDW]EE$  +2ev62@F NfژI@ژpi*sI-\ Y=/;Cy $~R}Zo+`_S&abKV4Ү@r\H.ݒK;;EiIdLc{8C.'hb(# SXnm*v[+G4Y!֍`H(ᨑp)> Yː3iEGB[=r{-0/W|B|(+7h(/X@%E TREK{:hH]-)3%vv2S>kQ!#hyd&tMgLMgI=8 endstream endobj 38 0 obj << /Producer (AFPL Ghostscript 8.53) /CreationDate (D:20070709231535) /ModDate (D:20070709231535) /Title (Microsoft Word - Eg-Queries.doc) /Creator (PScript5.dll Version 5.2.2) /Author (vganti) >> endobj 39 0 obj << /Type /ExtGState /OPM 1 >> endobj 40 0 obj << /BaseFont /Times-Bold /Type /Font /Subtype /Type1 >> endobj 41 0 obj << /BaseFont /Courier /Type /Font /Subtype /Type1 >> endobj 42 0 obj << /BaseFont /Times-Roman /Type /Font /Encoding 44 0 R /Subtype /Type1 >> endobj 43 0 obj 1107 endobj 44 0 obj << /Type /Encoding /Differences [ 151/emdash] >> endobj 15 0 obj << /Font << /F55 9 0 R /F56 10 0 R /F57 11 0 R /F31 18 0 R /F34 12 0 R /QQAPFce02551e 232 0 R >> /XObject << /Im1 1 0 R /Im2 2 0 R /Im3 14 0 R >> /ProcSet [ /PDF /Text ] >> endobj 47 0 obj << /Length 22694 /LC /QQAP >> stream q BT /F56 8.9664 Tf 76.214 728.239 Td [(while)-198(being)-197(a)-198(lot)-198(more)-197(scalable)-198(and)-198(ef)25(\002cient)-197(to)-198(e)15(x)15(ecute.)-293(F)15(or)-197(the)]TJ 0 -10.461 Td [(address)-248(domain)-249(in)-248(particular)40(,)-249(we)-248(sho)25(w)-249(that)-248(our)-248(auto-generated)]TJ 0 -10.46 Td [(operator)-287(trees)-286(are)-287(comparable)-287(in)-287(accurac)15(y)-286(to)-287(a)-287(carefully)-286(engi-)]TJ 0 -10.461 Td [(neered)-250(address-matching)-250(system)-250(T)35(rillium)-250([35].)]TJ -13.449 -19.968 Td [(W)80(e)-274(anticipate)-274(that)-274(our)-274(techniques)-274(w)10(ould)-274(enable)-274(interacti)25(v)15(e)-274(record)]TJ -8.967 -10.461 Td [(matching)-429(query)-430(design)-429(tools)-429(that)-430(furthe)1(r)-430(enhance)-429(interacti)25(v)15(e)-429(data)]TJ 0 -10.461 Td [(cleaning)-397(en)40(vironments)-397([31,)-434(32].)-751(W)80(e)-397(discuss)-397(these)-396(possibilities)-397(in)]TJ 0 -10.461 Td [(Section)-250(6.2.)]TJ 8.967 -10.46 Td [(The)-282(remai)1(nder)-282(of)-282(the)-281(paper)-282(is)-281(or)18(g)5(anized)-282(as)-281(follo)25(ws.)-405(In)-282(Section)-281(2,)]TJ -8.967 -10.461 Td [(we)-345(discuss)-345(related)-345(w)10(ork.)-596(In)-345(Section)-345(3,)-369(we)-345(formally)-345(de\002ne)-345(the)-345(op-)]TJ 0 -10.461 Td [(erator)-340(tree)-340(design)-340(problem,)-362(and)-340(then)-340(describe)-340(an)-340(algorithm)-340(in)-340(Sec-)]TJ 0 -10.461 Td [(tion)-310(4.)-489(W)80(e)-310(then)-310(incorporate)-310(\050domain-speci\002c\051)-310(attrib)20(ute)-310(v)25(alue)-309(trans-)]TJ 0 -10.46 Td [(formations)-311(in)-311(Section)-311(5.)-492(W)80(e)-311(discuss)-311(e)15(xtensions)-311(to)-311(our)-311(algorithm)-310(in)]TJ 0 -10.461 Td [(Section)-281(6.)-402(In)-280(Section)-281(7,)-288(we)-281(present)-280(an)-281(e)15(xperimental)-280(study)65(,)-289(and)-280(con-)]TJ 0 -10.461 Td [(clude)-250(in)-250(Section)-250(8.)]TJ/F55 11.9552 Tf 0 -24.366 Td [(2.)-1000(RELA)95(TED)-250(W)10(ORK)]TJ/F56 8.9664 Tf 8.967 -12.951 Td [(As)-410(discussed)-411(earlier)40(,)-451(s)1(e)25(v)15(eral)-411(ef)25(\002cient)-410(similarity)-411(join)-410(algorithms)]TJ -8.967 -10.461 Td [(ha)20(v)15(e)-264(been)-264(recently)-264(proposed)-264(in)-264(the)-264(conte)15(xt)-264(of)-264(record)-264(matching)-264(\050e.g.,)]TJ 0 -10.461 Td [([23,)-249(27,)-250(14,)-249(2]\051.)-310(K)35(oudas)-249(et)-250(al.)-249(present)-249(an)-250(e)15(xcellent)-249(tutorial)-249(of)-249(v)25(arious)]TJ 0 -10.461 Td [(similarity)-323(functions)-322(and)-323(similarity)-322(join)-323(algorithms)-323(in)-322(the)-323(conte)15(xt)-322(of)]TJ 0 -10.46 Td [(record)-250(matching)-250([28].)]TJ 8.967 -10.461 Td [(In)-321(contrast)-321(to)-321(our)-321(similarity)-321(join)-321(based)-321(combination)-321(of)-321(similarity)]TJ -8.967 -10.461 Td [(function)-347(v)25(alues)]TJ/F38 8.9664 Tf 58.793 6.725 Td [(V)]TJ/F35 5.9776 Tf 7.679 -9.465 Td [(i)]TJ/F34 8.9664 Tf 4.698 2.74 Td [(f)]TJ/F35 5.9776 Tf 4.473 -0.996 Td [(i)]TJ/F34 8.9664 Tf 7.378 0.996 Td [(>)-470(\013)]TJ/F35 5.9776 Tf 17.289 -0.996 Td [(i)]TJ/F56 8.9664 Tf 3.162 0.996 Td [(,)-371(another)-347(natural)-347(predicate)-347(w)10(ould)-347(ha)20(v)15(e)]TJ -103.472 -10.461 Td [(been)-281(a)-281(thresholded)-281(linear)-281(combination)-281(of)-281(all)-281(similarit)1(y)-281(function)-281(v)25(al-)]TJ 0 -10.46 Td [(ues)-213(being)-214(greater)-213(than)-214(a)-213(threshold)]TJ/F34 8.9664 Tf 121.043 0 Td [(\013)]TJ/F56 8.9664 Tf 5.913 0 Td [(:)]TJ/F31 8.9664 Tf 5.108 0 Td [(\006)]TJ/F35 5.9776 Tf 6.655 -0.997 Td [(i)]TJ/F34 8.9664 Tf 3.162 0.997 Td [(w)]TJ/F35 5.9776 Tf 6.605 -0.997 Td [(i)]TJ/F34 8.9664 Tf 3.161 0.997 Td [(f)]TJ/F35 5.9776 Tf 4.473 -0.997 Td [(i)]TJ/F34 8.9664 Tf 5.722 0.997 Td [(>)-285(\013)]TJ/F56 8.9664 Tf 15.64 0 Td [(.)-298(This)-213(combination)]TJ -177.482 -10.461 Td [(is)-239(adopted)-238(by)-239(SVM)-239(models)-238([18].)-306(As)-239(discussed)-239(earlier)40(,)-240(one)-239(of)-239(our)-238(de-)]TJ 0 -10.461 Td [(sign)-216(goals)-216(is)-216(to)-217(ensure)-216(that)-216(our)-216(primiti)25(v)15(e)-216(operators)-216(are)-216(ef)25(\002ciently)-216(e)15(x)15(e-)]TJ 0 -10.461 Td [(cutable.)-300(W)80(e)-222(are)-221(not)-222(a)15(w)10(are)-221(of)-221(an)15(y)-222(method)-221(to)-221(ef)25(\002ciently)-222(perform)-221(a)-221(join)]TJ 0 -10.461 Td [(between)-230(tw)10(o)-231(lar)18(ge)-230(input)-230(relations)-231(when)-230(the)-230(join)-230(predicate)-231(is)-230(a)-230(thresh-)]TJ 0 -10.46 Td [(olded)-273(linear)-273(combination.)-379(Especially)65(,)-279(when)-273(some)-273(of)-273(the)-273(weights)-273(are)]TJ 0 -10.461 Td [(ne)15(g)5(ati)25(v)15(e,)-363(which)-340(is)-340(often)-340(the)-340(case)-340(when)-340(one)-341(learns)-340(SVM)-340(models,)-362(it)]TJ 0 -10.461 Td [(is)-327(not)-327(clear)-327(ho)25(w)-327(to)-326(e)15(x)15(ecute)-327(the)-327(join)-327(ef)25(\002ciently)65(.)-541(Ev)15(en)-327(in)-327(the)-326(special)]TJ 0 -10.461 Td [(case)-325(when)-325(all)-326(weights)]TJ/F34 8.9664 Tf 83.377 0 Td [(w)]TJ/F35 5.9776 Tf 6.605 -0.996 Td [(i)]TJ/F56 8.9664 Tf 6.077 0.996 Td [(are)-325(positi)25(v)15(e,)-344(we)-325(may)-326(produce)-325(a)-325(conjunc-)]TJ -96.059 -10.46 Td [(tion)-261(of)-260(join)-261(predicates)]TJ/F34 8.9664 Tf 81.07 0 Td [(f)]TJ/F35 5.9776 Tf 4.472 -0.997 Td [(i)]TJ/F34 8.9664 Tf 5.904 0.997 Td [(>)]TJ/F35 5.9776 Tf 12.947 3.673 Td [(\013)]TJ ET q 1 0 0 1 156.348 359.372 cm []0 d 0 J 0.379 w 0 0 m 8.495 0 l S Q BT /F35 5.9776 Tf 156.348 354.088 Td [(w)]TJ/F9 4.9813 Tf 5.34 -1.261 Td [(i)]TJ/F56 8.9664 Tf 4.351 4.304 Td [(,)-263(which)-261(reduces)-261(to)-260(our)-261(similarity)-260(join)]TJ -112.241 -10.461 Td [(formalism.)]TJ 8.967 -10.461 Td [(Decision)-393(tree)-394(models)-393(ha)20(v)15(e)-393(also)-394(been)-393(applied)-394(to)-393(learn)-393(combina-)]TJ -8.967 -10.461 Td [(tions)-246(o)15(v)15(er)-247(similarity)-246(functions)-247(in)-246(the)-247(conte)15(xt)-246(of)-247(rec)1(ord)-247(matching)-246([32,)]TJ 0 -10.46 Td [(38,)-395(37].)-657(If)-365(we)]TJ/F57 8.9664 Tf 57.816 0 Td [(r)37(estrict)]TJ/F56 8.9664 Tf 28.85 0 Td [(the)-366(class)-365(of)-366(decision)-366(tree)-365(models)-366(learnt)-366(\050to)]TJ -86.666 -10.461 Td [(those)-348(which)-348(satisfy)-347(a)-348(certain)-348(\223monotonicity\224)-348(property)-348(with)-347(respect)]TJ 0 -10.461 Td [(to)-321(record)-321(matching\051,)-339(the)15(y)-321(can)-321(be)-321(cast)-321(as)-321(similarity)-321(joins.)-523(Ho)25(we)25(v)15(er)40(,)]TJ 0 -10.461 Td [(SVM)-218(models)-217(ha)20(v)15(e)-218(been)-217(sho)25(wn)-218(to)-217(be)-218(signi\002cantly)-217(more)-218(accurate)-217(than)]TJ 0 -10.46 Td [(decision)-250(tree)-250(models)-250(for)-250(record)-250(matching)-250(purposes)-250([9].)]TJ 8.967 -10.461 Td [(Our)-463(techniques)-462(e)14(xpl)1(oit)-463(the)]TJ/F57 8.9664 Tf 104.62 0 Td [(monotonicity)]TJ/F56 8.9664 Tf 50.972 0 Td [(property)-463(of)-463(simil)1(arity)]TJ -164.559 -10.461 Td [(functions)-202(for)-201(record)-202(matching.)-294(Informally)65(,)-211(the)-202(monotonicity)-201(property)]TJ 0 -10.461 Td [(requires)-344(that)-345(an)15(y)-344(pair)-345(of)-344(matching)-345(records)-344(ha)20(v)15(e)-345(a)-344(higher)-344(similarity)]TJ 0 -10.461 Td [(v)25(alue)-236(than)-236(a)-237(non-matching)-236(pair)-236(on)-236(at)-236(least)-237(one)-236(similarity)-236(function.)-305(In)]TJ 0 -10.46 Td [(contrast,)-318(machine)-304(learning)-304(techniques)-304(\050including)-304(SVMs)-304(or)-304(decision)]TJ 0 -10.461 Td [(trees\051)-311(are)-311(generically)-311(applicable)-312(to)-311(man)15(y)-311(other)-311(problems)-311(and)-311(hence)]TJ 0 -10.461 Td [(do)-250(not)-250(e)15(xploit)-250(the)-250(monotonicity)-250(property)65(.)]TJ 8.967 -10.461 Td [(Recently)65(,)-261(blocking)-260([5])-259(and)-259(canop)10(y)-259(cluster)-259([17,)-262(29])-259(heuristics)-259(ha)20(v)15(e)]TJ -8.967 -10.46 Td [(been)-258(applied)-257(to)-258(ef)25(\002ciently)-258(e)15(x)15(ecute)-257(more)-258(sophisticated)-258(record)-257(match-)]TJ 0 -10.461 Td [(ing)-408(functions)-407(\050say)65(,)-447(those)-408(learnt)-407(by)-408(machine)-407(learning)-408(models)-407(such)]TJ 0 -10.461 Td [(as)-372(SVMs\051.)-676(Blocking)-372(heuristics)-372(partition)-372(each)-372(of)-372(the)-371(tw)10(o)-372(relations)]TJ 0 -10.461 Td [(based)-313(on)-312(a)-313(k)10(e)15(y)-312(\050potentially)-312(deri)25(v)15(ed)-313(using)-312(a)-313(user)20(-speci\002ed)-312(function\051)]TJ 0 -10.461 Td [(and)-255(only)-255(records)-254(in)-255(groups)-255(that)-255(agree)-254(on)-255(the)-255(k)10(e)15(y)-255(v)25(alue)-255(are)-254(compared)]TJ 0 -10.46 Td [(further)55(.)-590(Thus,)-367(blocking)-344(forces)-343(an)-344(equi-join)-343(on)-343(the)-344(partitioning)-343(k)10(e)15(y)]TJ 0 -10.461 Td [(attrib)20(ute)-328(before)-328(further)-329(\002lters)-328(are)-328(applied.)-545(In)-328(the)-328(language)-328(of)-328(simi-)]TJ 0 -10.461 Td [(larity)-262(functions,)-265(blocki)1(ng)-262(functions)-262(are)-262(boolean)-262(similarity)-261(functions,)]TJ 0 -10.461 Td [(which)-265(indicate)-264(that)-265(a)-265(pair)-264(of)-265(records)-265(either)-264(match)-265(or)-265(do)-264(not.)-354(Canop)10(y)]TJ 0 -10.46 Td [(clustering)-323(generalizes)-323(the)-324(bl)1(ocking)-324(heuristics)-323(and)-323(allo)25(ws)-323(records)-323(in)]TJ 0 -10.461 Td [(a)-293(relation)-292(to)-293(be)-293(in)-292(multiple)-293(clusters.)-438(The)-292(clustering)-293(is)-293(performed)-292(by)]TJ 257.036 653.549 Td [(emplo)10(ying)-250(a)-250(\050user)20(-speci\002ed\051)-251(simil)1(arity)-251(function.)-310(Similar)-250(approaches)]TJ 0 -10.461 Td [(ha)20(v)15(e)-286(also)-286(been)-287(adopted)-286(by)-286(Sara)15(w)10(agi)-286(et)-286(al.)-286([33])-287(in)-286(the)-286(conte)15(xt)-286(of)-286(de-)]TJ 0 -10.461 Td [(cision)-391(tree)-392(models.)-734(Ho)25(we)25(v)15(er)40(,)-426(the)-392(bl)1(ocking)-392(and)-391(canop)10(y)-391(clustering)]TJ 0 -10.46 Td [(heuristics)-250(may)-250(not)-250(preserv)15(e)-250(the)-250(accurac)15(y)-250(of)-250(SVMs.)]TJ 8.967 -10.461 Td [(Independent)-604(of)-604(our)-604(w)10(ork,)-692(Bilenk)10(o)-604(et)-604(al.)-604([7])-604(and)-604(Knoblock)]TJ -8.967 -10.461 Td [(et)-210(al.)-209([30])-210(ha)20(v)15(e)-210(de)25(v)15(eloped)-210(techniques)-209(for)-210(choosing)-210(appropriate)-209(block-)]TJ 0 -10.461 Td [(ing)-237(heuristics)-237(to)-237(reduce)-237(the)-237(time)-237(required)-237(to)-237(e)15(x)15(ecute)-236(record)-237(matching)]TJ 0 -10.46 Td [(models)-429(without)-430(reduci)1(ng)-430(their)-429(accurac)15(y)65(.)-848(First,)-474(our)-429(frame)25(w)10(ork)-429(is)]TJ 0 -10.461 Td [(more)-473(general)-473(in)-472(that)-473(we)-473(consider)-472(the)-473(general)-473(class)-473(of)-472(similarity)]TJ 0 -10.461 Td [(functions,)-448(which)-408(includes)-409(all)-408(blocking)-409(and)-408(canop)10(y)-408(functions,)-448(and)]TJ 0 -10.461 Td [(attrib)20(ute)-235(v)25(alue)-235(transformations.)-305(Therefore,)-238(our)-235(techniques)-235(wil)1(l)-235(select)]TJ 0 -10.461 Td [(the)-390(blocking)-390(and)-390(canop)10(y)-390(functions)-390(if)-390(the)15(y)-390(impro)15(v)15(e)-390(quality)65(.)-729(Or)40(,)-425(a)]TJ 0 -10.46 Td [(programmer)-247(may)-246(constrain)-247(t)1(hat)-247(these)-246(\050blocking\051)-247(similarity)-246(functions)]TJ 0 -10.461 Td [(be)-256(chosen.)-328(\050W)80(e)-255(discuss)-256(constrained)-256(scenarios)-256(in)-256(Section)-256(6.\051)-327(Second,)]TJ 0 -10.461 Td [(man)15(y)-417(of)-417(the)-417(blocking)-417(and)-417(canop)10(y)-417(functions)-417(that)-416(were)-417(considered)]TJ 0 -10.461 Td [(in)-373([7,)-404(30])-373(can)-373(be)-373(implemented)-373(signi\002cantly)-373(more)-373(ef)25(\002ciently)-373(using)]TJ 0 -10.46 Td [(the)-290(set)-290(similarity)-291(join)-290(operator)-290(that)-290(we)-290(de)25(v)15(eloped)-291(in)-290(prior)-290(w)10(ork)-290([14,)]TJ 0 -10.461 Td [(2].)-429(Therefore,)-299(our)-290(frame)25(w)10(ork)-290(can)-289(handle)-290(a)-290(richer)-289(class)-290(of)-289(operators)]TJ 0 -10.461 Td [(during)-304(the)-303(design)-304(and)-304(can)-303(e)15(x)15(ecute)-304(the)-304(result)1(ing)-304(operator)-304(trees)-303(more)]TJ 0 -10.461 Td [(ef)25(\002ciently)65(.)-747(W)80(e)-396(note)-396(that)-395(operator)-396(trees)-396(in)-396(our)-395(class)-396(can)-396(be)-395(either)]TJ 0 -10.461 Td [(used)-303(directly)-303(to)-303(match)-303(records)-303(or)-303(as)-303(ef)25(\002cient)-303(\002lters)-303(before)-303(applying)]TJ 0 -10.46 Td [(more)-306(sophisticated)-306(decision)-306(functions)-306(such)-306(as)-306(SVMs)-305(from)-306(machine)]TJ 0 -10.461 Td [(learning,)-578(or)-512(e)25(v)15(en)-513(user)20(-de\002ned)-512(domain)-513(logic.)-1097(Thus,)-578(our)-512(record)]TJ 0 -10.461 Td [(matching)-397(operator)-396(trees)-397(enable)-397(ef)25(\002cient)-396(and)-397(scalable)-397(e)15(x)15(ecution)-396(of)]TJ 0 -10.461 Td [(sophisticated)-250(record)-250(matching)-250(programs.)]TJ 8.967 -10.46 Td [(Rahm)-349(et)-349(al.)-349(ha)20(v)15(e)-349(proposed)-349(an)-349(e)15(xtensible)-349(archi)1(tecture)-349(for)-349(collec-)]TJ -8.967 -10.461 Td [(ti)25(v)15(ely)-221(matching)-222(multiple)-221(object)-221(types)-222(across)-221(databases)-222([39].)-300(The)-221(sys-)]TJ 0 -10.461 Td [(tem)-264(\050itera)1(ti)25(v)15(ely\051)-264(matches)-263(objects)-264(of)-263(the)-264(same)-263(type)-264(\050say)65(,)-267(authors\051)-263(and)]TJ 0 -10.461 Td [(e)15(xploits)-216(them)-216(to)-216(match)-216(objects)-216(of)-216(other)-216(types)-216(\050say)65(,)-223(publications\051.)-298(Our)]TJ 0 -10.461 Td [(techniques)-195(are)-195(complementary)-195(to)-195(this)-195(approach)-195(and)-195(can)-195(be)-195(plugged)-195(in)]TJ 0 -10.46 Td [(their)-242(architecture)-241(to)-242(generate)-241(matches)-242(between)-242(the)-241(same)-242(object)-241(types)]TJ 0 -10.461 Td [(\050same-mappings,)-250(in)-250(their)-250(nomenclature\051.)]TJ/F55 11.9552 Tf 0 -23.578 Td [(3.)-1000(PR)30(OBLEM)-250(DEFINITION)]TJ/F56 8.9664 Tf 8.967 -12.952 Td [(In)-312(the)-312(rest)-312(of)-312(the)-311(paper)40(,)-328(we)-312(assume)-312(that)-311(the)-312(schemas)-312(of)]TJ/F34 8.9664 Tf 204.398 0 Td [(R)]TJ/F56 8.9664 Tf 9.833 0 Td [(and)]TJ/F34 8.9664 Tf 15.744 0 Td [(S)]TJ/F56 8.9664 Tf -238.942 -10.461 Td [(ha)20(v)15(e)-327(been)-326(reconciled)-327(\050i.e.,)-345(attrib)20(ute)-327(names)-326(in)]TJ/F34 8.9664 Tf 167.331 0 Td [(R)]TJ/F56 8.9664 Tf 9.963 0 Td [(ha)20(v)15(e)-327(been)-326(mapped)]TJ -177.294 -10.46 Td [(to)-267(corresponding)-267(attrib)20(ute)-267(names)-267(in)]TJ/F34 8.9664 Tf 129.838 0 Td [(S)]TJ/F56 8.9664 Tf 6.14 0 Td [(\051.)-361(Further)40(,)-272(we)-267(assume)-267(for)-267(ease)]TJ -135.978 -10.461 Td [(of)-335(e)15(xposition)-336(and)-335(without)-335(loss)-335(of)-336(generality)-335(that)-335(the)-335(corresponding)]TJ 0 -10.461 Td [(attrib)20(ute)-276(names)-276(in)]TJ/F34 8.9664 Tf 67.013 0 Td [(R)]TJ/F56 8.9664 Tf 9.511 0 Td [(and)]TJ/F34 8.9664 Tf 15.422 0 Td [(S)]TJ/F56 8.9664 Tf 8.613 0 Td [(are)-276(identical.)-388(Let)-276(the)-276(attrib)20(ute)]TJ/F34 8.9664 Tf 110.06 0 Td [(I)-78(D)]TJ/F56 8.9664 Tf 15.059 0 Td [(be)-276(an)]TJ -225.678 -10.461 Td [(identi\002er)-250(attrib)20(ute)-250(in)-250(both)]TJ/F34 8.9664 Tf 93.967 0 Td [(R)]TJ/F56 8.9664 Tf 9.277 0 Td [(and)]TJ/F34 8.9664 Tf 15.189 0 Td [(S)]TJ/F56 8.9664 Tf 6.139 0 Td [(.)]TJ/F55 11.9552 Tf -124.572 -18.265 Td [(3.1)-1000(SJU)-250(Operator)-250(T)74(r)18(ees)]TJ/F56 8.9664 Tf 8.967 -12.951 Td [(W)80(e)-224(no)25(w)-225(formall)1(y)-225(de\002ne)-224(the)-224(SJU)-225(operator)-224(trees)-224(containing)-224(similar)20(-)]TJ -8.967 -10.461 Td [(ity)-252(joins)-252(and)-253(unions.)-316(In)-252(Section)-253(5,)-252(we)-253(e)15(xtend)-252(this)-252(class)-252(with)-252(attrib)20(ute)]TJ 0 -10.461 Td [(v)25(alue)-250(transformation)-250(operators.)]TJ 8.967 -10.46 Td [(Let)]TJ/F34 8.9664 Tf 14.098 0 Td [(g)]TJ/F33 5.9776 Tf 4.395 -0.997 Td [(1)]TJ/F34 8.9664 Tf 4.151 0.997 Td [(;)-171(:)-172(:)-171(:)-171(;)-171(g)]TJ/F35 5.9776 Tf 24.872 -0.997 Td [(N)]TJ/F56 8.9664 Tf 9.071 0.997 Td [(be)-239(similarity)-240(functions)-239(such)-240(that)]TJ/F31 8.9664 Tf 116.831 0 Td [(0)]TJ/F36 8.9664 Tf 7.168 0 Td [(\024)]TJ/F34 8.9664 Tf 9.727 0 Td [(g)]TJ/F35 5.9776 Tf 4.394 -0.997 Td [(i)]TJ/F31 8.9664 Tf 3.162 0.997 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(v)]TJ/F33 5.9776 Tf 4.476 -0.997 Td [(1)]TJ/F34 8.9664 Tf 4.151 0.997 Td [(;)-171(v)]TJ/F33 5.9776 Tf 8.572 -0.997 Td [(2)]TJ/F31 8.9664 Tf 4.151 0.997 Td [(\051)]TJ/F36 8.9664 Tf 6.144 0 Td [(\024)]TJ/F31 8.9664 Tf -237.914 -10.461 Td [(1)]TJ/F56 8.9664 Tf 6.366 0 Td [(and)]TJ/F34 8.9664 Tf 14.705 0 Td [(g)]TJ/F35 5.9776 Tf 4.394 -0.996 Td [(i)]TJ/F31 8.9664 Tf 3.162 0.996 Td [(\050)]TJ/F34 8.9664 Tf 3.583 0 Td [(v)]TJ/F33 5.9776 Tf 4.477 -0.996 Td [(1)]TJ/F34 8.9664 Tf 4.151 0.996 Td [(;)-171(v)]TJ/F33 5.9776 Tf 8.572 -0.996 Td [(2)]TJ/F31 8.9664 Tf 4.151 0.996 Td [(\051)-285(=)-286(1)]TJ/F56 8.9664 Tf 22.236 0 Td [(if)25(f)]TJ/F34 8.9664 Tf 9.998 0 Td [(v)]TJ/F33 5.9776 Tf 4.476 -0.996 Td [(1)]TJ/F31 8.9664 Tf 6.711 0.996 Td [(=)]TJ/F34 8.9664 Tf 9.727 0 Td [(v)]TJ/F33 5.9776 Tf 4.476 -0.996 Td [(2)]TJ/F56 8.9664 Tf 4.151 0.996 Td [(.)-292(Let)]TJ/F34 8.9664 Tf 18.57 0 Td [(A)]TJ/F33 5.9776 Tf 6.91 -0.996 Td [(1)]TJ/F34 8.9664 Tf 4.151 0.996 Td [(;)-171(:)-172(:)-171(:)-171(;)-171(A)]TJ/F35 5.9776 Tf 27.389 -0.996 Td [(C)]TJ/F56 8.9664 Tf 7.952 0.996 Td [(denote)-196(the)]TJ/F57 8.9664 Tf 38.376 0 Td [(column)]TJ -218.684 -10.461 Td [(sequences)]TJ/F56 8.9664 Tf 38.632 0 Td [(in)]TJ/F34 8.9664 Tf 9.259 0 Td [(R)]TJ/F56 8.9664 Tf 9.318 0 Td [(and)]TJ/F34 8.9664 Tf 15.231 0 Td [(S)]TJ/F56 8.9664 Tf 8.422 0 Td [(we)-255(might)-254(compare)-255(using)-254(one)-255(or)-254(more)-255(similar)20(-)]TJ -80.862 -10.461 Td [(ity)-363(functions.)-651(Note)-363(that,)-392(in)-363(general,)-392(we)-364(may)-363(concatenate)-363(dif)25(ferent)]TJ 0 -10.46 Td [(column)-280(sequences)-280(\050e.g.,)-288(R.[City])-280(and)-280(S.[City)65(,)-287(State]\051)-280(while)-280(compar)20(-)]TJ 0 -10.461 Td [(ing)-294(tw)10(o)-294(tuples)-293(across)]TJ/F34 8.9664 Tf 79.183 0 Td [(R)]TJ/F56 8.9664 Tf 9.67 0 Td [(and)]TJ/F34 8.9664 Tf 15.582 0 Td [(S)]TJ/F56 8.9664 Tf 6.139 0 Td [(.)-441(F)15(or)-294(ease)-294(of)-294(e)15(xposition,)-305(and)-293(without)]TJ -110.574 -10.461 Td [(loss)-324(of)-324(generality)65(,)-342(we)-324(assume)-323(that)-324(the)-324(column)-324(sequence)-323(concatena-)]TJ 0 -10.461 Td [(tions)-290(compared)-291(acros)1(s)]TJ/F34 8.9664 Tf 83.009 0 Td [(R)]TJ/F56 8.9664 Tf 9.638 0 Td [(and)]TJ/F34 8.9664 Tf 15.55 0 Td [(S)]TJ/F56 8.9664 Tf 8.743 0 Td [(are)-290(identical.)-431(Gi)25(v)15(en)-290(a)-291(tuple)]TJ/F34 8.9664 Tf 101.812 0 Td [(r)]TJ/F36 8.9664 Tf 7.661 0 Td [(2)]TJ/F34 8.9664 Tf 9.391 0 Td [(R)]TJ/F56 8.9664 Tf 7.036 0 Td [(,)]TJ -242.84 -10.46 Td [(we)-223(use)]TJ/F34 8.9664 Tf 26.414 0 Td [(r)29(:A)]TJ/F56 8.9664 Tf 15.375 0 Td [(to)-223(denote)-224(the)-223(concatenation)-224(of)-223(\050with)-224(a)-223(white)-223(space)-224(delim-)]TJ -41.789 -10.461 Td [(iter)-243(inserted)-242(between\051)-243(attrib)20(ute)-242(v)25(alues)-243(in)-243(a)-242(column)-243(sequence)]TJ/F34 8.9664 Tf 215.887 0 Td [(A)]TJ/F56 8.9664 Tf 9.086 0 Td [(in)-243(the)]TJ -224.973 -10.461 Td [(relation)]TJ/F34 8.9664 Tf 29.634 0 Td [(R)]TJ/F56 8.9664 Tf 7.035 0 Td [(.)]TJ -27.702 -10.461 Td [(Gi)25(v)15(en)-363(an)15(y)-364(pair)-363(of)-364(tuples)]TJ/F34 8.9664 Tf 93.495 0 Td [(r)]TJ/F36 8.9664 Tf 8.91 0 Td [(2)]TJ/F34 8.9664 Tf 10.64 0 Td [(R)]TJ/F56 8.9664 Tf 10.295 0 Td [(and)]TJ/F34 8.9664 Tf 16.206 0 Td [(s)]TJ/F36 8.9664 Tf 8.79 0 Td [(2)]TJ/F34 8.9664 Tf 10.64 0 Td [(S)]TJ/F56 8.9664 Tf 6.139 0 Td [(,)-392(let)]TJ/F34 8.9664 Tf 17.98 0 Td [(g)]TJ/F35 5.9776 Tf 4.395 -0.996 Td [(j)]TJ/F31 8.9664 Tf 3.902 0.996 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(r)28(:)1(A)]TJ/F35 5.9776 Tf 13.372 -0.996 Td [(i)]TJ/F34 8.9664 Tf 3.162 0.996 Td [(;)-171(s:A)]TJ/F35 5.9776 Tf 17.859 -0.996 Td [(i)]TJ/F31 8.9664 Tf 3.161 0.996 Td [(\051)]TJ/F56 8.9664 Tf -241.497 -10.461 Td [(denote)-224(the)-224(simila)1(rity)-224(using)]TJ/F34 8.9664 Tf 96.694 0 Td [(g)]TJ/F35 5.9776 Tf 4.394 -0.996 Td [(j)]TJ/F56 8.9664 Tf 5.909 0.996 Td [(between)-224(attrib)20(ute)-224(v)25(alue)-223(concatenations)]TJ/F34 8.9664 Tf -106.997 -10.46 Td [(r)29(:A)]TJ/F35 5.9776 Tf 13.372 -0.997 Td [(i)]TJ/F56 8.9664 Tf 6.419 0.997 Td [(and)]TJ/F34 8.9664 Tf 16.205 0 Td [(s:A)]TJ/F35 5.9776 Tf 13.763 -0.997 Td [(i)]TJ/F56 8.9664 Tf 3.162 0.997 Td [(.)-650(F)15(or)-363(e)15(xample,)-392(jaccard\050r)55(.)]TJ/F36 8.9664 Tf 93.248 0 Td [(h)]TJ/F56 8.9664 Tf 3.583 0 Td [(city)65(,)-392(state)]TJ/F36 8.9664 Tf 35.055 0 Td [(i)]TJ/F56 8.9664 Tf 3.584 0 Td [(,)-392(s.)]TJ/F36 8.9664 Tf 11.482 0 Td [(h)]TJ/F56 8.9664 Tf 3.584 0 Td [(city)65(,)-392(state)]TJ/F36 8.9664 Tf 35.055 0 Td [(i)]TJ/F56 8.9664 Tf 3.583 0 Td [(\051)]TJ -242.095 -10.461 Td [(compares)-235(the)-235(jaccard)-235(similarity)-236(between)-235(the)-235(strings)-235(obtained)-235(by)-235(con-)]TJ 0 -10.461 Td [(catenating)-255(city)-256(and)-255(state)-255(v)25(alues)-255(of)]TJ/F34 8.9664 Tf 123.573 0 Td [(r)]TJ/F56 8.9664 Tf 6.703 0 Td [(and)]TJ/F34 8.9664 Tf 15.237 0 Td [(s)]TJ/F56 8.9664 Tf 4.293 0 Td [(.)-326(Let)]TJ/F34 8.9664 Tf 19.406 0 Td [(g)]TJ/F35 5.9776 Tf 4.394 -0.996 Td [(j)]TJ/F31 8.9664 Tf 3.903 0.996 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(R)-7(:A)]TJ/F35 5.9776 Tf 16.506 -0.996 Td [(i)]TJ/F34 8.9664 Tf 3.161 0.996 Td [(;)-171(S:A)]TJ/F35 5.9776 Tf 19.193 -0.996 Td [(i)]TJ/F31 8.9664 Tf 3.162 0.996 Td [(\051)]TJ/F34 8.9664 Tf 6.235 0 Td [(>)-296(\013)]TJ/F56 8.9664 Tf -229.35 -10.461 Td [(denote)-300(a)]TJ/F57 8.9664 Tf 33.268 0 Td [(similarity)-300(function)-300(pr)37(edicate)]TJ/F56 8.9664 Tf 105.376 0 Td [(which)-300(for)-300(an)15(y)-300(pair)-301(of)-300(records)]TJ/F34 8.9664 Tf -138.644 -10.46 Td [(r)]TJ/F36 8.9664 Tf 6.974 0 Td [(2)]TJ/F34 8.9664 Tf 8.703 0 Td [(R)]TJ/F56 8.9664 Tf 9.278 0 Td [(and)]TJ/F34 8.9664 Tf 15.189 0 Td [(s)]TJ/F36 8.9664 Tf 6.852 0 Td [(2)]TJ/F34 8.9664 Tf 8.704 0 Td [(S)]TJ/F56 8.9664 Tf 8.381 0 Td [(returns)-250(true)-250(if)]TJ/F34 8.9664 Tf 51.045 0 Td [(g)]TJ/F35 5.9776 Tf 4.394 -0.997 Td [(j)]TJ/F31 8.9664 Tf 3.903 0.997 Td [(\050)]TJ/F34 8.9664 Tf 3.583 0 Td [(r)28(:A)]TJ/F35 5.9776 Tf 13.372 -0.997 Td [(i)]TJ/F34 8.9664 Tf 3.162 0.997 Td [(;)-171(s:A)]TJ/F35 5.9776 Tf 17.859 -0.997 Td [(i)]TJ/F31 8.9664 Tf 3.162 0.997 Td [(\051)]TJ/F34 8.9664 Tf 6.143 0 Td [(>)-285(\013)]TJ/F56 8.9664 Tf 15.64 0 Td [(.)]TJ ET Q 1 0 0 1 295.992 36 cm 0 Tr /QQAPFce02551e 12 Tf 0 0 0 rg 100 Tz 0 Ts 0 Tw 0 Tc BT 1 0 0 1 0 0 Tm (329)Tj ET 1 0 0 1 0 0 cm 1 0 0 1 -295.992 -36 cm endstream endobj 46 0 obj << /Type /Page /Resources 45 0 R /MediaBox [ 0 0 612 792 ] /Parent 13 0 R /Contents [ 47 0 R ] >> endobj 45 0 obj << /Font << /F56 10 0 R /F55 9 0 R /F38 48 0 R /F35 49 0 R /F34 12 0 R /F31 18 0 R /F9 50 0 R /F57 11 0 R /F33 51 0 R /F36 8 0 R /QQAPFce02551e 232 0 R >> /ProcSet [ /PDF /Text ] >> endobj 54 0 obj << /Length 29179 /LC /QQAP >> stream q BT /F57 8.9664 Tf 63.761 728.239 Td [(De\002nition)-250(1.)]TJ/F56 8.9664 Tf 49.315 0 Td [(The)]TJ/F57 8.9664 Tf 21.075 0 Td [(similarity)-795(join)]TJ/F56 8.9664 Tf 62.592 0 Td [(between)-795(relations)]TJ/F34 8.9664 Tf 75.021 0 Td [(R)]TJ/F56 8.9664 Tf 14.168 0 Td [(and)]TJ/F34 8.9664 Tf -232.134 -10.461 Td [(S)]TJ/F56 8.9664 Tf 13.696 0 Td [(o)15(v)15(er)-843(similarity)-842(function)-843(predicates)]TJ/F34 8.9664 Tf 146.501 0 Td [(g)]TJ/F33 5.9776 Tf 4.394 -0.996 Td [(1)]TJ/F31 8.9664 Tf 4.151 0.996 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(R)-7(:A)]TJ/F35 5.9776 Tf 16.506 -0.996 Td [(i)]TJ/F33 5.9776 Tf 2.663 0 Td [(1)]TJ/F34 8.9664 Tf 4.151 0.996 Td [(;)-171(S:A)]TJ/F35 5.9776 Tf 19.193 -0.996 Td [(i)]TJ/F33 5.9776 Tf 2.664 0 Td [(1)]TJ/F31 8.9664 Tf 4.151 0.996 Td [(\051)]TJ/F34 8.9664 Tf 16.26 0 Td [(>)]TJ -237.914 -10.461 Td [(\013)]TJ/F33 5.9776 Tf 5.906 -0.996 Td [(1)]TJ/F34 8.9664 Tf 4.151 0.996 Td [(;)-171(:)-172(:)-171(:)-171(;)-171(g)]TJ/F35 5.9776 Tf 24.873 -1.062 Td [(d)]TJ/F31 8.9664 Tf 4.339 1.062 Td [(\050)]TJ/F34 8.9664 Tf 3.583 0 Td [(R)-7(:A)]TJ/F35 5.9776 Tf 16.506 -1.062 Td [(id)]TJ/F34 8.9664 Tf 7.002 1.062 Td [(;)-171(S:A)]TJ/F35 5.9776 Tf 19.193 -1.062 Td [(id)]TJ/F31 8.9664 Tf 7.003 1.062 Td [(\051)]TJ/F34 8.9664 Tf 9.86 0 Td [(>)-700(\013)]TJ/F35 5.9776 Tf 19.35 -1.062 Td [(d)]TJ/F56 8.9664 Tf 4.338 1.062 Td [(,)-522(is)-468(the)-468(join)-468(between)]TJ/F34 8.9664 Tf 84.466 0 Td [(R)]TJ/F56 8.9664 Tf 11.23 0 Td [(and)]TJ/F34 8.9664 Tf 17.142 0 Td [(S)]TJ/F56 8.9664 Tf -238.942 -11.65 Td [(where)-250(the)-250(join)-250(predicate)-250(is)]TJ/F38 8.9664 Tf 96.863 6.724 Td [(V)]TJ/F35 5.9776 Tf 7.679 -2.463 Td [(d)]TJ 0 -7.001 Td [(j)]TJ/F33 5.9776 Tf 3.405 0 Td [(=1)]TJ/F34 8.9664 Tf 11.277 2.74 Td [(g)]TJ/F35 5.9776 Tf 4.394 -0.997 Td [(j)]TJ/F31 8.9664 Tf 3.903 0.997 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(R)-7(:A)]TJ/F35 5.9776 Tf 16.505 -0.997 Td [(ij)]TJ/F34 8.9664 Tf 6.567 0.997 Td [(;)-171(S:A)]TJ/F35 5.9776 Tf 19.193 -0.997 Td [(ij)]TJ/F31 8.9664 Tf 6.566 0.997 Td [(\051)]TJ/F34 8.9664 Tf 6.144 0 Td [(>)-285(\013)]TJ/F35 5.9776 Tf 15.633 -0.997 Td [(j)]TJ/F56 8.9664 Tf 3.903 0.997 Td [(.)]TJ -196.649 -17.18 Td [(F)15(or)-1211(e)15(xample,)]TJ/F34 8.9664 Tf 68.674 0 Td [(edit)]TJ/F31 8.9664 Tf 15.54 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(R)-7(:N)-108(ame;)-171(S:N)-108(ame)]TJ/F31 8.9664 Tf 73.12 0 Td [(\051)]TJ/F34 8.9664 Tf 22.543 0 Td [(>)]TJ/F31 8.9664 Tf 26.127 0 Td [(0)]TJ/F34 8.9664 Tf 4.607 0 Td [(:)]TJ/F31 8.9664 Tf 2.56 0 Td [(9)]TJ/F36 8.9664 Tf 13.216 0 Td [(^)]TJ/F34 8.9664 Tf -238.938 -10.461 Td [(j)-57(accar)-29(d)]TJ/F31 8.9664 Tf 31.213 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(R)-7(:Addr)-29(ess;)-171(S:Addr)-28(ess)]TJ/F31 8.9664 Tf 89.366 0 Td [(\051)]TJ/F34 8.9664 Tf 11.747 0 Td [(>)]TJ/F31 8.9664 Tf 15.33 0 Td [(0)]TJ/F34 8.9664 Tf 4.608 0 Td [(:)]TJ/F31 8.9664 Tf 2.56 0 Td [(8)]TJ/F56 8.9664 Tf 9.793 0 Td [(is)-578(an)-579(e)15(xample)-578(of)-578(a)]TJ -168.201 -10.46 Td [(similarity)-250(join)-250(as)-250(sho)25(wn)-250(in)-250(the)-250(rightmost)-250(path)-250(in)-250(Figure)-250(1.)]TJ/F55 8.9664 Tf 0 -14.496 Td [(SJU)-271(T)74(r)18(ees)]TJ/F56 8.9664 Tf 38.958 0 Td [(:)-352(An)15(y)-271(operator)-271(t)1(ree)-271(which)-271(is)-271(a)-271(union)-271(of)-271(similarity)-271(joins)-270(is)]TJ -38.958 -10.461 Td [(an)-295(SJU)-296(tree.)-446(The)-296(class)-295(of)-295(SJU)-296(trees)-295(is)-296(rich)-295(enough)-296(to)-295(include)-295(man)15(y)]TJ 0 -10.461 Td [(pre)25(vious)-250(record)-250(matching)-250(techniques)-250([28].)]TJ/F55 11.9552 Tf 0 -18.112 Td [(3.2)-1000(Record)-250(Matching)-250(Operator)-250(T)74(r)18(ee)-250(Design)]TJ/F56 8.9664 Tf 8.967 -12.951 Td [(Gi)25(v)15(en)-216(tw)10(o)-216(rela)1(tions,)-223(there)-216(is)-216(a)-215(lar)18(ge)-216(number)-216(of)-216(choices)-216(for)-215(creating)]TJ -8.967 -10.461 Td [(a)-291(record)-291(matching)-291(opera)1(tor)-291(tree.)-433(Further)40(,)-301(these)-291(choices)-291(usually)-290(lead)]TJ 0 -10.461 Td [(to)-314(dif)25(ferent)-314(solutions)-315(\050i.e.,)-330(dif)25(ferent)-314(subsets)-314(of)]TJ/F34 8.9664 Tf 170.077 0 Td [(R)]TJ/F36 8.9664 Tf 9.521 0 Td [(\002)]TJ/F34 8.9664 Tf 9.654 0 Td [(S)]TJ/F56 8.9664 Tf 6.14 0 Td [(\051.)-503(T)80(o)-314(identify)]TJ -195.392 -10.461 Td [(the)-214(best)-213(record)-214(matching)-213(operator)-214(tree)-214(among)-213(all)-214(possible)-213(candidates,)]TJ 0 -10.461 Td [(we)-321(need)-322(to)-321(quantify)-321(the)-322(quality)-321(of)-321(a)-321(record)-322(matching)-321(operator)-321(tree.)]TJ 0 -10.46 Td [(Our)-387(approach)-386(is)-387(based)-386(on)-387(le)25(v)15(eraging)-386(a)-387(gi)25(v)15(en)-387(set)-386(of)-387(matching)-386(and)]TJ 0 -10.461 Td [(non-matching)-250(pairs)-250(of)-250(e)15(xamples.)]TJ/F57 8.9664 Tf 0 -12.478 Td [(Examples)]TJ/F56 8.9664 Tf 34.861 0 Td [(:)-490(An)]TJ/F57 8.9664 Tf 20.894 0 Td [(e)20(xample)]TJ/F56 8.9664 Tf 32.745 0 Td [(is)-340(a)-340(record)-340(pair)-340(belonging)-340(to)]TJ/F34 8.9664 Tf 107.941 0 Td [(R)]TJ/F36 8.9664 Tf 9.698 0 Td [(\002)]TJ/F34 8.9664 Tf 9.83 0 Td [(S)]TJ/F56 8.9664 Tf 9.189 0 Td [(along)]TJ -225.158 -10.461 Td [(with)-243(a)-244(label)-243(indicating)-244(whether)-243(or)-244(not)-243(the)-244(pair)-243(is)-243(considered)-244(a)-243(match.)]TJ 0 -10.461 Td [(Let)]TJ/F31 8.9664 Tf 15.247 0 Td [(\001)]TJ/F33 5.9776 Tf 7.679 3.809 Td [(+)]TJ/F56 8.9664 Tf 9.383 -3.809 Td [(denote)-367(the)-368(set)-367(of)-368(e)15(xample)-367(matching)-368(record)-367(pairs)-368(and)]TJ/F31 8.9664 Tf 198.838 0 Td [(\001)]TJ/F37 5.9776 Tf 7.68 3.809 Td [(\000)]TJ/F56 8.9664 Tf -238.827 -14.27 Td [(denote)-250(the)-250(set)-250(of)-250(e)15(xample)-250(non-matching)-250(pairs.)]TJ 8.967 -10.46 Td [(Let)]TJ/F34 8.9664 Tf 14.944 0 Td [(T)]TJ/F31 8.9664 Tf 6.656 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(R)-7(;)-171(S)]TJ/F31 8.9664 Tf 17.27 0 Td [(\051)]TJ/F56 8.9664 Tf 6.577 0 Td [(be)-334(an)-333(SJU)-334(operator)-334(tree)-333(o)15(v)15(er)-334(input)-334(relations)]TJ/F34 8.9664 Tf 164.108 0 Td [(R)]TJ/F56 8.9664 Tf 10.028 0 Td [(and)]TJ/F34 8.9664 Tf -232.134 -10.461 Td [(S)]TJ/F56 8.9664 Tf 6.14 0 Td [(.)-540(Since)-326(it)-327(will)-326(be)-327(clear)-326(from)-327(the)-326(conte)15(xt,)-346(we)-326(also)-327(use)]TJ/F34 8.9664 Tf 197.943 0 Td [(T)]TJ/F31 8.9664 Tf 6.656 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(R)-7(;)-171(S)]TJ/F31 8.9664 Tf 17.271 0 Td [(\051)]TJ/F56 8.9664 Tf 6.511 0 Td [(to)]TJ -238.105 -10.461 Td [(denote)-250(the)-250(result)-250(of)-250(e)15(x)15(ecuting)]TJ/F34 8.9664 Tf 108.053 0 Td [(T)]TJ/F31 8.9664 Tf 6.656 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(R)-7(;)-171(S)]TJ/F31 8.9664 Tf 17.271 0 Td [(\051)]TJ/F56 8.9664 Tf 5.825 0 Td [(on)-250(relations)]TJ/F34 8.9664 Tf 44.329 0 Td [(R)]TJ/F56 8.9664 Tf 9.277 0 Td [(and)]TJ/F34 8.9664 Tf 15.189 0 Td [(S)]TJ/F56 8.9664 Tf 6.14 0 Td [(.)]TJ/F57 8.9664 Tf -206.361 -18.034 Td [(De\002nition)-250(2.)]TJ/F56 8.9664 Tf 49.315 0 Td [(The)]TJ/F57 8.9664 Tf 18.295 0 Td [(co)10(ver)15(a)10(g)10(e)]TJ/F56 8.9664 Tf 36.811 0 Td [(of)]TJ/F34 8.9664 Tf 11.822 0 Td [(T)]TJ/F31 8.9664 Tf 6.656 0 Td [(\050)]TJ/F34 8.9664 Tf 3.583 0 Td [(R)-7(;)-171(S)]TJ/F31 8.9664 Tf 17.271 0 Td [(\051)]TJ/F56 8.9664 Tf 7.937 0 Td [(with)-485(respect)-486(to)]TJ/F34 8.9664 Tf 61.369 0 Td [(X)]TJ/F36 8.9664 Tf 14.892 0 Td [(\022)]TJ/F34 8.9664 Tf -237.914 -10.461 Td [(R)]TJ/F36 8.9664 Tf 9.826 0 Td [(\002)]TJ/F34 8.9664 Tf 9.957 0 Td [(S)]TJ/F56 8.9664 Tf 9.355 0 Td [(is)-359(the)-358(fraction)-359(of)-359(records)-358(in)]TJ/F31 8.9664 Tf 104.951 0 Td [(\005)]TJ/F35 5.9776 Tf 6.91 -0.997 Td [(R)-4(:I)-77(D)-32(;S)11(:I)-77(D)]TJ/F34 8.9664 Tf 37.087 0.997 Td [(X)]TJ/F56 8.9664 Tf 11.53 0 Td [(that)-359(are)-358(also)-359(in)]TJ/F31 8.9664 Tf -189.616 -10.461 Td [(\005)]TJ/F35 5.9776 Tf 6.91 -0.996 Td [(R)-4(:I)-77(D)-32(;S)11(:I)-77(D)]TJ/F34 8.9664 Tf 37.087 0.996 Td [(T)]TJ/F31 8.9664 Tf 6.656 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(R)-7(;)-171(S)]TJ/F31 8.9664 Tf 17.27 0 Td [(\051)]TJ/F56 8.9664 Tf 3.584 0 Td [(.)]TJ -66.124 -10.461 Td [(Gi)25(v)15(en)]TJ/F31 8.9664 Tf 24.251 0 Td [(0)]TJ/F36 8.9664 Tf 8.034 0 Td [(\024)]TJ/F34 8.9664 Tf 10.593 0 Td [(\014)]TJ/F36 8.9664 Tf 9.087 0 Td [(\024)]TJ/F31 8.9664 Tf 10.593 0 Td [(1)]TJ/F56 8.9664 Tf 4.608 0 Td [(,)-313(an)-301(operator)-301(tree)]TJ/F34 8.9664 Tf 64.921 0 Td [(T)]TJ/F31 8.9664 Tf 6.656 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(R)-7(;)-171(S)]TJ/F31 8.9664 Tf 17.271 0 Td [(\051)]TJ/F56 8.9664 Tf 6.28 0 Td [(is)]TJ/F34 8.9664 Tf 8.677 0 Td [(\014)]TJ/F57 8.9664 Tf 5.661 0 Td [(-ne)40(g)]TJ/F56 8.9664 Tf 18.271 0 Td [(if)-301(the)-300(co)15(v-)]TJ -207.454 -10.461 Td [(erage)-266(of)]TJ/F34 8.9664 Tf 31.66 0 Td [(T)]TJ/F31 8.9664 Tf 6.655 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(R)-7(;)-171(S)]TJ/F31 8.9664 Tf 17.271 0 Td [(\051)]TJ/F56 8.9664 Tf 5.973 0 Td [(with)-266(respect)-267(to)]TJ/F31 8.9664 Tf 55.478 0 Td [(\001)]TJ/F37 5.9776 Tf 7.679 3.809 Td [(\000)]TJ/F56 8.9664 Tf 8.644 -3.809 Td [(is)-266(less)-267(than)-266(or)-267(equal)-266(to)]TJ/F34 8.9664 Tf 83.07 0 Td [(\014)]TJ/F56 8.9664 Tf 5.661 0 Td [(.)-359(The)]TJ/F57 8.9664 Tf -225.675 -10.46 Td [(quality)]TJ/F56 8.9664 Tf 27.15 0 Td [(of)]TJ/F34 8.9664 Tf 9.711 0 Td [(T)]TJ/F31 8.9664 Tf 6.656 0 Td [(\050)]TJ/F34 8.9664 Tf 3.583 0 Td [(R)-7(;)-171(S)]TJ/F31 8.9664 Tf 17.271 0 Td [(\051)]TJ/F56 8.9664 Tf 5.826 0 Td [(is)-250(its)-250(co)15(v)15(erage)-250(with)-250(respect)-250(to)]TJ/F31 8.9664 Tf 108.303 0 Td [(\001)]TJ/F33 5.9776 Tf 7.68 3.809 Td [(+)]TJ/F56 8.9664 Tf 6.088 -3.809 Td [(.)]TJ/F57 8.9664 Tf -182.305 -18.035 Td [(De\002nition)-250(3.)]TJ/F56 8.9664 Tf 49.315 0 Td [(\050)]TJ/F57 8.9664 Tf 2.985 0 Td [(Oper)15(ator)-300(tr)37(ee)-300(design)-299(pr)45(oblem)]TJ/F56 8.9664 Tf 107.807 0 Td [(\051)-300(Gi)25(v)15(en)]TJ/F31 8.9664 Tf 29.917 0 Td [(0)]TJ/F36 8.9664 Tf 8.018 0 Td [(\024)]TJ/F34 8.9664 Tf 10.578 0 Td [(\014)-432(<)]TJ/F31 8.9664 Tf 19.649 0 Td [(1)]TJ/F56 8.9664 Tf 4.608 0 Td [(,)]TJ -242.84 -10.461 Td [(the)-248(goal)-248(in)-248(the)-247(operator)-248(tree)-248(design)-248(problem)-248(is)-248(to)-247(\002nd)-248(a)]TJ/F34 8.9664 Tf 198.499 0 Td [(\014)]TJ/F56 8.9664 Tf 5.661 0 Td [(-ne)15(g)-248(opera-)]TJ -204.16 -10.46 Td [(tor)-250(tree)]TJ/F34 8.9664 Tf 27.885 0 Td [(T)]TJ/F37 5.9776 Tf 6.656 3.809 Td [(\003)]TJ/F31 8.9664 Tf 4.317 -3.809 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(R)-7(;)-171(S)]TJ/F31 8.9664 Tf 17.271 0 Td [(\051)]TJ/F56 8.9664 Tf 5.825 0 Td [(with)-250(the)-250(maximum)-250(quality)65(.)]TJ -56.571 -18.035 Td [(A)-410(similarity)-411(join)-410(in)40(v)20(olv)15(es)-411(three)-410(dif)25(ferent)-411(elements:)-631(\050i\051)-410(a)-411(set)-410(of)]TJ -8.967 -10.461 Td [(similarity)-480(functions)-479(\050such)-480(as)-480(edit)-480(similarity)65(,)-537(hamming,)-537(etc.\051,)-537(\050ii\051)]TJ 0 -10.46 Td [(the)-308(column)-307(sequences)-308(compared)-308(us)1(ing)-308(the)-308(similarity)-307(functions,)-322(and)]TJ 0 -10.461 Td [(\050iii\051)-400(the)-400(thresholds)-400(o)15(v)15(er)-401(the)-400(resulting)-400(similarity)-400(v)25(alues)-400(in)-400(order)-400(to)]TJ 0 -10.461 Td [(de\002ne)-376(the)-376(join)-376(predicates.)-688(F)15(or)-376(e)15(xample,)-407(if)-376(we)-376(consider)-376(the)-376(set)-376(of)]TJ 0 -10.461 Td [(edit)-267(and)-267(jaccard)-266(similarity)-267(functions,)-271(the)-267(columns)]TJ/F36 8.9664 Tf 180.4 0 Td [(f)]TJ/F56 8.9664 Tf 4.608 0 Td [(Name,)-271(Address)]TJ/F36 8.9664 Tf 55.466 0 Td [(g)]TJ/F56 8.9664 Tf -240.474 -10.46 Td [(from)-463(tw)10(o)-463(relations)]TJ/F34 8.9664 Tf 74.122 0 Td [(R)]TJ/F56 8.9664 Tf 11.187 0 Td [(and)]TJ/F34 8.9664 Tf 17.098 0 Td [(S)]TJ/F56 8.9664 Tf 6.139 0 Td [(,)-516(then)-463(we)-463(get)-463(a)-463(total)-463(of)-463(eight)-463(si)1(mi-)]TJ -108.546 -10.461 Td [(larity)-468(functions:)-747(four)-469(corresponding)-468(to)-469(measuring)-468(edit)-468(similarity)]TJ 0 -10.461 Td [(between)-260(all)-259(non-empty)-260(sub-sequence)-259(pairs)]TJ/F36 8.9664 Tf 155.063 0 Td [(f)]TJ/F56 8.9664 Tf 4.607 0 Td [(\050)]TJ/F36 8.9664 Tf 2.986 0 Td [(h)]TJ/F56 8.9664 Tf 3.584 0 Td [(R.Name)]TJ/F36 8.9664 Tf 29.634 0 Td [(i)]TJ/F56 8.9664 Tf 3.583 0 Td [(,)]TJ/F36 8.9664 Tf 4.591 0 Td [(h)]TJ/F56 8.9664 Tf 3.584 0 Td [(S.Name)]TJ/F36 8.9664 Tf 28.638 0 Td [(i)]TJ/F56 8.9664 Tf 3.584 0 Td [(\051,)]TJ -239.854 -10.461 Td [(\050)]TJ/F36 8.9664 Tf 2.986 0 Td [(h)]TJ/F56 8.9664 Tf 3.584 0 Td [(R.Address)]TJ/F36 8.9664 Tf 37.604 0 Td [(i)]TJ/F56 8.9664 Tf 3.584 0 Td [(,)]TJ/F36 8.9664 Tf 9.676 0 Td [(h)]TJ/F56 8.9664 Tf 3.584 0 Td [(S.Address)]TJ/F36 8.9664 Tf 36.61 0 Td [(i)]TJ/F56 8.9664 Tf 3.583 0 Td [(\051,)-829(\050)]TJ/F36 8.9664 Tf 15.648 0 Td [(h)]TJ/F56 8.9664 Tf 3.584 0 Td [(R.Name,)-829(R.Address)]TJ/F36 8.9664 Tf 76.914 0 Td [(i)]TJ/F56 8.9664 Tf 3.584 0 Td [(,)]TJ/F36 8.9664 Tf 9.676 0 Td [(h)]TJ/F56 8.9664 Tf 3.584 0 Td [(S.Name,)]TJ -214.201 -10.461 Td [(S.Address)]TJ/F36 8.9664 Tf 36.61 0 Td [(i)]TJ/F56 8.9664 Tf 3.583 0 Td [(\051,)-441(\050)]TJ/F36 8.9664 Tf 12.164 0 Td [(h)]TJ/F56 8.9664 Tf 3.584 0 Td [(R.Address,)-441(R.Name)]TJ/F36 8.9664 Tf 73.43 0 Td [(i)]TJ/F56 8.9664 Tf 3.584 0 Td [(,)]TJ/F36 8.9664 Tf 6.193 0 Td [(h)]TJ/F56 8.9664 Tf 3.583 0 Td [(S.Address,)-441(S.Name)]TJ/F36 8.9664 Tf 71.44 0 Td [(i)]TJ/F56 8.9664 Tf 3.584 0 Td [(\051)]TJ/F36 8.9664 Tf 2.986 0 Td [(g)]TJ/F56 8.9664 Tf 4.608 0 Td [(;)-479(and)]TJ -225.349 -10.46 Td [(four)-209(corresponding)-209(to)-209(measuring)-209(jaccard)-209(similarity)-209(between)-209(the)-209(same)]TJ 0 -10.461 Td [(column)-277(combinations.)-391(N)1(ote)-277(that)-277(for)-277(certain)-277(similarity)-277(functions,)-283(the)]TJ 0 -10.461 Td [(order)-360(of)-359(the)-360(attrib)20(utes)-360(may)-359(not)-360(be)-360(important,)-387(or)-359(that)-360(the)15(y)-360(may)-359(not)]TJ 0 -10.461 Td [(be)-363(applied)-364(on)-363(certain)-364(combinations.)-650(In)-363(such)-364(cases,)-392(the)-363(number)-363(of)]TJ 0 -10.46 Td [(rele)25(v)25(ant)-373(combinations)-373(w)10(ould)-373(be)-373(less.)-678(In)-373(the)-373(rest)-373(of)-373(the)-373(paper)40(,)-403(we)]TJ 0 -10.461 Td [(assume)-395(that)-396(all)-395(rele)25(v)25(ant)-395(combinations)-395(of)-396(similarity)-395(functions)-395(with)]TJ 0 -10.461 Td [(column)-272(sequences)-273(are)-272(gi)25(v)15(en.)-378(If)-272(not,)-278(we)-273(can)-272(easily)-273(de\002ne)-272(a)-273(macro)-272(to)]TJ 0 -10.461 Td [(generate)-250(all)-250(possible)-250(combinations.)]TJ 8.967 -10.461 Td [(Let)-326(there)-327(be)]TJ/F34 8.9664 Tf 47.118 0 Td [(D)]TJ/F56 8.9664 Tf 10.781 0 Td [(such)-326(combinations)]TJ/F34 8.9664 Tf 70.606 0 Td [(f)]TJ/F33 5.9776 Tf 4.473 -0.996 Td [(1)]TJ/F34 8.9664 Tf 4.151 0.996 Td [(;)-171(:)-172(:)-171(:)-171(;)-171(f)]TJ/F35 5.9776 Tf 24.952 -0.996 Td [(D)]TJ/F56 8.9664 Tf 6.659 0.996 Td [(.)-539(Each)]TJ/F34 8.9664 Tf 27.924 0 Td [(f)]TJ/F35 5.9776 Tf 4.473 -0.996 Td [(i)]TJ/F56 8.9664 Tf 6.088 0.996 Td [(\050implic-)]TJ -216.192 -10.46 Td [(itly\051)-271(associates)-272(a)-271(similarity)-271(function)]TJ/F34 8.9664 Tf 131.21 0 Td [(g)]TJ/F35 5.9776 Tf 4.395 -0.997 Td [(j)]TJ/F56 8.9664 Tf 6.335 0.997 Td [(with)-271(a)-272(column)-271(sequence)]TJ/F34 8.9664 Tf 89.416 0 Td [(A)]TJ/F35 5.9776 Tf 6.91 -1.063 Td [(k)]TJ/F56 8.9664 Tf 4.574 1.063 Td [(.)]TJ -242.84 -10.461 Td [(A)-256(similarity)-256(join)-257(is)-256(written)-256(as)-256(a)-256(conjunction)-257(of)]TJ/F34 8.9664 Tf 168.118 0 Td [(f)]TJ/F35 5.9776 Tf 4.473 -0.996 Td [(i)]TJ/F34 8.9664 Tf 5.828 0.996 Td [(>)-297(\013)]TJ/F35 5.9776 Tf 15.74 -0.996 Td [(i)]TJ/F56 8.9664 Tf 3.161 0.996 Td [(.)-329(Henceforth,)]TJ -197.32 -10.461 Td [(we)-314(loosely)-314(refer)-314(to)-314(each)]TJ/F34 8.9664 Tf 90.76 0 Td [(f)]TJ/F35 5.9776 Tf 4.473 -0.996 Td [(i)]TJ/F56 8.9664 Tf 3.162 0.996 Td [(,)-330(denoting)-314(a)]TJ/F34 8.9664 Tf 46.197 0 Td [(g)]TJ/F35 5.9776 Tf 4.394 -0.996 Td [(j)]TJ/F56 8.9664 Tf 6.719 0.996 Td [(and)]TJ/F34 8.9664 Tf 15.763 0 Td [(A)]TJ/F35 5.9776 Tf 6.911 -1.063 Td [(k)]TJ/F56 8.9664 Tf 7.389 1.063 Td [(association,)-330(as)-314(a)]TJ -185.768 -10.461 Td [(similarity)-250(function.)]TJ/F55 8.9664 Tf 266.003 643.089 Td [(Bounded)-342(SJU)-342(T)74(r)18(ees)]TJ/F56 8.9664 Tf 77.046 0 Td [(:)-494(Let)]TJ/F34 8.9664 Tf 21.939 0 Td [(d)]TJ/F36 8.9664 Tf 8.904 0 Td [(\024)]TJ/F34 8.9664 Tf 11.297 0 Td [(D)]TJ/F56 8.9664 Tf 10.922 0 Td [(and)]TJ/F34 8.9664 Tf 16.013 0 Td [(K)]TJ/F36 8.9664 Tf 12.572 0 Td [(\025)]TJ/F31 8.9664 Tf 11.297 0 Td [(1)]TJ/F56 8.9664 Tf 7.673 0 Td [(be)-342(tw)10(o)-342(inte)15(gers.)]TJ -186.63 -10.461 Td [(W)80(e)-369(study)-369(a)-369(restricted)-368(class)-369(where)-369(each)-369(operator)-369(tree)-369(is)-369(allo)25(we)1(d)-369(to)]TJ 0 -10.461 Td [(be)-303(a)-302(union)-303(of)-302(at)-303(most)]TJ/F34 8.9664 Tf 80.531 0 Td [(K)]TJ/F56 8.9664 Tf 11.155 0 Td [(similarity)-303(joi)1(ns,)-316(and)-303(where)-302(each)-303(similarity)]TJ -91.686 -10.461 Td [(join)-333(may)-333(ha)20(v)15(e)-334(at)-333(most)]TJ/F34 8.9664 Tf 84.856 0 Td [(d)]TJ/F56 8.9664 Tf 7.762 0 Td [(similarity)-333(function)-333(predicates.)-560(W)80(e)-333(denote)]TJ -92.618 -10.46 Td [(this)-364(restricted)-365(clas)1(s)-365(of)-364(operator)-364(trees)-365(by)]TJ/F34 8.9664 Tf 149.854 0 Td [(S)-57(J)-95(U)]TJ/F31 8.9664 Tf 19.308 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(d;)-171(K)]TJ/F31 8.9664 Tf 17.312 0 Td [(\051)]TJ/F56 8.9664 Tf 3.584 0 Td [(.)-653(Con\002guring)]TJ -193.642 -10.461 Td [(a)-318(similarity)-318(join)-319(in)]TJ/F34 8.9664 Tf 70.698 0 Td [(S)-57(J)-95(U)]TJ/F31 8.9664 Tf 19.308 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(d;)]TJ/F31 8.9664 Tf 8.871 0 Td [(1\051)]TJ/F56 8.9664 Tf 11.044 0 Td [(requires)-318(us)-318(to)-319(\050i\051)-318(choose)]TJ/F34 8.9664 Tf 91.458 0 Td [(d)]TJ/F56 8.9664 Tf 7.628 0 Td [(out)-318(of)]TJ/F34 8.9664 Tf 24.635 0 Td [(D)]TJ/F56 8.9664 Tf -237.226 -10.461 Td [(similarity)-250(functions)-250(and)-249(\050ii\051)-250(the)-250(corresponding)-250(thresholds.)-310(And,)-249(con-)]TJ 0 -10.461 Td [(\002guring)-237(an)-237(operator)-236(tree)-237(in)]TJ/F34 8.9664 Tf 97.768 0 Td [(S)-57(J)-95(U)]TJ/F31 8.9664 Tf 19.308 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(d;)-171(K)]TJ/F31 8.9664 Tf 17.313 0 Td [(\051)]TJ/F56 8.9664 Tf 5.706 0 Td [(no)25(w)-237(requires)-237(us)-236(to)-237(con\002gure)]TJ -143.679 -10.46 Td [(the)-318(union)-319(of)]TJ/F34 8.9664 Tf 47.418 0 Td [(K)]TJ/F56 8.9664 Tf 11.297 0 Td [(such)-318(similarity)-319(joins.)-515(The)-319(number)-318(of)-319(these)-318(choices)]TJ -58.715 -10.461 Td [(de\002nes)-250(the)-250(SJU)-250(operator)-250(tree)-250(space.)]TJ 8.966 -10.461 Td [(W)80(e)-315(consider)-315(bounded)-315(operator)-314(trees)-315(for)-315(the)-315(follo)25(wing)-315(three)-314(intu-)]TJ -8.966 -10.461 Td [(iti)25(v)15(e)-356(reasons.)-627(First,)-382(the)-356(restriction)-356(is)-355(a)-356(mechanism)-356(to)-356(a)20(v)20(oid)-355(\223o)15(v)15(er)20(-)]TJ 0 -10.461 Td [(\002tting.)70(\224)-303(A)-227(v)15(ery)-228(lar)18(ge)-228(operator)-228(tree)-227(might)-228(be)-228(able)-228(to)-228(identify)-227(precisely)]TJ 0 -10.46 Td [(all)-369(the)-369(matching)-370(pairs)-369(in)-369(a)-369(gi)25(v)15(en)-369(set)-369(of)-370(e)15(xamples)-369(quite)-369(well)-369(b)20(ut)-369(it)]TJ 0 -10.461 Td [(may)-312(not)-312(generalize)-312(well)-312(to)-313(the)-312(remaining)-312(pairs)-312(of)-312(tuples)-312(in)]TJ/F34 8.9664 Tf 217.553 0 Td [(R)]TJ/F36 8.9664 Tf 9.508 0 Td [(\002)]TJ/F34 8.9664 Tf 9.639 0 Td [(S)]TJ/F56 8.9664 Tf 6.139 0 Td [(.)]TJ -242.839 -10.461 Td [(Second,)-240(programmers)-238(are)-238(able)-238(to)-238(easily)-238(interpret)-238(and)-238(modify)-238(smaller)]TJ 0 -10.461 Td [(operator)-349(trees.)-606(Third,)-374(smaller)-348(operator)-349(trees)-349(are)-349(usually)-349(more)-348(ef)25(\002-)]TJ 0 -10.46 Td [(ciently)-286(e)15(x)15(ecutable.)-418(Speci\002cally)65(,)-295(gi)25(v)15(en)-286(tw)10(o)-286(operator)-286(trees)-286(where)-286(one)]TJ 0 -10.461 Td [(is)-224(a)-225(sub-tree)-224(of)-225(the)-224(second,)-230(then)-224(the)-224(\002rst)-225(smaller)-224(operator)-225(tree)-224(is)-224(often)]TJ 0 -10.461 Td [(more)-250(ef)25(\002ciently)-250(e)15(x)15(ecutable.)]TJ/F57 8.9664 Tf 9.963 -17.96 Td [(De\002nition)-250(4.)]TJ/F56 8.9664 Tf 49.314 0 Td [(\050)]TJ/F57 8.9664 Tf 2.986 0 Td [(Bounded)-195(oper)15(ator)-195(tr)37(ee)-194(design)-195(pr)45(oblem)]TJ/F56 8.9664 Tf 136.614 0 Td [(\051)-195(Gi)25(v)15(en)]TJ/F34 8.9664 Tf 28.035 0 Td [(K)]TJ/F36 8.9664 Tf 11.002 0 Td [(\025)]TJ/F31 8.9664 Tf -237.914 -10.46 Td [(1)]TJ/F56 8.9664 Tf 4.608 0 Td [(,)]TJ/F34 8.9664 Tf 5.778 0 Td [(d)]TJ/F36 8.9664 Tf 9.305 0 Td [(\024)]TJ/F34 8.9664 Tf 11.699 0 Td [(D)]TJ/F56 8.9664 Tf 7.855 0 Td [(,)-394(and)]TJ/F31 8.9664 Tf 22.003 0 Td [(0)]TJ/F36 8.9664 Tf 9.138 0 Td [(\024)]TJ/F34 8.9664 Tf 11.699 0 Td [(\014)-557(<)]TJ/F31 8.9664 Tf 21.891 0 Td [(1)]TJ/F56 8.9664 Tf 4.607 0 Td [(,)-394(the)-366(goal)-365(in)-366(the)-365(operator)-366(tree)-365(design)]TJ -108.583 -10.461 Td [(problem)-372(is)-372(to)-372(\002nd)-372(a)]TJ/F34 8.9664 Tf 77.452 0 Td [(\014)]TJ/F56 8.9664 Tf 5.661 0 Td [(-ne)15(g)-372(operator)-372(tree)]TJ/F34 8.9664 Tf 69.122 0 Td [(T)]TJ/F37 5.9776 Tf 6.656 3.809 Td [(\003)]TJ/F31 8.9664 Tf 4.317 -3.809 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(R)-7(;)-171(S)]TJ/F31 8.9664 Tf 17.27 0 Td [(\051)]TJ/F56 8.9664 Tf 6.92 0 Td [(in)]TJ/F34 8.9664 Tf 10.311 0 Td [(S)-57(J)-95(U)]TJ/F31 8.9664 Tf 19.308 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(d;)-171(K)]TJ/F31 8.9664 Tf 17.312 0 Td [(\051)]TJ/F56 8.9664 Tf -241.497 -10.461 Td [(with)-250(the)-250(maximum)-250(quality)65(.)]TJ 0 -17.959 Td [(W)80(e)-311(only)-310(focus)-311(on)-311(the)-310(bounded)-311(operator)-311(tree)-310(design)-311(problem)-311(in)-310(this)]TJ 0 -10.461 Td [(paper)55(.)-488(Hence,)-324(we)-309(loosely)-309(say)-309(operator)-310(tree)-309(design)-309(problem)-309(to)-309(refer)]TJ 0 -10.461 Td [(to)-250(the)-250(bounded)-250(v)25(ariant.)]TJ/F55 11.9552 Tf 0 -18.098 Td [(3.3)-1000(Monotonicity)]TJ/F56 8.9664 Tf 8.967 -12.951 Td [(W)80(e)-404(say)-405(that)-404(the)-405(record)-404(matching)-405(problem)-404(between)]TJ/F34 8.9664 Tf 193.131 0 Td [(R)]TJ/F56 8.9664 Tf 10.663 0 Td [(and)]TJ/F34 8.9664 Tf 16.574 0 Td [(S)]TJ/F56 8.9664 Tf 9.766 0 Td [(is)]TJ/F57 8.9664 Tf -239.101 -10.461 Td [(monotonic)]TJ/F56 8.9664 Tf 40.112 0 Td [(with)-252(respect)-251(to)-252(a)-251(set)]TJ/F36 8.9664 Tf 73.533 0 Td [(f)]TJ/F34 8.9664 Tf 4.608 0 Td [(f)]TJ/F33 5.9776 Tf 4.473 -0.996 Td [(1)]TJ/F34 8.9664 Tf 4.151 0.996 Td [(;)-171(:)-172(:)-171(:)-171(;)-171(f)]TJ/F35 5.9776 Tf 24.951 -0.996 Td [(D)]TJ/F36 8.9664 Tf 6.659 0.996 Td [(g)]TJ/F56 8.9664 Tf 6.864 0 Td [(of)-252(similarity)-251(functions)]TJ -165.351 -10.461 Td [(if,)-313(for)-301(an)15(y)-301(matching)-300(pair)]TJ/F31 8.9664 Tf 91.896 0 Td [(\050)]TJ/F34 8.9664 Tf 3.583 0 Td [(r)]TJ/F33 5.9776 Tf 4.158 -0.996 Td [(1)]TJ/F34 8.9664 Tf 4.152 0.996 Td [(;)-171(s)]TJ/F33 5.9776 Tf 8.388 -0.996 Td [(1)]TJ/F31 8.9664 Tf 4.151 0.996 Td [(\051)]TJ/F56 8.9664 Tf 6.28 0 Td [(and)-301(non-matching)-300(pair)]TJ/F31 8.9664 Tf 84.785 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(r)]TJ/F33 5.9776 Tf 4.158 -0.996 Td [(0)]TJ/F34 8.9664 Tf 4.151 0.996 Td [(;)-171(s)]TJ/F33 5.9776 Tf 8.389 -0.996 Td [(0)]TJ/F31 8.9664 Tf 4.151 0.996 Td [(\051)]TJ/F56 8.9664 Tf 6.279 0 Td [(in)]TJ/F34 8.9664 Tf -238.105 -10.46 Td [(R)]TJ/F36 8.9664 Tf 9.084 0 Td [(\002)]TJ/F34 8.9664 Tf 9.215 0 Td [(S)]TJ/F56 8.9664 Tf 6.139 0 Td [(,)-250(there)-250(e)15(xists)-250(an)]TJ/F34 8.9664 Tf 57.887 0 Td [(f)]TJ/F35 5.9776 Tf 4.473 -0.997 Td [(i)]TJ/F56 8.9664 Tf 5.403 0.997 Td [(such)-250(that)]TJ/F34 8.9664 Tf 34.368 0 Td [(f)]TJ/F35 5.9776 Tf 4.472 -0.997 Td [(i)]TJ/F31 8.9664 Tf 3.162 0.997 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(r)]TJ/F33 5.9776 Tf 4.158 -0.997 Td [(1)]TJ/F34 8.9664 Tf 4.151 0.997 Td [(;)-171(s)]TJ/F33 5.9776 Tf 8.389 -0.997 Td [(1)]TJ/F31 8.9664 Tf 4.151 0.997 Td [(\051)]TJ/F34 8.9664 Tf 6.143 0 Td [(>)-285(f)]TJ/F35 5.9776 Tf 14.2 -0.997 Td [(i)]TJ/F31 8.9664 Tf 3.162 0.997 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(r)]TJ/F33 5.9776 Tf 4.158 -0.997 Td [(0)]TJ/F34 8.9664 Tf 4.151 0.997 Td [(;)-171(s)]TJ/F33 5.9776 Tf 8.389 -0.997 Td [(0)]TJ/F31 8.9664 Tf 4.151 0.997 Td [(\051)]TJ/F56 8.9664 Tf 3.583 0 Td [(.)]TJ -201.19 -10.461 Td [(Note)-263(that)-263(the)-263(monotonicity)-263(property)-263(only)-263(requires)-262(that)-263(an)15(y)-263(pair)-263(of)]TJ -8.967 -10.461 Td [(matching)-236(records)-235(ha)20(v)15(e)-236(a)-235(higher)-236(similarity)-236(v)25(alue)-235(than)-236(a)-235(non-matching)]TJ 0 -10.461 Td [(pair)-233(on)-234(at)-233(least)-233(one)-234(similarity)-233(function.)-304(W)80(e)-234(empirically)-233(observ)15(ed)-233(that)]TJ 0 -10.46 Td [(this)-317(property)-317(is)-317(satis\002ed)-317(in)-317(most)-317(record)-317(matching)-317(scenarios.)-510(Let)-317(us)]TJ 0 -10.461 Td [(consider)-308(all)-307(real)-308(e)15(xample)-308(sets)-307(from)-308(the)-307(RIDDLE)-308(repository)-308([8])-307(and)]TJ 0 -10.461 Td [(proprietary)-230(data)-230(that)-229(we)-230(used)-230(to)-230(e)25(v)25(aluate)-229(our)-230(techniques)-230(in)-230(Section)-229(7.)]TJ 0 -10.461 Td [(Ev)15(en)-365(with)-365(small)]TJ/F34 8.9664 Tf 63.482 0 Td [(d)]TJ/F56 8.9664 Tf 8.047 0 Td [(v)25(alues,)-394(more)-365(than)]TJ/F31 8.9664 Tf 68.868 0 Td [(99%)]TJ/F56 8.9664 Tf 20.168 0 Td [(of)-365(the)-365(matching)-365(record)]TJ -160.565 -10.461 Td [(pairs)-254(can)-255(be)-254(co)15(v)15(ered)-255(by)-254(an)-255(operator)-254(tree)-255(in)-254(the)-255(SJU)-254(class)-254(if)-255(we)-254(allo)25(w)]TJ 0 -10.46 Td [(a)-354(small)-354(number)-354(\050less)-354(than)]TJ/F31 8.9664 Tf 98.553 0 Td [(5%)]TJ/F56 8.9664 Tf 12.288 0 Td [(\051)-354(of)-354(gi)25(v)15(en)-354(non-matching)-354(pairs)-354(in)-355(t)1(he)]TJ -110.841 -10.461 Td [(result.)-421(These)-288(observ)25(ations)-287(pro)15(vide)-287(e)25(vidence)-287(that)-287(record)-287(matching)-287(is)]TJ 0 -10.461 Td [(monotonic)-250(with)-250(respect)-250(to)-250(a)-250(set)-250(of)-250(common)-250(similarity)-250(functions.)]TJ/F57 8.9664 Tf 0 -20.921 Td [(Observation)]TJ/F56 8.9664 Tf 44.329 0 Td [(:)-404(If)-298(t)1(he)-298(record)-297(matching)-297(problem)-297(is)-297(monotonic)-297(with)-297(re-)]TJ -44.329 -10.461 Td [(spect)-286(to)]TJ/F36 8.9664 Tf 30.524 0 Td [(f)]TJ/F34 8.9664 Tf 4.608 0 Td [(f)]TJ/F33 5.9776 Tf 4.473 -0.996 Td [(1)]TJ/F34 8.9664 Tf 4.151 0.996 Td [(;)-171(:)-172(:)-171(:)-171(;)-171(f)]TJ/F35 5.9776 Tf 24.951 -0.996 Td [(D)]TJ/F36 8.9664 Tf 6.659 0.996 Td [(g)]TJ/F56 8.9664 Tf 4.608 0 Td [(,)-295(then)-285(there)-286(e)15(xists)-286(a)1(n)-286(SJU)-286(operator)-285(tree)-286(which)]TJ -79.974 -10.461 Td [(correctly)-200(identi\002es)-200(all)-200(the)-200(matching)-200(records,)-210(and)-200(only)-200(those,)-210(in)]TJ/F34 8.9664 Tf 221.815 0 Td [(R)]TJ/F36 8.9664 Tf 7.377 0 Td [(\002)]TJ/F34 8.9664 Tf 7.508 0 Td [(S)]TJ/F56 8.9664 Tf 6.139 0 Td [(.)]TJ/F55 11.9552 Tf -242.839 -19.209 Td [(4.)-1000(ALGORITHMS)]TJ/F56 8.9664 Tf 8.966 -12.951 Td [(W)80(e)-426(no)25(w)-426(describe)-426(our)-425(algorithm)-426(for)-426(identifying)-426(the)-426(best)-425(record)]TJ -8.966 -10.461 Td [(matching)-260(operator)-261(tree.)-341(Since)-261(the)-260(problem)-261(\050as)-260(will)-261(be)-260(sho)25(wn)-261(in)-260(Sec-)]TJ 0 -10.461 Td [(tion)-256(4.3\051)-255(is)-256(NP-hard,)-257(we)-255(de)25(v)15(elop)-256(approximation)-255(algorithms.)-327(W)80(e)-255(\002rst)]TJ 0 -10.46 Td [(describe)-230(an)-230(algorithm)-230(for)-230(the)-230(restricted)-230(v)15(ersion)-230(of)-229(the)-230(problem)-230(where)]TJ 0 -10.461 Td [(the)-256(operator)-257(tre)1(e)-257(can)-256(only)-256(contain)-257(one)-256(similarity)-256(join.)-329(W)80(e)-256(reduce)-256(the)]TJ 0 -10.461 Td [(restricted)-263(operator)-263(tree)-263(design)-263(problem)-263(when)]TJ/F34 8.9664 Tf 163.546 0 Td [(K)]TJ/F31 8.9664 Tf 11.224 0 Td [(=)-310(1)]TJ/F56 8.9664 Tf 16.916 0 Td [(to)-263(that)-263(of)-263(iden-)]TJ -191.686 -10.461 Td [(tifying)-232(the)-231(\223best\224)]TJ/F34 8.9664 Tf 63.506 0 Td [(d)]TJ/F56 8.9664 Tf 4.774 0 Td [(-dimensional)-232(h)5(yper)20(-rectangle)-231(in)-232(a)]TJ/F34 8.9664 Tf 122.124 0 Td [(D)]TJ/F56 8.9664 Tf 7.855 0 Td [(-dimensional)]TJ -198.259 -10.461 Td [(\223similarity)-344(space\224)-344(induced)-344(by)-344(the)-344(similarity)-344(v)25(alues)-344(between)-344(record)]TJ 0 -10.46 Td [(pairs;)-214(each)-197(h)5(yper)20(-re)1(ctangle)-197(uniquely)-196(determines)-196(an)-197(operator)-196(tree)-196(with)]TJ 0 -10.461 Td [(one)-381(similarity)-381(join)-381(\050Se)1(ction)-381(4.1\051.)-703(W)80(e)-381(then)-381(describe)-381(our)-380(algorithm)]TJ 0 -10.461 Td [(\050Section)-314(4.2\051.)-501(W)80(e)-314(b)20(uild)-314(upon)-314(t)1(his)-314(algorithm)-314(to)-314(describe)-314(an)-313(approx-)]TJ 0 -10.461 Td [(imation)-370(algorithm)-370(when)-369(the)-370(operator)-370(tree)-370(is)-369(allo)25(wed)-370(to)-370(contain)]TJ/F34 8.9664 Tf 236.639 0 Td [(K)]TJ ET Q 1 0 0 1 295.992 36 cm 0 Tr /QQAPFce02551e 12 Tf 0 0 0 rg 100 Tz 0 Ts 0 Tw 0 Tc BT 1 0 0 1 0 0 Tm (330)Tj ET 1 0 0 1 0 0 cm 1 0 0 1 -295.992 -36 cm endstream endobj 53 0 obj << /Type /Page /Resources 52 0 R /MediaBox [ 0 0 612 792 ] /Parent 13 0 R /Contents [ 54 0 R ] >> endobj 52 0 obj << /Font << /F57 11 0 R /F56 10 0 R /F34 12 0 R /F33 51 0 R /F31 18 0 R /F35 49 0 R /F38 48 0 R /F36 8 0 R /F55 9 0 R /F37 55 0 R /QQAPFce02551e 232 0 R >> /ProcSet [ /PDF /Text ] >> endobj 60 0 obj << /Length 27838 /LC /QQAP >> stream q BT /F56 8.9664 Tf 53.798 728.239 Td [(similarity)-202(joins)-201(\050Section)-202(4.3\051.)-294(The)-201(algorithm)-202(for)-201(the)-202(restricted)-201(v)15(ersion)]TJ 0 -10.461 Td [(with)-286(one)-287(similarity)-286(join)-287(is)-286(one)-286(of)-287(our)-286(main)-287(contrib)20(uti)1(ons,)-296(and)-286(forms)]TJ 0 -10.46 Td [(the)-244(basis)-243(for)-244(applying)-243(kno)25(wn)-244(set)-243(co)15(v)15(erage)-244(approximation)-243(techniques)]TJ 0 -10.461 Td [(to)-250(the)-250(more)-250(general)-250(problem.)]TJ/F55 11.9552 Tf 0 -19.269 Td [(4.1)-1000(Reduction)-128(to)-129(Maximum)-128(Rectangle)-129(Pr)18(oblem)]TJ/F56 8.9664 Tf 8.967 -12.952 Td [(W)80(e)-309(de\002ne)-308(the)-309(maximum)-308(h)5(yper)20(-rectangle)-309(problem)-308(and)-309(then)-308(sho)25(w)]TJ -8.967 -10.46 Td [(its)-308(equi)25(v)25(alence)-308(with)-308(the)-308(operator)-308(tree)-308(design)-308(problem)-308(when)-308(it)-308(is)-308(re-)]TJ 0 -10.461 Td [(stricted)-255(to)-256(ha)20(v)15(e)-255(only)-256(one)-255(similarity)-256(join)-255(operator)55(.)-327(Recall)-255(that)-255(each)]TJ/F34 8.9664 Tf 237.447 0 Td [(f)]TJ/F35 5.9776 Tf 4.472 -0.997 Td [(i)]TJ/F56 8.9664 Tf -241.919 -9.464 Td [(associates)-250(a)-250(similarity)-250(function)]TJ/F34 8.9664 Tf 113.064 0 Td [(g)]TJ/F35 5.9776 Tf 4.395 -0.996 Td [(j)]TJ/F56 8.9664 Tf 6.144 0.996 Td [(with)-250(a)-250(column)-250(sequence)]TJ/F34 8.9664 Tf 88.65 0 Td [(A)]TJ/F35 5.9776 Tf 6.91 -1.063 Td [(k)]TJ/F56 8.9664 Tf 4.573 1.063 Td [(.)]TJ/F57 8.9664 Tf -213.773 -18.866 Td [(De\002nition)-250(5.)-500(Similarity)-674(Space)]TJ/F56 8.9664 Tf 112.142 0 Td [(:)-1158(Consider)-674(the)]TJ/F34 8.9664 Tf 68.299 0 Td [(D)]TJ/F56 8.9664 Tf 7.855 0 Td [(-dimensional)]TJ -198.259 -10.461 Td [(space)]TJ/F31 8.9664 Tf 21.786 0 Td [([)]TJ/F34 8.9664 Tf 2.56 0 Td [(X)]TJ/F33 5.9776 Tf 7.612 -0.996 Td [(1)]TJ/F34 8.9664 Tf 4.151 0.996 Td [(;)-171(:)-172(:)-171(:)-171(;)-171(X)]TJ/F35 5.9776 Tf 28.09 -0.996 Td [(D)]TJ/F31 8.9664 Tf 6.659 0.996 Td [(])]TJ/F56 8.9664 Tf 4.432 0 Td [(where)-209(each)-208(dimension)]TJ/F34 8.9664 Tf 81.308 0 Td [(X)]TJ/F35 5.9776 Tf 7.612 -0.996 Td [(i)]TJ/F56 8.9664 Tf 5.033 0.996 Td [(corresponds)-209(to)-208(a)-209(sim-)]TJ -169.243 -10.461 Td [(ilarity)-235(v)25(alue)-235(based)-235(on)]TJ/F34 8.9664 Tf 78.424 0 Td [(f)]TJ/F35 5.9776 Tf 4.473 -0.996 Td [(i)]TJ/F56 8.9664 Tf 5.267 0.996 Td [(between)-235(record)-235(pairs)-235(in)]TJ/F34 8.9664 Tf 85.606 0 Td [(R)]TJ/F36 8.9664 Tf 8.567 0 Td [(\002)]TJ/F34 8.9664 Tf 8.699 0 Td [(S)]TJ/F56 8.9664 Tf 6.14 0 Td [(.)-305(Each)-235(record)]TJ -197.176 -10.461 Td [(pair)]TJ/F31 8.9664 Tf 17.217 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(r)29(;)-172(s)]TJ/F31 8.9664 Tf 12.29 0 Td [(\051)]TJ/F36 8.9664 Tf 8.109 0 Td [(2)]TJ/F31 8.9664 Tf 10.668 0 Td [(\001)]TJ/F33 5.9776 Tf 7.679 3.809 Td [(+)]TJ/F36 8.9664 Tf 8.922 -3.809 Td [([)]TJ/F31 8.9664 Tf 8.978 0 Td [(\001)]TJ/F37 5.9776 Tf 7.679 3.809 Td [(\000)]TJ/F56 8.9664 Tf 9.529 -3.809 Td [(maps)-365(to)-365(a)-365(point,)]TJ/F31 8.9664 Tf 63.914 0 Td [([)]TJ/F34 8.9664 Tf 2.56 0 Td [(f)]TJ/F33 5.9776 Tf 4.473 -0.996 Td [(1)]TJ/F31 8.9664 Tf 4.151 0.996 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(r)29(;)-172(s)]TJ/F31 8.9664 Tf 12.29 0 Td [(\051)]TJ/F34 8.9664 Tf 3.584 0 Td [(;)-171(:)-172(:)-171(:)-171(;)-171(f)]TJ/F35 5.9776 Tf 24.952 -0.996 Td [(D)]TJ/F31 8.9664 Tf 6.659 0.996 Td [(\050)]TJ/F34 8.9664 Tf 3.583 0 Td [(r)28(;)-171(s)]TJ/F31 8.9664 Tf 12.291 0 Td [(\051])]TJ/F56 8.9664 Tf 6.144 0 Td [(,)]TJ -242.84 -10.46 Td [(in)-301(the)-300(similarity)-301(space.)-461(W)80(e)-301(tag)-300(the)-301(mapped)-300(points)-301(corresponding)-300(to)]TJ 0 -10.461 Td [(record)-275(pairs)-276(in)]TJ/F31 8.9664 Tf 54.713 0 Td [(\001)]TJ/F33 5.9776 Tf 7.679 3.809 Td [(+)]TJ/F56 8.9664 Tf 8.557 -3.809 Td [(as)]TJ/F57 8.9664 Tf 9.938 0 Td [(positive)-275(\050)]TJ/F31 8.9664 Tf 33.348 0 Td [(+)]TJ/F57 8.9664 Tf 7.168 0 Td [(\051)]TJ/F56 8.9664 Tf 5.454 0 Td [(and)-275(those)-276(in)]TJ/F31 8.9664 Tf 46.257 0 Td [(\001)]TJ/F37 5.9776 Tf 7.68 3.809 Td [(\000)]TJ/F56 8.9664 Tf 8.723 -3.809 Td [(as)]TJ/F57 8.9664 Tf 9.937 0 Td [(ne)40(gative)-275(\050)]TJ/F36 8.9664 Tf 35.474 0 Td [(\000)]TJ/F57 8.9664 Tf 7.167 0 Td [(\051)]TJ/F56 8.9664 Tf -242.095 -10.461 Td [(points.)-304(F)15(or)-231(ease)-231(of)-231(e)15(xposition,)-234(we)-231(will)-231(refer)-231(to)-231(the)-231(set)-231(of)-231(points)-231(in)-231(the)]TJ 0 -10.461 Td [(similarity)-302(space)-302(corresponding)-302(to)-302(matching)-302(and)-302(non-matching)-302(pairs)]TJ 0 -10.46 Td [(as)]TJ/F31 8.9664 Tf 9.711 0 Td [(\001)]TJ/F33 5.9776 Tf 7.679 3.809 Td [(+)]TJ/F56 8.9664 Tf 8.33 -3.809 Td [(and)]TJ/F31 8.9664 Tf 15.189 0 Td [(\001)]TJ/F37 5.9776 Tf 7.679 3.809 Td [(\000)]TJ/F56 8.9664 Tf 6.255 -3.809 Td [(,)-250(respecti)25(v)15(ely)65(.)]TJ -45.876 -20.884 Td [(Figure)-346(3)-346(illustrates)-346(an)-346(e)15(xample)-347(set)-346(of)-346(mapped)-346(points)-346(along)-346(with)]TJ -8.967 -10.461 Td [(their)-250(positi)25(v)15(e)-250(and)-250(ne)15(g)5(ati)25(v)15(e)-250(tags.)]TJ/F57 8.9664 Tf 9.963 -18.866 Td [(De\002nition)-250(6.)]TJ/F56 8.9664 Tf 49.315 0 Td [(A)-381(point)]TJ/F34 8.9664 Tf 31.741 0 Td [(p)]TJ/F33 5.9776 Tf 4.626 -0.996 Td [(1)]TJ/F57 8.9664 Tf 7.568 0.996 Td [(dominates)]TJ/F56 8.9664 Tf 40.277 0 Td [(a)-381(point)]TJ/F34 8.9664 Tf 29.25 0 Td [(p)]TJ/F33 5.9776 Tf 4.626 -0.996 Td [(2)]TJ/F56 8.9664 Tf 7.568 0.996 Td [(if)]TJ/F34 8.9664 Tf 8.895 0 Td [(p)]TJ/F33 5.9776 Tf 4.626 -0.996 Td [(1)]TJ/F56 8.9664 Tf 4.151 0.996 Td [(')55(s)-381(v)25(alues)-381(in)]TJ -202.606 -10.461 Td [(all)-365(dimensions)-365(are)-365(greater)-365(or)-366(equal)-365(to)-365(that)-365(of)]TJ/F34 8.9664 Tf 169.905 0 Td [(p)]TJ/F33 5.9776 Tf 4.626 -0.996 Td [(2)]TJ/F56 8.9664 Tf 4.151 0.996 Td [(')55(s,)-394(and)-365(at)-365(least)-365(on)]TJ -178.682 -10.461 Td [(one)-302(dimension)]TJ/F34 8.9664 Tf 55.724 0 Td [(p)]TJ/F33 5.9776 Tf 4.627 -0.996 Td [(1)]TJ/F56 8.9664 Tf 4.151 0.996 Td [(')55(s)-302(v)25(alue)-302(is)-302(greater)-302(than)-301(that)-302(of)]TJ/F34 8.9664 Tf 111.356 0 Td [(p)]TJ/F33 5.9776 Tf 4.626 -0.996 Td [(2)]TJ/F56 8.9664 Tf 4.151 0.996 Td [(.)-466(W)80(e)-302(say)-302(that)]TJ/F34 8.9664 Tf 51.669 0 Td [(p)]TJ/F33 5.9776 Tf 4.626 -0.996 Td [(1)]TJ/F57 8.9664 Tf -240.93 -9.464 Td [(str)45(ongly)-332(dominates)]TJ/F34 8.9664 Tf 71.794 0 Td [(p)]TJ/F33 5.9776 Tf 4.626 -0.997 Td [(2)]TJ/F56 8.9664 Tf 7.124 0.997 Td [(if)]TJ/F34 8.9664 Tf 8.452 0 Td [(p)]TJ/F33 5.9776 Tf 4.626 -0.997 Td [(1)]TJ/F31 8.9664 Tf 4.151 0.997 Td [([)]TJ/F34 8.9664 Tf 2.56 0 Td [(i)]TJ/F31 8.9664 Tf 3.153 0 Td [(])]TJ/F34 8.9664 Tf 6.512 0 Td [(>)-441(p)]TJ/F33 5.9776 Tf 15.745 -0.997 Td [(2)]TJ/F31 8.9664 Tf 4.151 0.997 Td [([)]TJ/F34 8.9664 Tf 2.56 0 Td [(i)]TJ/F31 8.9664 Tf 3.153 0 Td [(])]TJ/F56 8.9664 Tf 2.56 0 Td [(,)]TJ/F31 8.9664 Tf 5.397 0 Td [(1)]TJ/F36 8.9664 Tf 8.56 0 Td [(\024)]TJ/F34 8.9664 Tf 11.119 0 Td [(i)]TJ/F36 8.9664 Tf 7.105 0 Td [(\024)]TJ/F34 8.9664 Tf 11.12 0 Td [(D)]TJ/F56 8.9664 Tf 7.855 0 Td [(.)-555(That)-331(is,)]TJ/F34 8.9664 Tf 38.001 0 Td [(p)]TJ/F33 5.9776 Tf 4.626 -0.997 Td [(1)]TJ/F56 8.9664 Tf 4.151 0.997 Td [(')55(s)]TJ -239.101 -10.461 Td [(v)25(alues)-250(are)-250(strictly)-250(greater)-250(than)-250(that)-250(of)]TJ/F34 8.9664 Tf 135.48 0 Td [(p)]TJ/F33 5.9776 Tf 4.626 -0.996 Td [(2)]TJ/F56 8.9664 Tf 6.393 0.996 Td [(on)-250(each)-250(dimension.)]TJ/F47 8.9664 Tf 91.827 0 Td [(2)]TJ/F56 8.9664 Tf -229.359 -20.884 Td [(F)15(or)-374(reasons)-374(which)-374(will)-374(be)-374(clear)-374(later)40(,)-405(we)-373(require)-374(a)-374(point)-374(which)]TJ -8.967 -10.461 Td [(e)25(v)15(ery)-233(point)-233(in)-233(the)-234(simil)1(arity)-234(space)-233(strongly)-233(dominates.)-304(Since)-233(all)-233(sim-)]TJ 0 -10.46 Td [(ilarity)-298(v)25(alues)-299(are)-298(non-ne)15(g)5(ati)25(v)15(e,)-311(we)-298(use)]TJ ET q 1 0 0 1 195.938 403.481 cm []0 d 0 J 0.379 w 0 0 m 10.901 0 l S Q BT /F36 8.9664 Tf 195.938 396.843 Td [(\000)]TJ/F34 8.9664 Tf 7.167 0 Td [(\017)]TJ/F56 8.9664 Tf 6.41 0 Td [(\050)]TJ/F34 8.9664 Tf 2.986 0 Td [(X)]TJ/F35 5.9776 Tf 7.612 -0.997 Td [(i)]TJ/F31 8.9664 Tf 6.548 0.997 Td [(=)]TJ/F36 8.9664 Tf 10.553 0 Td [(\000)]TJ/F34 8.9664 Tf 7.168 0 Td [(\017)]TJ/F56 8.9664 Tf 3.733 0 Td [(,)]TJ/F31 8.9664 Tf 5.026 0 Td [(1)]TJ/F36 8.9664 Tf 7.994 0 Td [(\024)]TJ/F34 8.9664 Tf 10.554 0 Td [(i)]TJ/F36 8.9664 Tf 6.54 0 Td [(\024)]TJ/F34 8.9664 Tf 10.554 0 Td [(D)]TJ/F56 8.9664 Tf 7.855 0 Td [(,)]TJ -242.84 -10.461 Td [(for)-250(an)-250(arbitrarily)-250(small)]TJ/F34 8.9664 Tf 83.171 0 Td [(\017)-286(>)]TJ/F31 8.9664 Tf 16.021 0 Td [(0)]TJ/F56 8.9664 Tf 4.608 0 Td [(\051)-250(for)-250(this)-250(point.)]TJ/F57 8.9664 Tf -93.837 -18.866 Td [(De\002nition)-250(7.)]TJ/F56 8.9664 Tf 49.315 0 Td [(A)-267(point)]TJ/F34 8.9664 Tf 29.689 0 Td [(p)]TJ/F56 8.9664 Tf 7.017 0 Td [(in)-267(the)-266(similarity)-267(space)-266(de\002nes)-267(the)-267(foll)1(o)25(w-)]TJ -95.984 -10.461 Td [(ing)-323(tw)10(o)-324(h)5(yper)20(-rectangles.)-530(The)]TJ/F57 8.9664 Tf 113.984 0 Td [(lower)-323(r)37(ectangle)]TJ/F34 8.9664 Tf 59.758 0 Td [(l)-17(r)-28(ect)]TJ/F31 8.9664 Tf 18.915 0 Td [(\050)]TJ/F34 8.9664 Tf 3.583 0 Td [(p)]TJ/F31 8.9664 Tf 4.626 0 Td [(\051)]TJ/F56 8.9664 Tf 6.484 0 Td [(of)]TJ/F34 8.9664 Tf 10.369 0 Td [(p)]TJ/F56 8.9664 Tf 7.525 0 Td [(is)-323(the)]TJ -225.244 -10.461 Td [(set)-256(of)-257(points)-256(strongly)-256(dominated)-256(by)]TJ/F34 8.9664 Tf 129.355 0 Td [(p)]TJ/F56 8.9664 Tf 4.626 0 Td [(.)-329(W)80(e)-256(call)-256(this)]TJ/F34 8.9664 Tf 49.716 0 Td [(l)-17(r)-28(ect)]TJ/F31 8.9664 Tf 18.914 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(p)]TJ/F31 8.9664 Tf 4.626 0 Td [(\051)]TJ/F56 8.9664 Tf 5.882 0 Td [(because)]TJ -216.703 -10.461 Td [(it)-373(is)-372(the)-373(set)-373(of)-373(all)-372(points)]TJ/F57 8.9664 Tf 93.635 0 Td [(inside)]TJ/F56 8.9664 Tf 24.762 0 Td [(the)-373(h)5(yper)20(-rectangle)-372(de\002ned)-373(by)-373(the)]TJ -118.397 -10.46 Td [(corners)]TJ ET q 1 0 0 1 83.116 332.311 cm []0 d 0 J 0.379 w 0 0 m 10.901 0 l S Q BT /F36 8.9664 Tf 83.116 325.673 Td [(\000)]TJ/F34 8.9664 Tf 7.168 0 Td [(\017)]TJ/F56 8.9664 Tf 6.663 0 Td [(and)]TJ/F34 8.9664 Tf 15.878 0 Td [(p)]TJ/F56 8.9664 Tf 4.626 0 Td [(.)-540(The)]TJ/F57 8.9664 Tf 23.96 0 Td [(upper)-327(r)37(ectangle)]TJ/F34 8.9664 Tf 60.312 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(p)]TJ/F31 8.9664 Tf 4.626 0 Td [(\051)]TJ/F56 8.9664 Tf 6.514 0 Td [(of)]TJ/F34 8.9664 Tf 10.399 0 Td [(p)]TJ/F56 8.9664 Tf 7.556 0 Td [(is)-327(the)-327(set)-326(of)]TJ -201.923 -10.461 Td [(all)-259(points)-259(strongly)-259(dominating)]TJ/F34 8.9664 Tf 110.425 0 Td [(p)]TJ/F56 8.9664 Tf 4.626 0 Td [(.)]TJ/F34 8.9664 Tf 5.267 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.318 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(p)]TJ/F31 8.9664 Tf 4.626 0 Td [(\051)]TJ/F56 8.9664 Tf 5.907 0 Td [(is)-259(set)-259(of)-259(points)]TJ/F57 8.9664 Tf 54.628 0 Td [(inside)]TJ/F56 8.9664 Tf 23.743 0 Td [(the)]TJ -234.124 -10.461 Td [(h)5(yper)20(-rectangle)-250(de\002ned)-250(by)-250(corners)]TJ/F34 8.9664 Tf 126.757 0 Td [(p)]TJ/F56 8.9664 Tf 6.868 0 Td [(and)]TJ ET q 1 0 0 1 202.612 311.854 cm []0 d 0 J 0.379 w 0 0 m 4.608 0 l S Q BT /F31 8.9664 Tf 202.612 304.751 Td [(1)]TJ/F56 8.9664 Tf 6.849 0 Td [(\050)]TJ/F34 8.9664 Tf 2.986 0 Td [(X)]TJ/F35 5.9776 Tf 7.612 -0.996 Td [(i)]TJ/F31 8.9664 Tf 5.721 0.996 Td [(=)-285(1)]TJ/F56 8.9664 Tf 14.335 0 Td [(,)]TJ/F31 8.9664 Tf 4.483 0 Td [(1)]TJ/F36 8.9664 Tf 7.168 0 Td [(\024)]TJ/F34 8.9664 Tf 9.727 0 Td [(i)]TJ/F36 8.9664 Tf 5.714 0 Td [(\024)]TJ/F34 8.9664 Tf 9.727 0 Td [(D)]TJ/F56 8.9664 Tf 7.855 0 Td [(\051.)]TJ -222.024 -10.461 Td [(Gi)25(v)15(en)-281(a)-282(point)]TJ/F34 8.9664 Tf 51.539 0 Td [(p)]TJ/F56 8.9664 Tf 4.626 0 Td [(,)-289(we)-282(say)-281(that)]TJ/F34 8.9664 Tf 48.259 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050)]TJ/F34 8.9664 Tf 3.583 0 Td [(p)]TJ/F31 8.9664 Tf 4.626 0 Td [(\051)]TJ/F56 8.9664 Tf 6.107 0 Td [(is)]TJ/F34 8.9664 Tf 8.503 0 Td [(d)]TJ/F57 8.9664 Tf 4.775 0 Td [(-dimensional)]TJ/F56 8.9664 Tf 49.345 0 Td [(if)-281(at)-282(least)]TJ/F34 8.9664 Tf -211.649 -10.46 Td [(d)]TJ/F56 8.9664 Tf 8.035 0 Td [(attrib)20(ute)-364(v)25(al)1(ues)-364(of)]TJ/F34 8.9664 Tf 69.638 0 Td [(p)]TJ/F56 8.9664 Tf 7.886 0 Td [(are)-364(non-ne)15(g)5(ati)25(v)15(e,)-392(i.e.,)-391(we)-364(require)-364(at)-363(least)]TJ/F34 8.9664 Tf 154.747 0 Td [(d)]TJ/F56 8.9664 Tf -240.306 -10.461 Td [(h)5(yper)20(-planes)-250(\050)]TJ/F34 8.9664 Tf 51.314 0 Td [(X)]TJ/F35 5.9776 Tf 7.612 -0.997 Td [(i)]TJ/F34 8.9664 Tf 5.722 0.997 Td [(>)-285(p)]TJ/F31 8.9664 Tf 14.353 0 Td [([)]TJ/F34 8.9664 Tf 2.56 0 Td [(i)]TJ/F31 8.9664 Tf 3.154 0 Td [(])]TJ/F56 8.9664 Tf 2.559 0 Td [(\051)-250(to)-250(de\002ne)]TJ/F34 8.9664 Tf 38.6 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(p)]TJ/F31 8.9664 Tf 4.626 0 Td [(\051)]TJ/F56 8.9664 Tf 3.583 0 Td [(.)]TJ -150.019 -10.461 Td [(A)-355(h)5(yper)20(-rectangle)-355(containing)-355(less)-355(than)]TJ/F34 8.9664 Tf 145.178 0 Td [(\014)]TJ/F36 8.9664 Tf 8.426 0 Td [(\001)-308(j)]TJ/F31 8.9664 Tf 7.886 0 Td [(\001)]TJ/F37 5.9776 Tf 7.679 3.809 Td [(\000)]TJ/F36 8.9664 Tf 6.254 -3.809 Td [(j)]TJ/F56 8.9664 Tf 5.744 0 Td [(ne)15(g)5(ati)25(v)15(e)-355(points)]TJ -190.134 -10.461 Td [(is)-366(a)]TJ/F34 8.9664 Tf 16.524 0 Td [(\014)]TJ/F57 8.9664 Tf 5.661 0 Td [(-ne)40(g)-366(r)37(ectangle)]TJ/F56 8.9664 Tf 52.389 0 Td [(.)-658(Lik)10(e)25(wise,)-395(the)]TJ/F57 8.9664 Tf 60.717 0 Td [(co)10(ver)15(a)10(g)10(e)]TJ/F56 8.9664 Tf 35.739 0 Td [(of)-366(a)-366(h)5(yper)20(-rectangle)]TJ/F34 8.9664 Tf -171.03 -10.461 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(p)]TJ/F31 8.9664 Tf 4.626 0 Td [(\051)]TJ/F56 8.9664 Tf 5.785 0 Td [(with)-245(respect)-246(to)-246(a)-245(set)]TJ/F34 8.9664 Tf 73.26 0 Td [(X)]TJ/F56 8.9664 Tf 10.516 0 Td [(of)-245(points)-246(is)-245(the)-246(fraction)-245(of)-246(points)-246(in)]TJ/F34 8.9664 Tf -119.09 -10.46 Td [(X)]TJ/F56 8.9664 Tf 10.556 0 Td [(that)-250(are)-250(inside)]TJ/F34 8.9664 Tf 52.542 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050)]TJ/F34 8.9664 Tf 3.583 0 Td [(p)]TJ/F31 8.9664 Tf 4.626 0 Td [(\051)]TJ/F56 8.9664 Tf 3.584 0 Td [(.)]TJ/F47 8.9664 Tf 142.116 0 Td [(2)]TJ/F56 8.9664 Tf -229.359 -20.884 Td [(W)80(e)-426(often)-426(loosely)-426(use)-426(rectangle)-426(to)-426(also)-426(mean)-426(a)-426(h)5(yper)20(-rectangle)]TJ -8.967 -10.461 Td [(when)-501(the)-501(dimensionality)-501(is)-501(greater)-501(than)]TJ/F31 8.9664 Tf 156.95 0 Td [(2)]TJ/F56 8.9664 Tf 4.607 0 Td [(.)-1063(Figure)-501(3)-501(illustrates)]TJ -161.557 -10.461 Td [(the)-620(lo)25(wer)-620(and)-620(upper)]TJ/F31 8.9664 Tf 86.752 0 Td [(2)]TJ/F56 8.9664 Tf 4.607 0 Td [(-dimensional)-620(rectangles,)]TJ/F34 8.9664 Tf 97.362 0 Td [(l)-17(r)-28(ect)]TJ/F31 8.9664 Tf 18.914 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(P)]TJ/F31 8.9664 Tf 7.164 0 Td [(2\051)]TJ/F56 8.9664 Tf 13.751 0 Td [(and)]TJ/F34 8.9664 Tf -232.134 -10.46 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(P)]TJ/F31 8.9664 Tf 7.163 0 Td [(2\051)]TJ/F56 8.9664 Tf 10.508 0 Td [(respecti)25(v)15(ely)65(.)-335(The)-258(problem)-258(of)-259(designing)-258(\050from)-258(e)15(xamples\051)]TJ -42.574 -10.461 Td [(the)-391(best)]TJ/F34 8.9664 Tf 32.419 0 Td [(\014)]TJ/F56 8.9664 Tf 5.661 0 Td [(-ne)15(g)-391(operator)-392(tree)-391(with)-391(one)-392(simil)1(arity)-392(join)-391(no)25(w)-391(reduces)]TJ -38.08 -10.461 Td [(to)-521(that)-522(of)-521(identifying)-522(a)]TJ/F34 8.9664 Tf 94.606 0 Td [(d)]TJ/F56 8.9664 Tf 4.775 0 Td [(-dimensional)-521(upper)-522(rectangle)-521(with)-522(the)]TJ -99.381 -10.461 Td [(maximum)-328(number)-327(of)-328(positi)25(v)15(e)-327(points)-328(b)20(ut)-327(at)-328(most)]TJ/F34 8.9664 Tf 179.876 0 Td [(\014)]TJ/F36 8.9664 Tf 8.238 0 Td [(\001)-287(j)]TJ/F31 8.9664 Tf 7.697 0 Td [(\001)]TJ/F37 5.9776 Tf 7.679 3.809 Td [(\000)]TJ/F36 8.9664 Tf 6.255 -3.809 Td [(j)]TJ/F56 8.9664 Tf 5.496 0 Td [(ne)15(g)5(ati)25(v)15(e)]TJ -215.241 -10.46 Td [(points.)]TJ/F57 8.9664 Tf 9.963 -20.884 Td [(De\002nition)-250(8.)]TJ/F55 8.9664 Tf 49.315 0 Td [(Maximum)-427(r)18(ectangle)-427(pr)18(oblem)]TJ/F56 8.9664 Tf 114.913 0 Td [(:)-664(Gi)25(v)15(en)-427(an)-427(inte)15(ger)]TJ/F34 8.9664 Tf -174.191 -10.461 Td [(d)]TJ/F36 8.9664 Tf 7.903 0 Td [(\024)]TJ/F34 8.9664 Tf 10.295 0 Td [(D)]TJ/F56 8.9664 Tf 10.395 0 Td [(and)-283(a)-284(constant)]TJ/F31 8.9664 Tf 54.433 0 Td [(0)]TJ/F36 8.9664 Tf 7.736 0 Td [(\024)]TJ/F34 8.9664 Tf 10.295 0 Td [(\014)-401(<)]TJ/F31 8.9664 Tf 19.084 0 Td [(1)]TJ/F56 8.9664 Tf 7.148 0 Td [(and)-283(sets)]TJ/F31 8.9664 Tf 31.477 0 Td [(\001)]TJ/F33 5.9776 Tf 7.679 3.809 Td [(+)]TJ/F56 8.9664 Tf 8.628 -3.809 Td [(and)]TJ/F31 8.9664 Tf 15.488 0 Td [(\001)]TJ/F37 5.9776 Tf 7.679 3.809 Td [(\000)]TJ/F56 8.9664 Tf 8.795 -3.809 Td [(of)-283(positi)25(v)15(e)]TJ -207.035 -10.461 Td [(and)-337(ne)15(g)5(ati)25(v)15(e)-337(points,)-359(respecti)25(v)15(ely)65(,)-359(in)-337(a)]TJ/F34 8.9664 Tf 141.055 0 Td [(D)]TJ/F56 8.9664 Tf 7.855 0 Td [(-dimensional)-337(space,)-359(\002nd)-337(a)]TJ -148.91 -10.46 Td [(point)]TJ ET q 1 0 0 1 74.165 90.336 cm []0 d 0 J 0.379 w 0 0 m 5.913 0 l S Q BT /F34 8.9664 Tf 74.165 85.151 Td [(\013)]TJ/F56 8.9664 Tf 7.846 0 Td [(such)-216(t)1(hat)]TJ/F34 8.9664 Tf 33.749 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050)]TJ ET q 1 0 0 1 140.663 90.336 cm []0 d 0 J 0.379 w 0 0 m 5.913 0 l S Q BT /F34 8.9664 Tf 140.663 85.151 Td [(\013)]TJ/F31 8.9664 Tf 5.913 0 Td [(\051)]TJ/F56 8.9664 Tf 5.516 0 Td [(is)-216(a)]TJ/F34 8.9664 Tf 13.826 0 Td [(d)]TJ/F56 8.9664 Tf 4.775 0 Td [(-dimensional)]TJ/F34 8.9664 Tf 48.755 0 Td [(\014)]TJ/F56 8.9664 Tf 5.661 0 Td [(-ne)15(g)-215(h)5(yper)20(-rectangle)]TJ -171.311 -10.461 Td [(whose)-250(co)15(v)15(erage)-250(with)-250(respect)-250(to)]TJ/F31 8.9664 Tf 114.518 0 Td [(\001)]TJ/F33 5.9776 Tf 7.679 3.809 Td [(+)]TJ/F56 8.9664 Tf 8.33 -3.809 Td [(is)-250(maximum.)]TJ/F47 8.9664 Tf 107.799 0 Td [(2)]TJ ET 1 0 0 1 318.172 623.001 cm q 0.69191 0 0 0.8348 0 0 cm q 1 0 0 1 0 0 cm /Im4 Do Q Q 1 0 0 1 -318.172 -623.001 cm BT /F55 8.9664 Tf 322.915 609.778 Td [(Figur)18(e)-250(3:)-310(Operator)-250(tr)18(ee)-250(and)-250(Hyper)37(-r)18(ectangle)-250(equi)10(v)10(alence)]TJ ET 1 0 0 1 339.769 489.174 cm q 0.88307 0 0 0.74324 0 0 cm q 1 0 0 1 0 0 cm /Im5 Do Q Q 1 0 0 1 -339.769 -489.174 cm BT /F55 8.9664 Tf 367.526 475.951 Td [(Figur)18(e)-250(4:)-310(Best)-250(r)18(ectangle)-250(algorithm)]TJ/F56 8.9664 Tf -47.725 -26.641 Td [(Consider)-255(the)-255(rect)1(angle)]TJ/F34 8.9664 Tf 83.049 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050[)]TJ/F34 8.9664 Tf 6.143 0 Td [(\013)]TJ/F33 5.9776 Tf 5.906 -0.996 Td [(1)]TJ/F34 8.9664 Tf 4.151 0.996 Td [(;)-171(:)-172(:)-171(:)-171(;)-171(\013)]TJ/F35 5.9776 Tf 26.385 -0.996 Td [(D)]TJ/F31 8.9664 Tf 6.659 0.996 Td [(]\051)]TJ/F56 8.9664 Tf 8.428 0 Td [(and)-255(the)-255(operator)-254(tree)]TJ/F34 8.9664 Tf -171.007 -11.584 Td [(T)]TJ/F56 8.9664 Tf 10.412 0 Td [(with)-419(the)-419(similarity)-418(join)-419(predicate)]TJ/F38 8.9664 Tf 126.865 6.725 Td [(V)]TJ/F35 5.9776 Tf 7.68 -2.463 Td [(D)]TJ 0 -7.002 Td [(i)]TJ/F33 5.9776 Tf 2.663 0 Td [(=1)]TJ/F34 8.9664 Tf 11.277 2.74 Td [(f)]TJ/F35 5.9776 Tf 4.473 -0.996 Td [(i)]TJ/F31 8.9664 Tf 3.162 0.996 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(R)-7(:A)]TJ/F35 5.9776 Tf 16.505 -0.996 Td [(i)]TJ/F34 8.9664 Tf 3.162 0.996 Td [(;)-171(S:A)]TJ/F35 5.9776 Tf 19.193 -0.996 Td [(i)]TJ/F31 8.9664 Tf 3.162 0.996 Td [(\051)]TJ/F34 8.9664 Tf 9.025 0 Td [(>)-607(\013)]TJ/F35 5.9776 Tf 18.515 -0.996 Td [(i)]TJ/F56 8.9664 Tf 3.162 0.996 Td [(.)]TJ -242.84 -10.461 Td [(Each)-376(record)-376(pair)-376(in)-376(the)-376(result)-376(of)]TJ/F34 8.9664 Tf 123.687 0 Td [(T)]TJ/F56 8.9664 Tf 10.027 0 Td [(maps)-376(to)-376(a)-376(point)-376(in)-376(the)-376(rectan-)]TJ -133.714 -10.461 Td [(gle.)-537(Figure)-326(3)-326(illustrates)-326(the)-325(equi)25(v)25(alence)-326(of)-326(the)-326(problems)-326(of)-325(\002nding)]TJ 0 -10.461 Td [(the)-322(best)]TJ/F31 8.9664 Tf 31.183 0 Td [(0)]TJ/F56 8.9664 Tf 4.608 0 Td [(-ne)15(g)-322(operator)-323(tree)-322(and)-323(that)-322(of)-322(\002nding)-323(the)-322(best)]TJ/F31 8.9664 Tf 169.809 0 Td [(0)]TJ/F56 8.9664 Tf 4.608 0 Td [(-ne)15(g)-322(\050i.e.,)]TJ/F34 8.9664 Tf -210.208 -10.46 Td [(\014)]TJ/F31 8.9664 Tf 9.746 0 Td [(=)-456(0)]TJ/F56 8.9664 Tf 15.86 0 Td [(\051)-339(h)5(yper)20(-rectangle)-340(in)]TJ/F31 8.9664 Tf 75.13 0 Td [(2)]TJ/F56 8.9664 Tf 7.65 0 Td [(dimensions)-339(when)-340(the)-339(similarity)-339(func-)]TJ -108.386 -10.461 Td [(tions)-295(are)-295(edit)-294(similarity)-295(on)-295(the)-294(Name)-295(column)-295(and)-295(Jaccard)-294(similarity)]TJ 0 -10.461 Td [(on)-225(the)-226(Address)-225(column.)-301(The)-226(\002gure)-225(on)-225(the)-225(left)-226(side)-225(sho)25(ws)-225(an)-225(operator)]TJ 0 -10.461 Td [(tree)]TJ/F34 8.9664 Tf 15.522 0 Td [(T)]TJ/F56 8.9664 Tf 8.737 0 Td [(with)-232(one)-232(similarity)-232(join)-232(while)-232(the)-232(rectangle)-233(on)-232(the)-232(right)-232(sho)25(ws)]TJ -24.259 -10.46 Td [(a)-267(rectangle)-267(whose)-267(bottom)-267(left)-267(corner)-267(is)]TJ/F31 8.9664 Tf 142.75 0 Td [([)]TJ/F34 8.9664 Tf 2.56 0 Td [(\013)]TJ/F33 5.9776 Tf 5.906 -0.997 Td [(1)]TJ/F34 8.9664 Tf 4.151 0.997 Td [(;)-171(\013)]TJ/F33 5.9776 Tf 10.001 -0.997 Td [(2)]TJ/F31 8.9664 Tf 4.152 0.997 Td [(])]TJ/F56 8.9664 Tf 2.559 0 Td [(.)-361(The)-267(rectangle)-267(con-)]TJ -172.079 -10.461 Td [(sists)-338(of)-338(all)-339(the)-338(points)-338(corresponding)-338(to)-338(record)-339(pairs)-338(in)-338(the)-338(result)-338(of)]TJ/F34 8.9664 Tf 0 -10.461 Td [(T)]TJ/F56 8.9664 Tf 6.656 0 Td [(.)-513(The)-318(intuition)-318(e)15(xtends)-318(to)-317(the)-318(case)-318(when)-318(similarity)-318(j)1(oins)-318(are)-318(only)]TJ -6.656 -10.461 Td [(allo)25(wed)-301(to)-301(contain)-301(at)-301(most)]TJ/F34 8.9664 Tf 98.94 0 Td [(d)]TJ/F56 8.9664 Tf 7.474 0 Td [(similarity)-301(functions,)-313(and)-301(is)-301(formalized)]TJ -106.414 -10.461 Td [(belo)25(w)65(.)]TJ 10.187 -14.191 Td [(L)]TJ/F56 7.1731 Tf 5.927 0 Td [(E)-61(M)-63(M)-62(A)]TJ/F56 8.9664 Tf 28.849 0 Td [(1.)]TJ/F57 8.9664 Tf 10.58 0 Td [(The)-260(maximum)-260(hyper)20(-r)37(ectangle)-260(pr)45(oblem)-260(is)-260(equivalent)]TJ -55.543 -10.46 Td [(to)-250(that)-250(of)-250(\002nding)-250(the)-250(best)-250(oper)15(ator)-250(tr)37(ee)-250(with)-250(one)-250(similarity)-250(join.)]TJ/F55 11.9552 Tf 0 -22.071 Td [(4.2)-1000(Algorithm)-250(f)25(or)-250(Maximum)-250(Hyper)37(\255r)18(ectangle)]TJ/F56 8.9664 Tf 8.967 -12.951 Td [(Our)-1009(goal)-1008(here)-1009(is)-1008(to)-1009(identify)]TJ/F31 8.9664 Tf 139.923 0 Td [([)]TJ/F34 8.9664 Tf 2.56 0 Td [(\013)]TJ/F33 5.9776 Tf 5.906 -0.996 Td [(1)]TJ/F34 8.9664 Tf 4.151 0.996 Td [(;)-171(:)-172(:)-171(:)-171(;)-171(\013)]TJ/F35 5.9776 Tf 26.384 -0.996 Td [(D)]TJ/F31 8.9664 Tf 6.659 0.996 Td [(])]TJ/F56 8.9664 Tf 11.603 0 Td [(such)-1009(that)]TJ/F34 8.9664 Tf -206.153 -10.461 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050[)]TJ/F34 8.9664 Tf 6.143 0 Td [(\013)]TJ/F33 5.9776 Tf 5.906 -0.996 Td [(1)]TJ/F34 8.9664 Tf 4.151 0.996 Td [(;)-171(:)-172(:)-171(:)-171(;)-171(\013)]TJ/F35 5.9776 Tf 26.385 -0.996 Td [(D)]TJ/F31 8.9664 Tf 6.659 0.996 Td [(]\051)]TJ/F56 8.9664 Tf 10.949 0 Td [(is)-536(the)-536(best)]TJ/F34 8.9664 Tf 45.799 0 Td [(d)]TJ/F56 8.9664 Tf 4.775 0 Td [(-dimensional)]TJ/F34 8.9664 Tf 51.627 0 Td [(\014)]TJ/F56 8.9664 Tf 5.661 0 Td [(-ne)15(g)-536(rectangle.)]TJ -189.374 -10.461 Td [(Such)-378(a)-378(rectangle)-378(w)10(ould)-378(uniquely)-378(correspond)-378(to)-378(the)-378(sim)1(ilarity)-378(join)]TJ 0 -10.46 Td [(with)-359(predicate)]TJ/F38 8.9664 Tf 55.242 6.724 Td [(V)]TJ/F35 5.9776 Tf 7.679 -9.464 Td [(\013)]TJ/F9 4.9813 Tf 4.809 -1.261 Td [(i)]TJ/F37 5.9776 Tf 3.156 1.261 Td [(\025)]TJ/F33 5.9776 Tf 5.756 0 Td [(0)]TJ/F34 8.9664 Tf 5.687 2.74 Td [(f)]TJ/F35 5.9776 Tf 4.473 -0.997 Td [(i)]TJ/F31 8.9664 Tf 3.162 0.997 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(R)-7(:A)]TJ/F35 5.9776 Tf 16.505 -1.063 Td [(k)]TJ/F34 8.9664 Tf 4.573 1.063 Td [(;)-171(S:A)]TJ/F35 5.9776 Tf 19.194 -1.063 Td [(k)]TJ/F31 8.9664 Tf 4.573 1.063 Td [(\051)]TJ/F34 8.9664 Tf 8.004 0 Td [(>)-493(\013)]TJ/F35 5.9776 Tf 17.493 -0.997 Td [(i)]TJ/F56 8.9664 Tf 3.162 0.997 Td [(.)-637(Recall)-359(that)-359(each)]TJ/F34 8.9664 Tf 70.395 0 Td [(f)]TJ/F35 5.9776 Tf 4.473 -0.997 Td [(i)]TJ/F56 8.9664 Tf -241.92 -9.464 Td [(associates)-293(a)-292(similarity)-293(function)]TJ/F34 8.9664 Tf 114.597 0 Td [(g)]TJ/F35 5.9776 Tf 4.394 -0.996 Td [(j)]TJ/F56 8.9664 Tf 6.527 0.996 Td [(with)-293(a)-292(column)-293(sequence)]TJ/F34 8.9664 Tf 90.182 0 Td [(A)]TJ/F35 5.9776 Tf 6.91 -1.063 Td [(k)]TJ/F56 8.9664 Tf 4.573 1.063 Td [(.)-438(W)80(e)]TJ -227.183 -10.461 Td [(start)-362(by)-363(describing)-362(our)-363(algorithm)-362(for)-362(the)]TJ/F31 8.9664 Tf 152.74 0 Td [(0)]TJ/F57 8.9664 Tf 4.608 0 Td [(-ne)40(g)-362(r)37(ectangle)]TJ/F56 8.9664 Tf 55.607 0 Td [(problem.)]TJ -212.955 -10.461 Td [(W)80(e)-319(then)-318(relax)-319(this)-319(constraint)-318(and)-319(allo)25(w)]TJ/F34 8.9664 Tf 146.061 0 Td [(\014)-468(>)]TJ/F31 8.9664 Tf 20.293 0 Td [(0)]TJ/F56 8.9664 Tf 4.608 0 Td [(.)-516(In)-319(this)-319(sec)1(tion,)-336(we)]TJ -170.962 -10.46 Td [(assume)-255(that)-255(the)-255(numbers)-256(of)-255(e)15(xamples)-255(in)]TJ/F31 8.9664 Tf 145.874 0 Td [(\001)]TJ/F33 5.9776 Tf 7.679 3.809 Td [(+)]TJ/F56 8.9664 Tf 8.376 -3.809 Td [(and)]TJ/F31 8.9664 Tf 15.236 0 Td [(\001)]TJ/F37 5.9776 Tf 7.679 3.809 Td [(\000)]TJ/F56 8.9664 Tf 8.542 -3.809 Td [(can)-255(\002t)-255(in)-255(main)]TJ -193.386 -10.461 Td [(memory)65(.)-409(In)-283(Section)-283(6.1,)-291(we)-283(discuss)-283(techniques)-283(to)-283(handle)-282(v)15(ery)-283(lar)18(ge)]TJ 0 -10.461 Td [(sets)-250(of)-250(e)15(xamples.)]TJ 8.967 -10.461 Td [(W)80(e)-227(adopt)-226(a)-227(recursi)25(v)15(e)-227(di)25(vide)-227(and)-226(conquer)-227(strate)15(gy)-227(and)-226(successi)25(v)15(ely)]TJ -8.967 -10.46 Td [(eliminate)-372(re)15(gions)-373(in)-372(the)-373(simi)1(larity)-373(space)-372(which)-373(cannot)-372(contain)-372(the)]TJ 0 -10.461 Td [(bottom)-338(left)-338(corner)-338(of)-338(a)]TJ/F31 8.9664 Tf 86.865 0 Td [(0)]TJ/F56 8.9664 Tf 4.607 0 Td [(-ne)15(g)-338(rectangle.)-574(W)80(e)-338(then)-338(recursi)25(v)15(ely)-338(solv)15(e)]TJ -91.472 -10.461 Td [(the)-327(problem)-327(in)-327(the)-327(remaining)-327(smaller)-327(sub-re)15(gions.)-541(Let)-326(us)-327(illustrate)]TJ 0 -10.461 Td [(our)-236(approach)-236(with)-237(an)-236(e)15(xample)-236(in)]TJ/F31 8.9664 Tf 119.148 0 Td [(2)]TJ/F56 8.9664 Tf 6.725 0 Td [(dimensions)-236(as)-236(sho)25(wn)-237(in)-236(Figure)-236(4.)]TJ -125.873 -10.461 Td [(Consider)-266(the)-267(point)]TJ/F34 8.9664 Tf 68.938 0 Td [(P)]TJ/F31 8.9664 Tf 7.163 0 Td [(2)]TJ/F56 8.9664 Tf 4.608 0 Td [(.)-359(W)80(e)-267(\002rst)-266(observ)15(e)-267(that)]TJ/F34 8.9664 Tf 81.903 0 Td [(l)-17(r)-28(ect)]TJ/F31 8.9664 Tf 18.914 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(P)]TJ/F31 8.9664 Tf 7.163 0 Td [(2\051)]TJ/F56 8.9664 Tf 10.581 0 Td [(cannot)-267(con-)]TJ -202.854 -10.46 Td [(tain)-296(the)-297(bottom)-296(left)-297(corner)-296(of)-296(an)15(y)]TJ/F31 8.9664 Tf 123.556 0 Td [(0)]TJ/F56 8.9664 Tf 4.607 0 Td [(-ne)15(g)-296(rectangle)-297(because)-296(an)15(y)-297(such)]TJ -128.163 -10.461 Td [(rectangle)-268(contains)-268(the)-268(ne)15(g)5(ati)25(v)15(e)-268(point)]TJ/F34 8.9664 Tf 133.997 0 Td [(P)]TJ/F31 8.9664 Tf 7.164 0 Td [(2)]TJ/F56 8.9664 Tf 4.607 0 Td [(.)-364(In)-268(f)10(act,)-273(an)15(y)-268(ne)15(g)5(ati)25(v)15(e)-268(point)]TJ ET Q 1 0 0 1 295.992 36 cm 0 Tr /QQAPFce02551e 12 Tf 0 0 0 rg 100 Tz 0 Ts 0 Tw 0 Tc BT 1 0 0 1 0 0 Tm (331)Tj ET 1 0 0 1 0 0 cm 1 0 0 1 -295.992 -36 cm endstream endobj 59 0 obj << /Type /Page /Resources 58 0 R /MediaBox [ 0 0 612 792 ] /Parent 13 0 R /Contents [ 60 0 R ] >> endobj 56 0 obj << /Type /XObject /Subtype /Form /FormType 1 /PTEX.FileName (figures/SimSpace.pdf) /PTEX.PageNumber 1 /PTEX.InfoDict 62 0 R /BBox [0 0 333 138] /Resources << /ProcSet [ /PDF /Text ] /ExtGState << /R7 63 0 R >>/Font << /R10 64 0 R/R9 65 0 R/R8 66 0 R>> >> /Length 67 0 R /Filter /FlateDecode >> stream xZ[o~?bߺ')`0$CG$x#Ję~$~1o-:-?>0{y7-<|?3kT x%WYW_r=J/ӡŅň6ٰ<>~sI[K2[RoGX?|:iKJ7+MY?5ʮ? i?F?F(Lmgt_WRKٷԏlݢ c6lQܖyDA6zsVT0ޢCS>Su%=e[wGdR-!ZX緘8>XH\~Xn5lY]cp5E= ]2R5*{< y*5u#Ös]=c] 1X,3g9;h-nrp2 SNRFALP(n%9b<.^vj:~-I rLV<U*@d پ2+l@qaUl`q <9ȺU>._$09K0;߿r4IBͧÒD'ӏ4^T bm7T;ZI;#sb004~ n<(,')#vZvshҢUzn&+ mpw1Ш_p偄95GTKkp(Vl(sR ޯl#eʣʩՉ@Q< _^yG\i™R%D'J}**0T*6&FfB^VJZUu_-xzk&]+Hk2AǸs"h;26۵.lX_)rt Μ bTM!cr&2T蜠Y"J,*MUAnHUM)RE$9 RX&P ut, ŽeL-l "RdP/-+U@J4:$JdȞc)Y8D ;*luXͥ)vy`[AhPYM;J& g]",k̀($YZ,6QXNRC΢uP+-vs4GNh顎!-:mLө ZٮZn6׆Is7]Cu6cRAv49:!K[cyGX.5ޛ;:6m@w=zOB*˹E1#;.Ts_"K4쌭#EL->שtGQ'ރ=LNur!]:I<v$JE;2 J#OB SR-'Nɲ̱1ݐ 882,$VGx9a5ui:Lu?Jꍗ)*~zě;y~Fw=:@n/^c8_8IBw齫_^8qY9ƩiiW7{rh01J;C=t8;p#0^kN|/ҳC0gP:%VL[+!1H8 {{㌼8GVF7uw:񦼧I&1SXT럥 yt3>X0@7B>u^ 0 4|傆~C=ly489$xڻ,pfѭy^\(km8| ~tTⸯ)58m0>)"X?Z/|yѯ_~K_2 JN7ݏS8٣0w>YW#],vTa.SBZ\(prE> endobj 63 0 obj << /Type /ExtGState /OPM 1 >> endobj 64 0 obj << /BaseFont /Times-Bold /Type /Font /Subtype /Type1 >> endobj 65 0 obj << /BaseFont /Courier /Type /Font /Subtype /Type1 >> endobj 66 0 obj << /BaseFont /Times-Roman /Type /Font /Subtype /Type1 >> endobj 67 0 obj 2807 endobj 57 0 obj << /Type /XObject /Subtype /Form /FormType 1 /PTEX.FileName (figures/SimSpaceAlg.pdf) /PTEX.PageNumber 1 /PTEX.InfoDict 68 0 R /BBox [0 0 212 155] /Resources << /ProcSet [ /PDF /Text ] /ExtGState << /R7 69 0 R >>/Font << /R11 70 0 R/R9 71 0 R/R8 72 0 R>> >> /Length 73 0 R /Filter /FlateDecode >> stream x[O\ G)qH$J"(C $Cag)O\=7c\,?REQyZjbʟ|~<|~=l?O5.~ iw?|x ĭ`K睔^!Q1׏ -umWV +%589ĈHīgSKdV=._`jKKFն[ 6wrDyi#q0MݮoNwON#B܈9<1a>5pR #R4H'W#%pGY <̎S`^cyW:5&q&/ӝYSѥ;8o_ώݑYg-=0Nwv.__l*#!fZoC\FmX`%)u$^t,l)׾ϤxNQ4rpSJ%E/v1k68;oxW'Z9_ 2)E݌r 9VJ9) "r1w`TKːH7*R.iܓDɔ̦ŅAY0JwҒ*W=s |AgΆP9-O~%YSR@'l 7.j܊(y.$*Y*C_j+Yq*rnBMz08Y89'Mu$'w}V.8a7u`U΁dň:ejr\B#[[8 ; L< ⻯I4~8(GwXO6 $KY/1!`5@u9+(zcgo`eoqbLޭA9q w>! 5\/AڇrH8^SKXK33Ë:Ô!NcO{r*GZ-%(}GPA9cwpeRܑ!".E8 V@˩n!2>`M5>#2Mr6u`d6&)م -FF#U4R,mZ%[aSȭf@ mr7;E-JRP IXZX$2Q*k\nZmDXHR ]ǹ‹ {VfګbPa{7@q#D}aSoz%oNń%gK2plŦ훚x!$ԝtIr);u,nr +!qkU5b/ԃSTeFZ]H Y"MK7HѤDb.N <Ƒl9P4W*W'FhEBUg<C$LohT64ir7I ˑr؞132Ҫr>=ph? ~&z'5ĤI1(g_]!p8L8qTr).s%P\F߫V\j_/eŇhdɺ㤎W rʙ]T"'41vWvCr?jC'E я±\(gf98aw#'#$U-S9m%F5Ya rp 8 jH  )iT2ShW(hP9\Gm[8i:RsR1}M&{];bfuy{4U" 'v) Z=(@urJ8{+ ⵊsj!{@fiɮOkAճ⑫rt{'QOq"GS7e'(;-diٟA=u`i${{Җx l908p1v|^[yh"Z:죫krľ#/ښy56a x0qsF!9f噓F`m#Nup8ԑ*GG*6VBCS-s/d?j$ͷ+.M2u+&k4kS7ȡS`4ۻXg;jPeҠ=qJ֦^X{t?kHlIʕc$G Bo3!=2,wTFiNw=TקEX5-2jA~u}ƬM'zx^\fZp{7Сe}G< ? Le׹gnY_ ?Tvۖ)/?~hMD9MN =Y endstream endobj 68 0 obj << /Producer (AFPL Ghostscript 8.53) /CreationDate (D:20070710073530) /ModDate (D:20070710073530) /Title (Microsoft Word - SimSpaceAlg.doc) /Creator (PScript5.dll Version 5.2.2) /Author (vganti) >> endobj 69 0 obj << /Type /ExtGState /OPM 1 >> endobj 70 0 obj << /BaseFont /KPSHBO#2BTimesNewRoman /FontDescriptor 74 0 R /ToUnicode 75 0 R /Type /Font /FirstChar 1 /LastChar 1 /Widths [ 420] /Encoding 76 0 R /Subtype /TrueType >> endobj 71 0 obj << /BaseFont /Courier /Type /Font /Subtype /Type1 >> endobj 72 0 obj << /BaseFont /Times-Roman /Type /Font /Encoding 77 0 R /Subtype /Type1 >> endobj 73 0 obj 3240 endobj 74 0 obj << /Type /FontDescriptor /FontName /KPSHBO#2BTimesNewRoman /FontBBox [ 34 -13 638 625] /Flags 4 /Ascent 625 /CapHeight 625 /Descent -13 /ItalicAngle 0 /StemV 95 /MissingWidth 777 /FontFile2 78 0 R >> endobj 75 0 obj << /Filter /FlateDecode /Length 154 >> stream x]0C|ЪbKVe0KtNWM\=:1_"NTs"8_<頪@kV5[4#jںZk;1^lMR򇓫y1>%FH*X#8<[J}̠M endstream endobj 76 0 obj << /Type /Encoding /BaseEncoding /WinAnsiEncoding /Differences [ 1/epsilon] >> endobj 77 0 obj << /Type /Encoding /Differences [ 146/quoteright] >> endobj 78 0 obj << /Filter /FlateDecode /Length1 13056 /Length 5807 >> stream xZ xTյ^{sf& C&!q2!0&(F2yLx!<͠ !Lb`-*QP Rr2 h%ZUVRS_ms}f@~w}kkgB촎Θ] *2qeCKRѸQ~%+kz2zɊ5Ë{Kd wP[DLjV476p*se-vOH +KA-ͭmz`Է\rlV JN#'0Wl"C 2>jP/'qT BGH;h;QMR/M]TN&!Ki {Ҩv9S5 a*Mҥt%}LGj~B4#h m0**t`|yKCxxcgtd@i4:ǔN%CF$Cl-#)J1Jq9M}&A"ZVՃl5 &CcrQ>]Hөлl-B¸҇ /+[~D-:F_v>խvyu=Bh6C!4Bvbn:jXgN0:x_b`mpM 3\Daz ~|MgxqIh&ͧfZMWXg9+'zg܆S|{#V)F=04,Ʊl[6;X{-Wτ.^+Q2i8bZѾ MӋl0g[h C^lVN7SF'YevzQe‡l9ke-11P8&b brGyO6{ Wf?B,YYlt=uҭȗhҋ& 0Jdzv+n{=^do$p_x%KzV~?QtumqBj0Yݨ>dyZ`l]h{NFN~OL'N/+34dV&)L\l>-dKl!~b]Ns8 v&;>c_p$1f/x̴O3, hWXx7WJ-~!o(\+EJP,QnP))(ߪN5.UZr,c,s--wYZ>Zօֵ7͋ט>:*bjr5?"K7+ĭwb'\=)ˍE5hfANT,Md=CD? ,*E VnP?%oS) TncGm5r)G :&~'/N~KW#6Jlƿd}Jg{d8[E-'bO߳blxMZ:x* L#Y-sS|ưKa#wN]t|0vYN_?%wlu#~YTL T{c@H:@.Zkc_S[NE,ցE&`/ǨvpgR"50v(ߍE{6>u)߆,.3#MA7WڅyZ?BeZ<y2;rpQL|wR%nqKi 6vc]mIyO=EG6bߞLa?, 4MTNme&Mxxxm襒˨-xBC%RcvާhU޳;;'T6^p Q# F{4>,7'{h֐̌Aiԁ)I6EUgkQՕ|mBY h8C]Uml,P2tڒ9\A ]aͥZzu(RE\q|Yb(h g-r, իvU+%RlJ.SWr )(C.6d"3 |Hl*ժ3U9nwЯFmNZ3MFTVs29vnq¨o"mQåuh1|Jrͱ<393%73Ժ%DЇνj !X|}Ng1KC)>&-,%.=IЖv.ba;u7Rv9Nse9Z*+:gr =[Sr505Q`?tZgLsYu:LzMA:F<0q4q0ah/z,ӓ*Rzkk|!!x_,,9hП*>>jLk%V>N4Wp]kq>El"E-wcOYhaNBEΣR{J3xԬ;9KWͪZsUwF;zu 5C/D]gK8zj{sMLb)+Ejs؆]!a6̩q+py& 엊XvnC^e昚bQ#f}vR9{y+п$^[lb̞@Of_[0^>B!n* gH#ϝh Zln*4G< 咊b9N &x6$G]=Rӄn3J;!<;Oբlז;DklQ>z(PڊVn+jz <2kcn\k @HEEE%lm ZجZجETE+kł Ľqrxؔt pǑfP42@cU@E4tZi@gJW"@6BJB `>FZ% G+8)T6`Y(ebj&YJKHSzSrrgQ]bKRkZZ,,[,;,I[,[<Ғ.E8R\))ie;׋u[[ b\K\j#ANx*jK]*BJRS [Ziͩ6ҾOj#@(h,fG͎V xuk”"k@O(bLSlOFdHc$2e偐$==^TfosANe6;`NL+T"oQANũ9NeN;4MtA9Aef:> 4XTQ::)ndIYz?+-Q>[n=p;PGĴr)aʝlpmn>nTU:$.#@ 1p? x?"!Nģ%=(w;mһLzIL8TS7N@gg[M+(,!&;lRO&nR(mW>}~[Žk&MGlI4?ⴿ_촏ulTa&͑}XjU*%=ɾ*bN)'N_6GOa~PW6%~󐿇ywV{|^s{lPpم q^磚ݩA,tޣwE=tVb':8= PڕaS8GHWǞǝ0bf2w~>YY{om.γδNX .0k5Önsؒm6Ŧظl=ѐOeX4"b\RqD ]SXY8_n[#|^/!Ah}<'Ɗߒ#D"Fm.٘G2^U"2WeOL_]=$,ߙW0u"z@a};K=RRY4zaJ^tyǚ=ߩ5oܝyq,bw6qdA†`*ƬEBT 7Ku ]E'6G6.I_kiUQ7JuVE9u]XC!5TEwuT֜5ͧǪ:dgr]5ߣ]r9VkWh9Vͬ VS[eN&)ɸ9HEeysLpg]s@!FCm IIrveO; ^t2He(;N.vӼ ,W.{"ҷRzI1Q*z;]==7:> /XObject << /Im4 56 0 R /Im5 57 0 R >> /ProcSet [ /PDF /Text ] >> endobj 81 0 obj << /Length 33129 /LC /QQAP >> stream q BT /F56 8.9664 Tf 53.798 728.239 Td [(de\002nes)-232(such)-232(a)-232(re)15(gion)-232(which)-232(can)-232(be)-232(eliminated)-232(from)-231(further)-232(consider)20(-)]TJ 0 -10.461 Td [(ation.)-638(The)-360(remaining)-359(re)15(gion)-360(is)-359(the)-360(union)-359(of)-359(tw)10(o)-360(ne)25(w)-359(sub-re)15(gions:)]TJ/F34 8.9664 Tf 0 -10.46 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050[)]TJ/F34 8.9664 Tf 6.143 0 Td [(P)]TJ/F31 8.9664 Tf 7.164 0 Td [(2[)]TJ/F34 8.9664 Tf 7.168 0 Td [(X)]TJ/F31 8.9664 Tf 8.314 0 Td [(1])]TJ/F34 8.9664 Tf 7.167 0 Td [(;)]TJ/F36 8.9664 Tf 4.096 0 Td [(\000)]TJ/F34 8.9664 Tf 7.167 0 Td [(\017)]TJ/F31 8.9664 Tf 3.734 0 Td [(]\051)]TJ/F56 8.9664 Tf 10.101 0 Td [(and)]TJ/F34 8.9664 Tf 16.905 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.318 0 Td [(\050[)]TJ/F36 8.9664 Tf 6.144 0 Td [(\000)]TJ/F34 8.9664 Tf 7.167 0 Td [(\017;)-171(P)]TJ/F31 8.9664 Tf 14.993 0 Td [(2[)]TJ/F34 8.9664 Tf 7.168 0 Td [(X)]TJ/F31 8.9664 Tf 8.314 0 Td [(2]]\051)]TJ/F56 8.9664 Tf 13.311 0 Td [(.)-884(Note)-441(that)-442(these)]TJ -177.693 -10.461 Td [(ne)25(w)-420(re)15(gions)-421(correspond)-420(to)-420(translating)-421(the)-420(origin)-421(t)1(o)]TJ/F31 8.9664 Tf 195.152 0 Td [([)]TJ/F34 8.9664 Tf 2.56 0 Td [(P)]TJ/F31 8.9664 Tf 7.164 0 Td [(2[)]TJ/F34 8.9664 Tf 7.167 0 Td [(X)]TJ/F31 8.9664 Tf 8.314 0 Td [(1])]TJ/F34 8.9664 Tf 7.168 0 Td [(;)]TJ/F36 8.9664 Tf 4.095 0 Td [(\000)]TJ/F34 8.9664 Tf 7.168 0 Td [(\017)]TJ/F31 8.9664 Tf 3.733 0 Td [(])]TJ/F56 8.9664 Tf -242.521 -10.461 Td [(and)]TJ/F31 8.9664 Tf 16.015 0 Td [([)]TJ/F36 8.9664 Tf 2.56 0 Td [(\000)]TJ/F34 8.9664 Tf 7.167 0 Td [(\017;)-171(P)]TJ/F31 8.9664 Tf 14.993 0 Td [(2[)]TJ/F34 8.9664 Tf 7.168 0 Td [(X)]TJ/F31 8.9664 Tf 8.314 0 Td [(2]])]TJ/F56 8.9664 Tf 9.727 0 Td [(,)-365(respecti)25(v)15(ely)65(.)-586(W)80(e)-342(no)25(w)-342(recurse)-343(o)15(v)15(er)-342(each)-342(one)-342(of)]TJ -65.944 -10.461 Td [(these)-252(tw)10(o)-253(re)15(gions)-252(for)-253(determining)-252(the)-252(best)-253(rectangle.)-317(While)-252(process-)]TJ 0 -10.461 Td [(ing)]TJ/F34 8.9664 Tf 13.994 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050)]TJ/F34 8.9664 Tf 3.583 0 Td [(P)]TJ/F31 8.9664 Tf 7.164 0 Td [(2[)]TJ/F34 8.9664 Tf 7.168 0 Td [(X)]TJ/F31 8.9664 Tf 8.314 0 Td [(1])]TJ/F34 8.9664 Tf 7.167 0 Td [(;)]TJ/F36 8.9664 Tf 4.096 0 Td [(\000)]TJ/F34 8.9664 Tf 7.167 0 Td [(\017)]TJ/F31 8.9664 Tf 3.734 0 Td [(]\051)]TJ/F56 8.9664 Tf 8.678 0 Td [(suppose)-283(we)-282(choose)-283(the)-283(ne)15(g)5(ati)25(v)15(e)-282(point)]TJ/F34 8.9664 Tf 138.684 0 Td [(P)]TJ/F31 8.9664 Tf 7.164 0 Td [(3)]TJ/F56 8.9664 Tf 4.608 0 Td [(.)]TJ -242.84 -10.46 Td [(One)-232(of)-232(the)-232(ne)25(wer)-232(re)15(gions)-232(is)-233(the)-232(rectangle)]TJ/F34 8.9664 Tf 147.754 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050[)]TJ/F34 8.9664 Tf 6.144 0 Td [(P)]TJ/F31 8.9664 Tf 7.163 0 Td [(2[)]TJ/F34 8.9664 Tf 7.168 0 Td [(X)]TJ/F31 8.9664 Tf 8.314 0 Td [(1])]TJ/F34 8.9664 Tf 7.167 0 Td [(;)-171(P)]TJ/F31 8.9664 Tf 11.26 0 Td [(3[)]TJ/F34 8.9664 Tf 7.167 0 Td [(X)]TJ/F31 8.9664 Tf 8.314 0 Td [(2]]\051)]TJ/F56 8.9664 Tf -231.77 -10.461 Td [(which)-340(contains)-341(only)-340(positi)25(v)15(e)-341(points)-340(and)-341(hence)-340(is)-341(a)]TJ/F57 8.9664 Tf 188.993 0 Td [(valid)]TJ/F56 8.9664 Tf 20.985 0 Td [(rectangle.)]TJ -209.978 -10.461 Td [(Among)-391(all)-391(such)-390(v)25(alid)-391(rectangles)-391(encountered)-391(during)-391(the)-390(recursi)25(v)15(e)]TJ 0 -10.461 Td [(tra)20(v)15(ersal)-273(of)-273(our)-274(algorithm,)-279(we)-273(choose)-273(the)-273(one)-274(with)-273(the)-273(highest)-273(num-)]TJ 0 -10.46 Td [(ber)-250(of)-250(positi)25(v)15(e)-250(points.)]TJ 8.967 -10.461 Td [(As)-316(illustrated)-316(abo)15(v)15(e,)-333(each)-316(of)-316(the)-317(ne)15(g)5(ati)25(v)15(e)-316(points)-316(de\002nes)-316(a)-316(candi-)]TJ -8.967 -10.461 Td [(date)-235(lo)25(wer)-235(rectangle)-235(which)-235(can)-235(be)-235(eliminated.)-305(W)80(e)-235(can)-235(further)-235(reduce)]TJ 0 -10.461 Td [(the)-292(number)-292(of)-292(candidate)-292(lo)25(wer)-292(rectangles)-292(for)-292(elimination)-291(due)-292(to)-292(the)]TJ 0 -10.461 Td [(follo)25(wing)-250(observ)25(ation.)]TJ/F57 8.9664 Tf 0 -13.486 Td [(Sk)10(yline)]TJ/F56 8.9664 Tf 25.805 0 Td [(:)-450(The)]TJ/F57 8.9664 Tf 23.334 0 Td [(sk)10(yline)]TJ/F56 8.9664 Tf 27.678 0 Td [(of)-320(a)-320(set)-319(of)-320(points)-320(contains)-320(all)-320(points)-319(which)-320(do)]TJ -76.817 -10.461 Td [(not)-363(\223dominate\224)-364(each)-363(other)-364([12].)-650(F)15(or)-363(the)-363(e)15(xample)-364(in)-363(Figure)-364(4,)-391(the)]TJ 0 -10.461 Td [(points)]TJ/F34 8.9664 Tf 25.181 0 Td [(P)]TJ/F31 8.9664 Tf 7.164 0 Td [(2)]TJ/F56 8.9664 Tf 7.866 0 Td [(and)]TJ/F34 8.9664 Tf 16.206 0 Td [(P)]TJ/F31 8.9664 Tf 7.164 0 Td [(3)]TJ/F56 8.9664 Tf 7.866 0 Td [(are)-363(on)-364(the)-363(sk)15(yline)-364(of)-363(ne)15(g)5(ati)25(v)15(e)-363(points)-364(while)]TJ/F34 8.9664 Tf 161.863 0 Td [(P)]TJ/F31 8.9664 Tf 7.163 0 Td [(1)]TJ/F56 8.9664 Tf -240.473 -10.461 Td [(is)-308(not)-308(because)-308(it)-307(is)-308(dominated)-308(by)-308(both)]TJ/F34 8.9664 Tf 141.631 0 Td [(P)]TJ/F31 8.9664 Tf 7.164 0 Td [(2)]TJ/F56 8.9664 Tf 7.368 0 Td [(and)]TJ/F34 8.9664 Tf 15.708 0 Td [(P)]TJ/F31 8.9664 Tf 7.164 0 Td [(3)]TJ/F56 8.9664 Tf 4.607 0 Td [(.)-484(W)80(e)-307(refer)-308(to)-308(the)]TJ -183.642 -10.461 Td [(sk)15(yline)-250(of)-250(the)-250(ne)15(g)5(ati)25(v)15(e)-250(points)]TJ/F31 8.9664 Tf 107.165 0 Td [(\001)]TJ/F37 5.9776 Tf 7.68 3.809 Td [(\000)]TJ/F56 8.9664 Tf 8.496 -3.809 Td [(as)-250(the)]TJ/F57 8.9664 Tf 22.909 0 Td [(ne)40(gative)-250(sk)10(yline)]TJ/F34 8.9664 Tf 59.311 0 Td [(S)]TJ/F37 5.9776 Tf 6.14 3.809 Td [(\000)]TJ/F56 8.9664 Tf 6.254 -3.809 Td [(.)]TJ -207.768 -21.41 Td [(P)]TJ/F56 7.1731 Tf 5.434 0 Td [(R)-22(O)-61(P)-62(E)-61(R)-2(T)-62(Y)]TJ/F56 8.9664 Tf 39.815 0 Td [(1.)]TJ/F57 8.9664 Tf 11.444 0 Td [(Let)]TJ/F34 8.9664 Tf 14.078 0 Td [(p)]TJ/F57 8.9664 Tf 7.245 0 Td [(be)-292(a)-292(point)-292(in)]TJ/F34 8.9664 Tf 48.834 0 Td [(S)]TJ/F37 5.9776 Tf 6.14 3.809 Td [(\000)]TJ/F57 8.9664 Tf 6.254 -3.809 Td [(.)-436(Then,)-303(for)-292(any)-292(point)]TJ/F34 8.9664 Tf 78.745 0 Td [(p)]TJ/F37 5.9776 Tf 4.626 3.809 Td [(0)]TJ/F57 8.9664 Tf 5.303 -3.809 Td [(in)]TJ/F34 8.9664 Tf -238.105 -10.461 Td [(l)-17(r)-28(ect)]TJ/F31 8.9664 Tf 18.915 0 Td [(\050)]TJ/F34 8.9664 Tf 3.583 0 Td [(p)]TJ/F31 8.9664 Tf 4.626 0 Td [(\051)]TJ/F57 8.9664 Tf 3.584 0 Td [(,)]TJ/F34 8.9664 Tf 4.483 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(p)]TJ/F37 5.9776 Tf 4.626 3.809 Td [(0)]TJ/F31 8.9664 Tf 2.684 -3.809 Td [(\051)]TJ/F57 8.9664 Tf 5.825 0 Td [(cannot)-250(be)-250(a)]TJ/F31 8.9664 Tf 44.079 0 Td [(0)]TJ/F57 8.9664 Tf 4.608 0 Td [(-ne)40(g)-250(hyper)20(-r)37(ectangle)15(.)]TJ/F47 8.9664 Tf 116.41 0 Td [(2)]TJ/F56 8.9664 Tf -229.359 -21.41 Td [(F)15(or)-340(e)15(xample,)-363(the)-340(rectangle)]TJ/F34 8.9664 Tf 101.029 0 Td [(l)-17(r)-28(ect)]TJ/F31 8.9664 Tf 18.914 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(P)]TJ/F31 8.9664 Tf 7.164 0 Td [(2\051)]TJ/F56 8.9664 Tf 11.242 0 Td [(corresponding)-340(to)-341(the)-340(ne)15(g-)]TJ -150.9 -10.461 Td [(ati)25(v)15(e)-391(sk)15(yline)-391(point)]TJ/F34 8.9664 Tf 71.788 0 Td [(P)]TJ/F31 8.9664 Tf 7.164 0 Td [(2)]TJ/F56 8.9664 Tf 8.111 0 Td [(in)-391(Figure)-391(4)-390(cannot)-391(contain)-391(the)-391(bottom)-390(left)]TJ -87.063 -10.461 Td [(corner)]TJ/F34 8.9664 Tf 25.069 0 Td [(p)]TJ/F37 5.9776 Tf 4.626 3.809 Td [(0)]TJ/F56 8.9664 Tf 4.853 -3.809 Td [(of)-242(an)15(y)]TJ/F31 8.9664 Tf 24.619 0 Td [(0)]TJ/F56 8.9664 Tf 4.607 0 Td [(-ne)15(g)-242(rectangle)]TJ/F34 8.9664 Tf 52.998 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.318 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(p)]TJ/F37 5.9776 Tf 4.626 3.809 Td [(0)]TJ/F31 8.9664 Tf 2.684 -3.809 Td [(\051)]TJ/F56 8.9664 Tf 3.584 0 Td [(.)-307(Among)-242(all)-242(ne)15(g)5(ati)25(v)15(e)-242(sk)15(y-)]TJ -152.568 -10.461 Td [(line)-339(points,)-360(we)-339(choose)-339(one)-338(point)]TJ/F34 8.9664 Tf 122.767 0 Td [(p)]TJ/F56 8.9664 Tf 7.662 0 Td [(uniformly)-339(at)-338(random,)-361(eliminate)]TJ -130.429 -10.46 Td [(the)-227(rectangle)]TJ/F34 8.9664 Tf 47.889 0 Td [(l)-17(r)-28(ect)]TJ/F31 8.9664 Tf 18.915 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(p)]TJ/F31 8.9664 Tf 4.626 0 Td [(\051)]TJ/F56 8.9664 Tf 3.583 0 Td [(,)-232(and)-227(then)-227(recurse)-227(on)-227(the)-227(ne)25(w)-227(upper)-227(rectangles.)]TJ/F57 8.9664 Tf -78.597 -20.922 Td [(Stopping)-358(Condition)]TJ/F56 8.9664 Tf 70.97 0 Td [(:)-526(During)-358(an)15(y)-359(gi)25(v)15(en)-358(recursi)25(v)15(e)-358(call)-358(we)-358(e)15(xplore)-358(a)]TJ -70.97 -10.461 Td [(sub-re)15(gion)-202(which)-202(is)-202(t)1(he)-202(upper)-202(rectangle)]TJ/F34 8.9664 Tf 141.202 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(O)]TJ/F31 8.9664 Tf 7.268 0 Td [(\051)]TJ/F56 8.9664 Tf 5.393 0 Td [(of)-202(some)-202(point)]TJ/F34 8.9664 Tf 50.261 0 Td [(O)]TJ/F56 8.9664 Tf 9.078 0 Td [(in)]TJ -238.105 -10.46 Td [(the)-250(similarity)-250(space.)-310(When)-249(an)-250(upper)-250(rectangle)-250(is)-250(\223v)25(alid\224)-250(\050i.e.,)-250(it)-249(does)]TJ 0 -10.461 Td [(not)-268(contain)-268(an)15(y)-268(ne)15(g)5(ati)25(v)15(e)-269(sk)15(yline)-268(point)-268(and)-268(hence)-268(no)-268(ne)15(g)5(ati)25(v)15(e)-268(point\051,)]TJ 0 -10.461 Td [(we)-320(stop)-319(recursing)-320(on)-319(this)-320(sub-re)15(gion.)-519(F)15(or)-319(the)-320(e)15(xample)-319(in)-320(Figure)-319(4,)]TJ 0 -10.461 Td [(suppose)-264(we)-264(choose)]TJ/F34 8.9664 Tf 71.342 0 Td [(P)]TJ/F31 8.9664 Tf 7.164 0 Td [(4)]TJ/F56 8.9664 Tf 4.608 0 Td [(.)-352(W)80(e)-264(then)-263(generate)-264(tw)10(o)-264(ne)25(w)-264(upper)-264(rectangles)]TJ/F34 8.9664 Tf -83.114 -10.461 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050[)]TJ/F36 8.9664 Tf 6.143 0 Td [(\000)]TJ/F34 8.9664 Tf 7.168 0 Td [(\017;)-171(P)]TJ/F31 8.9664 Tf 14.993 0 Td [(4[)]TJ/F34 8.9664 Tf 7.167 0 Td [(X)]TJ/F31 8.9664 Tf 8.314 0 Td [(2]]\051)]TJ/F56 8.9664 Tf 16.351 0 Td [(and)]TJ/F34 8.9664 Tf 15.988 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.318 0 Td [(\050[)]TJ/F34 8.9664 Tf 6.144 0 Td [(P)]TJ/F31 8.9664 Tf 7.163 0 Td [(4[)]TJ/F34 8.9664 Tf 7.168 0 Td [(X)]TJ/F31 8.9664 Tf 8.314 0 Td [(1])]TJ/F34 8.9664 Tf 7.167 0 Td [(;)]TJ/F36 8.9664 Tf 4.096 0 Td [(\000)]TJ/F34 8.9664 Tf 7.168 0 Td [(\017)]TJ/F31 8.9664 Tf 3.733 0 Td [(]\051)]TJ/F56 8.9664 Tf 6.144 0 Td [(,)-361(respecti)25(v)15(ely)65(.)-577(The)]TJ -175.858 -10.46 Td [(\002rst)-365(upper)-365(rectangle)-365(is)-365(v)25(alid)-365(since)-365(it)-365(contains)-365(only)-364(positi)25(v)15(e)-365(points,)]TJ 0 -10.461 Td [(and)-250(we)-250(w)10(ould)-250(not)-250(recurse.)]TJ 8.967 -10.461 Td [(The)-306(abo)15(v)15(e)-307(approach)-306(can)-307(be)-306(e)15(xtended)-307(e)25(v)15(en)-306(if)-307(we)-306(require)-307(the)-306(\002nal)]TJ -8.967 -10.461 Td [(rectangles)-323(to)-324(be)]TJ/F34 8.9664 Tf 60.492 0 Td [(d)]TJ/F56 8.9664 Tf 4.775 0 Td [(-dimensional)-323(for)-324(some)]TJ/F34 8.9664 Tf 84.907 0 Td [(d)-425(<)-426(D)]TJ/F56 8.9664 Tf 27.426 0 Td [(.)-531(If)-323(the)-324(number)]TJ/F34 8.9664 Tf 60.022 0 Td [(d)]TJ/F37 5.9776 Tf 4.775 3.809 Td [(0)]TJ/F56 8.9664 Tf -242.397 -14.269 Td [(of)-275(non-ne)15(g)5(ati)25(v)15(e)-276(dimension)-275(v)25(alues)-275(of)]TJ/F34 8.9664 Tf 133.602 0 Td [(O)]TJ/F56 8.9664 Tf 9.737 0 Td [(is)-275(greater)-275(than)]TJ/F34 8.9664 Tf 53.715 0 Td [(d)]TJ/F56 8.9664 Tf 7.243 0 Td [(then)-275(we)-276(re-)]TJ -204.297 -10.461 Td [(quire)-288(at)-288(least)]TJ/F34 8.9664 Tf 49.086 0 Td [(d)]TJ/F37 5.9776 Tf 4.775 3.809 Td [(0)]TJ/F56 8.9664 Tf 5.268 -3.809 Td [(h)5(yper)20(-planes)-288(to)-288(describe)-288(an)15(y)-289(rectangle)-288(contained)-288(in)]TJ/F34 8.9664 Tf -59.129 -10.461 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(O)]TJ/F31 8.9664 Tf 7.268 0 Td [(\051)]TJ/F56 8.9664 Tf 3.584 0 Td [(.)-540(Hence,)]TJ/F34 8.9664 Tf 35.332 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050)]TJ/F34 8.9664 Tf 3.583 0 Td [(O)]TJ/F31 8.9664 Tf 7.269 0 Td [(\051)]TJ/F56 8.9664 Tf 6.514 0 Td [(cannot)-327(contain)-327(a)-326(v)25(alid)]TJ/F34 8.9664 Tf 83.713 0 Td [(d)]TJ/F56 8.9664 Tf 4.774 0 Td [(-dimensional)]TJ -198.259 -10.461 Td [(rectangle.)-343(Therefore,)-264(we)-261(stop)-261(recursing.)-343(This)-261(intuition)-261(is)-261(formalized)]TJ 0 -10.461 Td [(belo)25(w)65(.)]TJ 10.187 -21.41 Td [(P)]TJ/F56 7.1731 Tf 5.434 0 Td [(R)-22(O)-61(P)-62(E)-61(R)-2(T)-62(Y)]TJ/F56 8.9664 Tf 39.815 0 Td [(2.)]TJ/F57 8.9664 Tf 9.035 0 Td [(Let)]TJ/F34 8.9664 Tf 13.275 0 Td [(O)]TJ/F57 8.9664 Tf 9.085 0 Td [(be)-203(a)-202(point,)-212(and)]TJ/F34 8.9664 Tf 54.423 0 Td [(p)]TJ/F57 8.9664 Tf 6.442 0 Td [(be)-203(any)-202(point)-203(whic)15(h)-202(str)45(ongly)]TJ -147.696 -10.461 Td [(dominates)]TJ/F34 8.9664 Tf 39.643 0 Td [(O)]TJ/F57 8.9664 Tf 7.269 0 Td [(.)-491(The)-310(dimensionality)-311(of)]TJ/F34 8.9664 Tf 88.22 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(O)]TJ/F31 8.9664 Tf 7.268 0 Td [(\051)]TJ/F57 8.9664 Tf 6.367 0 Td [(is)-310(a)-311(lower)-310(bound)-310(of)]TJ -173.67 -10.46 Td [(the)-250(minimum)-250(dimensionality)-250(of)]TJ/F34 8.9664 Tf 113.074 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050)]TJ/F34 8.9664 Tf 3.583 0 Td [(p)]TJ/F31 8.9664 Tf 4.626 0 Td [(\051)]TJ/F57 8.9664 Tf 3.584 0 Td [(.)]TJ/F56 8.9664 Tf -137.219 -21.411 Td [(W)80(e)-214(no)25(w)-213(describe)-214(our)-213(algorithm,)-221(which)-214(is)-214(outlined)-213(in)-214(Figure)-213(5.)-298(The)]TJ -8.967 -10.461 Td [(o)15(v)15(erall)-254(algorithm)-255(consists)-254(of)-254(three)-254(steps.)-323(First,)-256(we)-254(b)20(uild)-254(the)-254(ne)15(g)5(ati)25(v)15(e)]TJ 0 -10.46 Td [(sk)15(yline.)-685(The)-376(second)-375(main)-375(step)-375(is)-375(the)]TJ/F57 8.9664 Tf 142.495 0 Td [(Quic)20(kCorner)10(s)]TJ/F56 8.9664 Tf 53.898 0 Td [(algorithm)-375(for)]TJ -196.393 -10.461 Td [(identifying)-318(the)-319(best)-318(corner)55(.)-515(The)-318(third)-319(step)-318(adjusts)-318(the)-319(corner)-318(of)-318(the)]TJ 0 -10.461 Td [(rectangle)-250(returned)-250(by)-250(QuickCorners.)]TJ/F55 8.9664 Tf 0 -20.921 Td [(Step)-377(1)]TJ/F31 8.9664 Tf 24.8 0 Td [(|)]TJ/F55 8.9664 Tf 9.215 0 Td [(Negati)10(v)10(e)-377(sk)15(yline)-377(identi\002cation)]TJ/F56 8.9664 Tf 117.034 0 Td [(:)-564(W)80(e)-377(identify)-376(the)-377(sk)15(yline)]TJ/F34 8.9664 Tf -151.049 -10.461 Td [(S)]TJ/F37 5.9776 Tf 6.14 3.809 Td [(\000)]TJ/F56 8.9664 Tf 9.186 -3.809 Td [(of)-327(all)-327(ne)15(g)5(ati)25(v)15(e)-327(points.)-541(An)15(y)-327(of)-327(the)-327(kno)25(wn)-327(sk)15(yline)-327(identi\002cation)]TJ -15.326 -10.461 Td [(algorithms)-286(can)-286(be)-287(used)-286(for)-286(this)-286(purpose.)-419(In)-286(our)-286(implementation,)-295(we)]TJ 0 -10.461 Td [(use)-250(the)-250(algorithm)-250(based)-250(on)-250(nested)-250(loop)-250(joins)-250([12].)]TJ/F55 7.9701 Tf 257.036 646.42 Td [(BestHyperRectangle\050)]TJ/F67 7.9701 Tf 72.599 0 Td [(\001)]TJ/F33 5.9776 Tf 7.057 2.812 Td [(+)]TJ/F55 7.9701 Tf 6.089 -2.812 Td [(,)]TJ/F67 7.9701 Tf 3.985 0 Td [(\001)]TJ/F37 5.9776 Tf 7.057 2.812 Td [(\000)]TJ/F55 7.9701 Tf 6.254 -2.812 Td [(,)]TJ/F68 7.9701 Tf 3.985 0 Td [(d)]TJ/F55 7.9701 Tf 4.357 0 Td [(\051)]TJ/F56 7.9701 Tf -111.383 -8.967 Td [(Initialization:)]TJ/F68 7.9701 Tf 45.421 0 Td [(C)]TJ/F67 7.9701 Tf 8.951 0 Td [(=)-295([)]TJ/F69 7.9701 Tf 11.291 0 Td [(\000)]TJ/F68 7.9701 Tf 6.587 0 Td [(";)-177(:)-177(:)-177(:)-178(;)]TJ/F69 7.9701 Tf 22.729 0 Td [(\000)]TJ/F68 7.9701 Tf 6.586 0 Td [(")]TJ/F67 7.9701 Tf 3.911 0 Td [(])]TJ/F56 7.9701 Tf 4.345 0 Td [(where)]TJ/F68 7.9701 Tf 21.463 0 Td [(")-295(>)]TJ/F67 7.9701 Tf 15.202 0 Td [(0)]TJ/F56 7.9701 Tf 6.226 0 Td [(is)-250(a)-250(small)-250(constant.)]TJ -152.712 -8.966 Td [(\0501\051)-250(Build)-250(the)-250(sk)15(yline)]TJ/F68 7.9701 Tf 67.626 0 Td [(S)]TJ/F37 5.9776 Tf 5.596 2.813 Td [(\000)]TJ/F56 7.9701 Tf 8.247 -2.813 Td [(of)-250(ne)15(g)5(ati)25(v)15(e)-250(points)]TJ/F67 7.9701 Tf 58.628 0 Td [(\001)]TJ/F37 5.9776 Tf 7.057 2.813 Td [(\000)]TJ/F56 7.9701 Tf -147.154 -11.78 Td [(\0502\051)-250(co)15(v)15(erage)-250(=)-250(QuickCorners\050)]TJ/F67 7.9701 Tf 95.657 0 Td [(\001)]TJ/F33 5.9776 Tf 7.057 2.813 Td [(+)]TJ/F56 7.9701 Tf 6.088 -2.813 Td [(,)]TJ/F67 7.9701 Tf 3.985 0 Td [(\001)]TJ/F37 5.9776 Tf 7.057 2.813 Td [(\000)]TJ/F56 7.9701 Tf 6.255 -2.813 Td [(,)]TJ/F68 7.9701 Tf 3.985 0 Td [(S)]TJ/F37 5.9776 Tf 5.595 2.813 Td [(\000)]TJ/F56 7.9701 Tf 6.255 -2.813 Td [(,)-250(ref)]TJ/F68 7.9701 Tf 14.824 0 Td [(C)]TJ/F56 7.9701 Tf 6.599 0 Td [(,)]TJ/F68 7.9701 Tf 3.985 0 Td [(d)]TJ/F56 7.9701 Tf 4.357 0 Td [(,)-250(0\051)]TJ -171.699 -8.966 Td [(\0503\051)-250(AdjustCorner\050ref)]TJ/F68 7.9701 Tf 68.168 0 Td [(C)]TJ/F56 7.9701 Tf 6.599 0 Td [(,)]TJ/F67 7.9701 Tf 1.992 0 Td [(\001)]TJ/F33 5.9776 Tf 7.057 2.813 Td [(+)]TJ/F56 7.9701 Tf 6.089 -2.813 Td [(\051)]TJ/F55 7.9701 Tf -89.905 -17.933 Td [(QuickCor)15(ners\050)]TJ/F67 7.9701 Tf 51.24 0 Td [(\001)]TJ/F33 5.9776 Tf 7.057 2.813 Td [(+)]TJ/F55 7.9701 Tf 6.088 -2.813 Td [(,)]TJ/F67 7.9701 Tf 3.985 0 Td [(\001)]TJ/F37 5.9776 Tf 7.057 2.813 Td [(\000)]TJ/F55 7.9701 Tf 6.254 -2.813 Td [(,)]TJ/F68 7.9701 Tf 3.985 0 Td [(S)]TJ/F37 5.9776 Tf 5.596 2.813 Td [(\000)]TJ/F55 7.9701 Tf 6.254 -2.813 Td [(,)-250(r)18(ef)]TJ/F68 7.9701 Tf 15.566 0 Td [(C)]TJ/F55 7.9701 Tf 6.599 0 Td [(,)]TJ/F68 7.9701 Tf 3.985 0 Td [(d)]TJ/F55 7.9701 Tf 4.357 0 Td [(,)]TJ/F68 7.9701 Tf 3.985 0 Td [(d)]TJ/F37 5.9776 Tf 4.357 2.813 Td [(0)]TJ/F55 7.9701 Tf 2.685 -2.813 Td [(\051)]TJ/F56 7.9701 Tf -139.05 -8.966 Td [(/*)-250(Stop)-250(conditions)-250(*/)]TJ 0 -8.967 Td [(\0501\051)-250(if)-250(\050)]TJ/F68 7.9701 Tf 20.802 0 Td [(d)]TJ/F37 5.9776 Tf 4.357 2.813 Td [(0)]TJ/F68 7.9701 Tf 5.037 -2.813 Td [(>)-295(d)]TJ/F56 7.9701 Tf 13.296 0 Td [(\051)-250(return)]TJ/F67 7.9701 Tf 25.672 0 Td [(0)]TJ/F56 7.9701 Tf -69.164 -8.966 Td [(\0502\051)-250(If)]TJ/F68 7.9701 Tf 18.587 0 Td [(V)-236(al)-12(idC)-71(or)-29(ner)]TJ/F67 7.9701 Tf 49.045 0 Td [(\050)]TJ/F68 7.9701 Tf 3.293 0 Td [(C)-12(;)-177(S)]TJ/F37 5.9776 Tf 15.488 2.813 Td [(\000)]TJ/F67 7.9701 Tf 6.254 -2.813 Td [(\051)]TJ/F56 7.9701 Tf -72.674 -8.966 Td [(return)]TJ/F68 7.9701 Tf 21.025 0 Td [(v)]TJ/F67 7.9701 Tf 6.762 0 Td [(=)]TJ/F68 7.9701 Tf 8.938 0 Td [(C)-71(ov)-36(er)-29(ag)-36(e)]TJ/F67 7.9701 Tf 35.829 0 Td [(\050)]TJ/F68 7.9701 Tf 3.293 0 Td [(ur)-29(ect)]TJ/F67 7.9701 Tf 19.614 0 Td [(\050)]TJ/F68 7.9701 Tf 3.293 0 Td [(C)]TJ/F67 7.9701 Tf 6.599 0 Td [(\051)]TJ/F68 7.9701 Tf 3.293 0 Td [(;)]TJ/F67 7.9701 Tf 3.764 0 Td [(\001)]TJ/F33 5.9776 Tf 7.057 2.812 Td [(+)]TJ/F67 7.9701 Tf 6.088 -2.812 Td [(\051)]TJ/F56 7.9701 Tf -145.548 -8.967 Td [(/*)-250(Recursion)-250(*/)]TJ 0 -8.966 Td [(\0503\051)-250(Else,)-250(randomly)-250(pick)-250(a)-250(point)]TJ/F68 7.9701 Tf 101.164 0 Td [(p)]TJ/F69 7.9701 Tf 6.615 0 Td [(2)]TJ/F68 7.9701 Tf 7.998 0 Td [(S)]TJ/F37 5.9776 Tf 5.596 2.813 Td [(\000)]TJ/F56 7.9701 Tf 8.247 -2.813 Td [(which)-250(strongly)-250(dominates)]TJ/F68 7.9701 Tf 84.347 0 Td [(C)]TJ/F56 7.9701 Tf 6.598 0 Td [(.)]TJ -220.565 -8.966 Td [(\0504\051)]TJ/F68 7.9701 Tf 11.286 0 Td [(v)]TJ/F37 5.9776 Tf 4.409 2.812 Td [(\003)]TJ/F67 7.9701 Tf 6.67 -2.812 Td [(=)-295(0)]TJ/F56 7.9701 Tf 13.173 0 Td [(;)]TJ/F68 7.9701 Tf 4.208 0 Td [(C)]TJ/F37 5.9776 Tf 6.599 2.812 Td [(\003)]TJ/F67 7.9701 Tf 6.669 -2.812 Td [(=)]TJ/F68 7.9701 Tf 8.939 0 Td [(nul)-12(l)]TJ/F56 7.9701 Tf -61.953 -8.967 Td [(\0505\051)-250(foreach)-250(dimension)]TJ/F68 7.9701 Tf 72.376 0 Td [(i)]TJ/F56 7.9701 Tf 2.883 0 Td [(,)]TJ/F68 7.9701 Tf -55.266 -8.966 Td [(C)]TJ/F37 5.9776 Tf 6.599 2.813 Td [(0)]TJ/F67 7.9701 Tf 5.036 -2.813 Td [(=)-295([)]TJ/F68 7.9701 Tf 11.291 0 Td [(C)]TJ/F67 7.9701 Tf 6.599 0 Td [([1])]TJ/F68 7.9701 Tf 8.939 0 Td [(;)-177(:)-177(:)-177(:)-177(;)-178(p)]TJ/F67 7.9701 Tf 23.081 0 Td [([)]TJ/F68 7.9701 Tf 2.353 0 Td [(i)]TJ/F67 7.9701 Tf 2.883 0 Td [(])]TJ/F68 7.9701 Tf 2.352 0 Td [(;)-177(:)-177(:)-177(:)-178(;)-177(C)]TJ/F67 7.9701 Tf 25.417 0 Td [([)]TJ/F68 7.9701 Tf 2.353 0 Td [(D)]TJ/F67 7.9701 Tf 7.182 0 Td [(]])]TJ/F68 7.9701 Tf -104.085 -8.966 Td [(d)]TJ/F37 5.9776 Tf 4.357 2.812 Td [(00)]TJ/F67 7.9701 Tf 7.223 -2.812 Td [(=)]TJ/F68 7.9701 Tf 8.939 0 Td [(d)]TJ/F37 5.9776 Tf 4.357 2.812 Td [(0)]TJ/F56 7.9701 Tf -24.876 -11.779 Td [(if)-250(\050)]TJ/F68 7.9701 Tf 9.516 0 Td [(C)]TJ/F67 7.9701 Tf 6.599 0 Td [([)]TJ/F68 7.9701 Tf 2.352 0 Td [(i)]TJ/F67 7.9701 Tf 2.883 0 Td [(])-295(==)]TJ/F69 7.9701 Tf 20.23 0 Td [(\000)]TJ/F68 7.9701 Tf 6.587 0 Td [(")]TJ/F56 7.9701 Tf 3.91 0 Td [(\051)]TJ/F68 7.9701 Tf 4.647 0 Td [(d)]TJ/F37 5.9776 Tf 4.357 2.813 Td [(00)]TJ/F67 7.9701 Tf 7.223 -2.813 Td [(=)]TJ/F68 7.9701 Tf 8.939 0 Td [(d)]TJ/F37 5.9776 Tf 4.357 2.813 Td [(0)]TJ/F67 7.9701 Tf 4.566 -2.813 Td [(+)-236(1)]TJ/F68 7.9701 Tf -86.166 -8.966 Td [(v)]TJ/F56 7.9701 Tf 6.402 0 Td [(=)-250(QuickCorners\050)]TJ/F67 7.9701 Tf 53.853 0 Td [(\001)]TJ/F33 5.9776 Tf 7.057 2.813 Td [(+)]TJ/F56 7.9701 Tf 6.089 -2.813 Td [(,)]TJ/F67 7.9701 Tf 3.985 0 Td [(\001)]TJ/F37 5.9776 Tf 7.057 2.813 Td [(\000)]TJ/F56 7.9701 Tf 6.254 -2.813 Td [(,)]TJ/F68 7.9701 Tf 3.985 0 Td [(S)]TJ/F37 5.9776 Tf 5.596 2.813 Td [(\000)]TJ/F56 7.9701 Tf 6.254 -2.813 Td [(,)]TJ/F68 7.9701 Tf 3.985 0 Td [(C)]TJ/F37 5.9776 Tf 6.599 2.813 Td [(0)]TJ/F56 7.9701 Tf 2.684 -2.813 Td [(,)]TJ/F68 7.9701 Tf 3.985 0 Td [(d)]TJ/F56 7.9701 Tf 4.357 0 Td [(,)]TJ/F68 7.9701 Tf 3.985 0 Td [(d)]TJ/F37 5.9776 Tf 4.358 2.813 Td [(00)]TJ/F56 7.9701 Tf 4.87 -2.813 Td [(\051)]TJ -141.355 -8.967 Td [(if)-250(\050)]TJ/F68 7.9701 Tf 9.516 0 Td [(v)-331(>)-295(v)]TJ/F37 5.9776 Tf 20.11 2.813 Td [(\003)]TJ/F67 7.9701 Tf 4.317 -2.813 Td [(\051)]TJ/F68 7.9701 Tf 3.293 0 Td [(thenv)]TJ/F37 5.9776 Tf 21.414 2.813 Td [(\003)]TJ/F67 7.9701 Tf 6.67 -2.813 Td [(=)]TJ/F68 7.9701 Tf 8.939 0 Td [(v)]TJ/F67 7.9701 Tf 4.409 0 Td [(;)]TJ/F68 7.9701 Tf 3.764 0 Td [(C)]TJ/F37 5.9776 Tf 6.599 2.813 Td [(\003)]TJ/F67 7.9701 Tf 6.669 -2.813 Td [(=)]TJ/F68 7.9701 Tf 8.939 0 Td [(C)]TJ/F37 5.9776 Tf 6.598 2.813 Td [(0)]TJ/F56 7.9701 Tf 4.677 -2.813 Td [(endif)]TJ -124.914 -8.966 Td [(end)-250(foreach)]TJ -10.993 -8.966 Td [(\0506\051)]TJ/F68 7.9701 Tf 11.286 0 Td [(C)]TJ/F67 7.9701 Tf 8.951 0 Td [(=)]TJ/F68 7.9701 Tf 8.939 0 Td [(C)]TJ/F37 5.9776 Tf 6.598 2.812 Td [(\003)]TJ/F55 7.9701 Tf -35.774 -17.145 Td [(V)92(alidCor)15(ner\050C,)]TJ/F68 7.9701 Tf 54.93 0 Td [(S)]TJ/F37 5.9776 Tf 5.596 2.813 Td [(\000)]TJ/F55 7.9701 Tf 6.254 -2.813 Td [(\051)]TJ/F56 7.9701 Tf -66.78 -8.966 Td [(\0501\051)-250(foreach)]TJ/F68 7.9701 Tf 37.173 0 Td [(p)]TJ/F69 7.9701 Tf 6.615 0 Td [(2)]TJ/F68 7.9701 Tf 7.998 0 Td [(S)]TJ/F37 5.9776 Tf 5.595 2.813 Td [(\000)]TJ/F56 7.9701 Tf -57.381 -11.78 Td [(\0502\051)-1379(if)]TJ/F68 7.9701 Tf 27.148 0 Td [(p)]TJ/F56 7.9701 Tf 6.255 0 Td [(strongly)-250(dominates)]TJ/F68 7.9701 Tf 62.876 0 Td [(C)]TJ/F56 7.9701 Tf -69.086 -8.966 Td [(return)-250(f)10(alse)]TJ -27.193 -8.966 Td [(\0503\051)-250(return)-250(true)]TJ/F55 7.9701 Tf 0 -17.933 Td [(AdjustCor)15(ner\050r)18(ef)]TJ/F68 7.9701 Tf 61.928 0 Td [(C)]TJ/F55 7.9701 Tf 6.598 0 Td [(,)]TJ/F67 7.9701 Tf 3.985 0 Td [(\001)]TJ/F33 5.9776 Tf 7.057 2.813 Td [(+)]TJ/F55 7.9701 Tf 6.089 -2.813 Td [(\051)]TJ/F56 7.9701 Tf -85.657 -8.966 Td [(foreach)-250(dimension)]TJ/F68 7.9701 Tf 61.091 0 Td [(i)]TJ -41.098 -8.967 Td [(C)]TJ/F37 5.9776 Tf 6.599 2.813 Td [(0)]TJ/F67 7.9701 Tf 2.684 -2.813 Td [([)]TJ/F68 7.9701 Tf 2.352 0 Td [(i)]TJ/F67 7.9701 Tf 2.883 0 Td [(])]TJ/F56 7.9701 Tf 4.345 0 Td [(=)-250(MIN)]TJ/F69 7.9701 Tf 23.974 0 Td [(f)]TJ/F68 7.9701 Tf 4.234 0 Td [(p)]TJ/F67 7.9701 Tf 4.263 0 Td [([)]TJ/F68 7.9701 Tf 2.352 0 Td [(i)]TJ/F67 7.9701 Tf 2.883 0 Td [(])]TJ/F56 7.9701 Tf 4.345 0 Td [(such)-250(that)]TJ/F68 7.9701 Tf 30.549 0 Td [(p)]TJ/F69 7.9701 Tf 6.616 0 Td [(2)]TJ/F67 7.9701 Tf 7.997 0 Td [(\001)]TJ/F33 5.9776 Tf 7.057 2.813 Td [(+)]TJ/F56 7.9701 Tf 8.081 -2.813 Td [(strongly)-250(dominates)]TJ/F68 7.9701 Tf 62.876 0 Td [(C)]TJ/F69 7.9701 Tf 6.598 0 Td [(g)]TJ/F56 7.9701 Tf -210.681 -8.966 Td [(end)-250(foreach)]TJ/F68 7.9701 Tf 0 -8.967 Td [(C)]TJ/F67 7.9701 Tf 8.951 0 Td [(=)]TJ/F35 5.9776 Tf 10.135 3.361 Td [(C)]TJ/F33 5.9776 Tf 5.696 0 Td [(+)]TJ/F35 5.9776 Tf 5.59 0 Td [(C)]TJ/F12 4.9813 Tf 5.696 2.509 Td [(0)]TJ ET q 1 0 0 1 329.92 441.272 cm []0 d 0 J 0.359 w 0 0 m 19.677 0 l S Q BT /F33 5.9776 Tf 337.932 436.154 Td [(2)]TJ/F55 8.9664 Tf 6.247 -17.298 Td [(Figur)18(e)-250(5:)-310(Maximum)]TJ/F31 8.9664 Tf 79.818 0 Td [(0)]TJ/F55 8.9664 Tf 4.607 0 Td [(-neg)-250(r)18(ectangle)-250(algorithm)]TJ -117.77 -19.882 Td [(Step)-569(2)]TJ/F31 8.9664 Tf 26.521 0 Td [(|)]TJ/F55 8.9664 Tf 9.216 0 Td [(QuickCor)15(ners)]TJ/F56 8.9664 Tf 54.658 0 Td [(:)-948(W)80(e)-568(recursi)25(v)15(ely)-569(e)15(xplore)-569(the)-569(similarity)]TJ -90.395 -10.461 Td [(space.)-496(Eac)1(h)-312(call)-312(to)-312(the)-312(recursi)25(v)15(e)-312(algorithm)-311(tak)10(es)-312(a)-312(corner)]TJ/F34 8.9664 Tf 213.156 0 Td [(C)]TJ/F56 8.9664 Tf 10.012 0 Td [(which)]TJ -223.168 -10.461 Td [(de\002nes)-203(a)-203(candidate)-203(h)5(yper)20(-rectangle)]TJ/F34 8.9664 Tf 127.062 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(C)]TJ/F31 8.9664 Tf 7.215 0 Td [(\051)]TJ/F56 8.9664 Tf 3.584 0 Td [(.)-294(Initially)65(,)-213(we)-203(start)-203(with)]TJ -162.764 -10.461 Td [(the)-259(corner)]TJ ET q 1 0 0 1 349.328 374.23 cm []0 d 0 J 0.379 w 0 0 m 11.446 0 l S Q BT /F36 8.9664 Tf 349.328 367.592 Td [(\000)]TJ/F34 8.9664 Tf 7.168 0 Td [(")]TJ/F56 8.9664 Tf 4.278 0 Td [(,)-261(where)-258(each)-259(attrib)20(ute)-258(v)25(alue)-259(is)-258(set)-259(to)-259(the)-258(lo)25(west)-259(bound-)]TJ -49.94 -10.461 Td [(ary)-313(v)25(alue.)-498(Gi)25(v)15(en)-313(a)-313(corner)]TJ/F34 8.9664 Tf 97.017 0 Td [(C)]TJ/F56 8.9664 Tf 7.216 0 Td [(,)-329(we)-312(\002rst)-313(check)-313(whether)-313(or)-313(not)-313(we)-313(ca)1(n)]TJ -104.233 -10.461 Td [(stop.)-304(W)80(e)-231(stop)-232(when)-232(we)-231(\002nd)-232(a)-231(v)25(alid)-232(rectangle)-231(or)-232(when)-231(we)-232(cannot)-231(\002nd)]TJ 0 -10.461 Td [(a)-356(v)25(alid)-357(re)1(ctangle.)-629(If)-356(we)-357(found)-356(a)-356(v)25(alid)-356(h)5(yper)20(-rectangle,)-383(the)-356(current)]TJ 0 -10.461 Td [(QuickCorners)-239(call)-240(returns)-239(the)-240(num)1(ber)-240(of)-239(positi)25(v)15(e)-240(points)-239(contained)-239(in)]TJ/F34 8.9664 Tf 0 -10.46 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(C)]TJ/F31 8.9664 Tf 7.215 0 Td [(\051)]TJ/F56 8.9664 Tf 3.584 0 Td [(.)-569(If)-336(we)-337(determined)-336(that)]TJ/F34 8.9664 Tf 89.623 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(C)]TJ/F31 8.9664 Tf 7.215 0 Td [(\051)]TJ/F56 8.9664 Tf 6.6 0 Td [(cannot)-336(contain)-337(a)-336(v)25(alid)]TJ -164.043 -10.461 Td [(rectangle,)-302(we)-292(return)]TJ/F31 8.9664 Tf 74.912 0 Td [(0)]TJ/F56 8.9664 Tf 4.607 0 Td [(.)-435(W)80(e)-292(discuss)-292(the)-292(stopping)-291(conditions)-292(after)-292(we)]TJ -79.519 -10.461 Td [(discuss)-250(the)-250(sub-re)15(gion)-250(enumeration.)]TJ/F55 8.9664 Tf 0 -10.461 Td [(Step)-227(2.1)]TJ/F31 8.9664 Tf 30.185 0 Td [(|)]TJ/F55 8.9664 Tf 9.216 0 Td [(New)-227(ur)18(ect)-228(enumeration)]TJ/F56 8.9664 Tf 89.572 0 Td [(:)-299(If)-227(we)-228(could)-227(not)-228(stop,)]TJ/F34 8.9664 Tf 80.406 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(C)]TJ/F31 8.9664 Tf 7.216 0 Td [(\051)]TJ/F56 8.9664 Tf -241.498 -10.46 Td [(must)-235(contain)-236(at)-235(least)-236(one)-235(ne)15(g)5(ati)25(v)15(e)-236(sk)15(yline)-235(point)-236(which)-235(strongly)-235(dom-)]TJ 0 -10.461 Td [(inates)]TJ/F34 8.9664 Tf 24.107 0 Td [(C)]TJ/F56 8.9664 Tf 7.215 0 Td [(.)-627(\050Otherwise,)-382(from)-355(Property)-356(1)-355(we)-356(kno)25(w)-355(that)]TJ/F34 8.9664 Tf 168.889 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050)]TJ/F34 8.9664 Tf 3.583 0 Td [(C)]TJ/F31 8.9664 Tf 7.216 0 Td [(\051)]TJ/F56 8.9664 Tf 6.772 0 Td [(is)]TJ -239.101 -10.461 Td [(a)-434(v)25(alid)-434(rectangle)-434(and)-434(we)-435(w)10(ould)-434(ha)20(v)15(e)-434(stopped.\051)-862(Among)-434(all)-434(such)]TJ 0 -10.461 Td [(strongly)-401(dominating)-400(ne)15(g)5(ati)25(v)15(e)-401(sk)15(yline)-401(points,)-438(we)-401(choos)1(e)-401(a)-401(point)]TJ/F34 8.9664 Tf 240.455 0 Td [(p)]TJ/F56 8.9664 Tf -240.455 -10.461 Td [(uniformly)-201(at)-200(random)-201(and)-201(identify)-200(ne)25(w)-201(sub-re)15(gions)-201(of)]TJ/F34 8.9664 Tf 188.852 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(C)]TJ/F31 8.9664 Tf 7.216 0 Td [(\051)]TJ/F56 8.9664 Tf 5.383 0 Td [(to)-201(re-)]TJ -226.354 -10.46 Td [(curse)-266(on.)-356(The)-266(ne)25(w)-265(sub-re)15(gions)-266(are)-265(obtained)-266(by)-265(eliminating)]TJ/F34 8.9664 Tf 214.373 0 Td [(l)-17(r)-28(ect)]TJ/F31 8.9664 Tf 18.915 0 Td [(\050)]TJ/F34 8.9664 Tf 3.583 0 Td [(p)]TJ/F31 8.9664 Tf 4.627 0 Td [(\051)]TJ/F56 8.9664 Tf -241.498 -10.461 Td [(from)]TJ/F34 8.9664 Tf 20.457 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(C)]TJ/F31 8.9664 Tf 7.215 0 Td [(\051)]TJ/F56 8.9664 Tf 6.611 0 Td [(such)-337(that)-338(their)-337(union)-338(equals)]TJ/F34 8.9664 Tf 104.786 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.318 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(C)]TJ/F31 8.9664 Tf 7.216 0 Td [(\051)]TJ/F36 8.9664 Tf 6.229 0 Td [(\000)]TJ/F34 8.9664 Tf 9.813 0 Td [(l)-17(r)-28(ect)]TJ/F31 8.9664 Tf 18.914 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(p)]TJ/F31 8.9664 Tf 4.626 0 Td [(\051)]TJ/F56 8.9664 Tf 3.584 0 Td [(.)]TJ -242.84 -10.461 Td [(Consider)-356(the)-357(upper)-356(rectangles)-357(of)-356(ne)25(w)-357(corners)]TJ/F34 8.9664 Tf 171.044 0 Td [(C)]TJ/F33 5.9776 Tf 6.578 -0.996 Td [(1)]TJ/F34 8.9664 Tf 4.151 0.996 Td [(;)-171(:)-172(:)-171(:)-171(;)-171(C)]TJ/F35 5.9776 Tf 27.056 -0.996 Td [(D)]TJ/F56 8.9664 Tf 9.855 0.996 Td [(de\002ned)]TJ -218.684 -10.461 Td [(as)-324(follo)25(w)1(s:)]TJ/F34 8.9664 Tf 43.635 0 Td [(C)]TJ/F35 5.9776 Tf 6.578 -0.996 Td [(i)]TJ/F56 8.9664 Tf 6.062 0.996 Td [(is)-323(obtained)-324(by)-323(replacing)]TJ/F34 8.9664 Tf 90.793 0 Td [(C)]TJ/F31 8.9664 Tf 7.216 0 Td [([)]TJ/F34 8.9664 Tf 2.559 0 Td [(i)]TJ/F31 8.9664 Tf 3.154 0 Td [(])]TJ/F56 8.9664 Tf 5.46 0 Td [(with)]TJ/F34 8.9664 Tf 18.843 0 Td [(p)]TJ/F31 8.9664 Tf 4.626 0 Td [([)]TJ/F34 8.9664 Tf 2.56 0 Td [(i)]TJ/F31 8.9664 Tf 3.153 0 Td [(])]TJ/F56 8.9664 Tf 2.56 0 Td [(;)-360(on)-324(all)-323(other)]TJ -197.199 -10.46 Td [(dimensions)]TJ/F34 8.9664 Tf 43.565 0 Td [(j)]TJ/F36 8.9664 Tf 7.74 0 Td [(6)]TJ/F31 8.9664 Tf 0 0 Td [(=)]TJ/F34 8.9664 Tf 10.627 0 Td [(i;)-171(C)]TJ/F35 5.9776 Tf 13.827 -0.997 Td [(i)]TJ/F31 8.9664 Tf 3.161 0.997 Td [([)]TJ/F34 8.9664 Tf 2.56 0 Td [(j)]TJ/F31 8.9664 Tf 4.281 0 Td [(])-386(=)]TJ/F34 8.9664 Tf 16.646 0 Td [(C)]TJ/F31 8.9664 Tf 7.216 0 Td [([)]TJ/F34 8.9664 Tf 2.56 0 Td [(j)]TJ/F31 8.9664 Tf 4.281 0 Td [(])]TJ/F56 8.9664 Tf 2.56 0 Td [(.)-468(Intuiti)25(v)15(ely)65(,)-316(these)-303(ne)25(w)-302(upper)-303(rect-)]TJ -119.024 -10.461 Td [(angles)-315(are)-314(obtained)-315(by)-314(translating)-315(the)-314(original)-315(corner)]TJ/F34 8.9664 Tf 195.875 0 Td [(C)]TJ/F56 8.9664 Tf 10.036 0 Td [(along)-315(each)]TJ -205.911 -10.461 Td [(of)-308(the)-308(dimensions)-308(until)]TJ/F34 8.9664 Tf 86.772 0 Td [(p)]TJ/F56 8.9664 Tf 4.626 0 Td [(.)-484(W)80(e)-308(then)-309(call)-308(QuickCorners)-308(on)-308(each)-308(ne)25(w)]TJ -91.398 -10.461 Td [(corner)55(.)]TJ 8.967 -10.461 Td [(By)-466(construction,)-521(the)-466(point)]TJ/F34 8.9664 Tf 103.634 0 Td [(p)]TJ/F56 8.9664 Tf 8.807 0 Td [(cannot)-466(strongly)-466(dominate)-467(an)15(y)-466(of)]TJ -121.408 -10.46 Td [(the)-382(ne)25(w)-381(corners)]TJ/F34 8.9664 Tf 62.32 0 Td [(C)]TJ/F33 5.9776 Tf 6.578 -0.997 Td [(1)]TJ/F34 8.9664 Tf 4.151 0.997 Td [(;)-171(:)-172(:)-171(:)-171(;)-171(C)]TJ/F35 5.9776 Tf 27.057 -0.997 Td [(D)]TJ/F56 8.9664 Tf 6.659 0.997 Td [(.)-704(Therefore,)-415(the)-381(number)-382(of)-381(dominat-)]TJ -106.765 -10.461 Td [(ing)-392(ne)15(g)5(ati)25(v)15(e)-392(sk)15(yline)-392(points)-392(in)-393(each)]TJ/F34 8.9664 Tf 133.488 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(C)]TJ/F35 5.9776 Tf 6.577 -0.996 Td [(i)]TJ/F31 8.9664 Tf 3.162 0.996 Td [(\051)]TJ/F56 8.9664 Tf 7.1 0 Td [(is)-392(less)-392(than)-392(that)-392(of)]TJ/F34 8.9664 Tf -175.23 -10.461 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(C)]TJ/F31 8.9664 Tf 7.215 0 Td [(\051)]TJ/F56 8.9664 Tf 6.619 0 Td [(by)-338(at)-339(least)-338(one.)-576(Thus,)-360(each)-339(call)-338(to)-339(QuickCorners)-338(mak)10(es)]TJ -38.737 -10.461 Td [(de\002nite)-320(progress)-321(by)-320(eliminating)-320(at)-320(least)-321(one)-320(ne)15(g)5(ati)25(v)15(e)-320(sk)15(yline)-320(point.)]TJ 0 -10.46 Td [(Therefore,)-250(the)-250(algorithm)-250(terminates.)]TJ ET Q 1 0 0 1 295.992 36 cm 0 Tr /QQAPFce02551e 12 Tf 0 0 0 rg 100 Tz 0 Ts 0 Tw 0 Tc BT 1 0 0 1 0 0 Tm (332)Tj ET 1 0 0 1 0 0 cm 1 0 0 1 -295.992 -36 cm endstream endobj 80 0 obj << /Type /Page /Resources 79 0 R /MediaBox [ 0 0 612 792 ] /Parent 13 0 R /Contents [ 81 0 R ] >> endobj 79 0 obj << /Font << /F56 10 0 R /F34 12 0 R /F31 18 0 R /F36 8 0 R /F57 11 0 R /F37 55 0 R /F47 61 0 R /F55 9 0 R /F67 82 0 R /F33 51 0 R /F68 83 0 R /F69 84 0 R /F35 49 0 R /F12 85 0 R /QQAPFce02551e 232 0 R >> /ProcSet [ /PDF /Text ] >> endobj 90 0 obj << /Length 23818 /LC /QQAP >> stream q 1 0 0 1 86.333 622.999 cm q 0.98367 0 0 0.80562 0 0 cm q 1 0 0 1 0 0 cm /Im6 Do Q Q 1 0 0 1 -86.333 -622.999 cm BT /F55 8.9664 Tf 119.327 609.776 Td [(Figur)18(e)-250(6:)-310(Union)-250(of)-250(r)18(ectangles)]TJ -65.529 -21.527 Td [(Step)-327(2.2)]TJ/F31 8.9664 Tf 31.076 0 Td [(|)]TJ/F55 8.9664 Tf 9.216 0 Td [(Stopping)-327(and)-327(V)92(alidation)-326(Check)]TJ/F56 8.9664 Tf 121.57 0 Td [(:)-464(W)80(e)-327(no)25(w)-326(describe)-327(the)]TJ -161.862 -10.461 Td [(conditions)-228(for)-228(stopping)-228(and)-229(for)-228(determining)-228(whether)-228(or)-228(not)-228(we)-228(found)]TJ 0 -10.461 Td [(a)-433(v)25(alid)-433(h)5(yper)20(-rectangle)]TJ/F34 8.9664 Tf 89.373 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.318 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(C)]TJ/F31 8.9664 Tf 7.216 0 Td [(\051)]TJ/F56 8.9664 Tf 3.584 0 Td [(.)-859(The)-432(tw)10(o)-433(conditions)-433(when)-433(we)]TJ -125.075 -10.461 Td [(can)-308(stop)-308(are)-307(\050i\051)-308(we)-308(found)-308(a)-308(v)25(alid)-307(h)5(yper)20(-rectangle)-308(in)-308(that)-308(there)-308(is)-307(no)]TJ 0 -10.461 Td [(ne)15(g)5(ati)25(v)15(e)-262(point)-261(which)-262(strongly)-262(dominates)]TJ/F34 8.9664 Tf 148.172 0 Td [(C)]TJ/F56 8.9664 Tf 9.562 0 Td [(\050Property)-262(1\051,)-264(and)-262(\050ii\051)-262(we)]TJ -157.734 -10.46 Td [(are)-298(sure)-297(that)-298(there)-298(c)1(an)-298(be)-298(no)-297(v)25(alid)-298(h)5(yper)20(-rectangle)-298(in)]TJ/F34 8.9664 Tf 194.546 0 Td [(d)]TJ/F56 8.9664 Tf 7.443 0 Td [(dimensions,)]TJ -201.989 -10.461 Td [(i.e.,)]TJ/F34 8.9664 Tf 15.44 0 Td [(d)]TJ/F37 5.9776 Tf 4.775 3.809 Td [(0)]TJ/F34 8.9664 Tf 5.244 -3.809 Td [(>)-285(d)]TJ/F56 8.9664 Tf 16.744 0 Td [(from)-250(Property)-250(2.)]TJ/F55 8.9664 Tf -42.203 -20.922 Td [(Step)-250(3)]TJ/F31 8.9664 Tf 23.662 0 Td [(|)]TJ/F55 8.9664 Tf 9.216 0 Td [(Cor)15(ner)-250(Adjustment)]TJ/F56 8.9664 Tf 75.316 0 Td [(:)]TJ -99.227 -10.46 Td [(The)-564(rectangle)-564(returned)-565(by)-564(the)-564(maximum)-564(rectangle)-564(algorithm)]TJ -8.967 -10.461 Td [(touches)-280(the)-281(ne)15(g)5(ati)25(v)15(e)-280(points)-281(and)-280(may)-281(be)-280(f)10(ar)-281(from)-280(the)-281(positi)25(v)15(e)-280(points.)]TJ 0 -10.461 Td [(Once)-406(we)-405(ha)20(v)15(e)-406(identi\002ed)-406(the)-405(best)-406(v)25(alid)-406(rectangl)1(e,)-445(we)-406(can)-405(analyze)]TJ 0 -10.461 Td [(the)-370(distrib)20(ution)-371(of)-370(the)-370(positi)25(v)15(e)-371(points)-370(and)-370(\223mo)15(v)15(e\224)-371(the)-370(rectangle)-370(to)]TJ 0 -10.461 Td [(be)-397(closer)-396(to)-397(the)-397(positi)25(v)15(es.)-750(After)-397(we)-396(\002nd)-397(the)-397(best)-396(h)5(yper)20(-rectangle)]TJ/F34 8.9664 Tf 0 -10.46 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050)]TJ/F34 8.9664 Tf 3.583 0 Td [(C)]TJ/F31 8.9664 Tf 7.216 0 Td [(\051)]TJ/F56 8.9664 Tf 5.867 0 Td [(we)-255(adjust)-254(its)-255(corner)-254(such)-255(that)-255(the)-254(adjusted)-255(rectangle)-254(is)-255(be-)]TJ -37.985 -10.461 Td [(tween)-219(the)-219(positi)25(v)15(e)-219(points)-218(and)-219(ne)15(g)5(ati)25(v)15(e)-219(points.)-300(W)80(e)-219(\002rst)-219(\002nd)-218(the)-219(corner)]TJ/F34 8.9664 Tf 0 -10.461 Td [(C)]TJ/F37 5.9776 Tf 7.216 3.809 Td [(0)]TJ/F56 8.9664 Tf 5.1 -3.809 Td [(as)-269(follo)25(ws.)-369(On)-269(each)-269(dimension)]TJ/F34 8.9664 Tf 114.096 0 Td [(X)]TJ/F35 5.9776 Tf 7.612 -0.996 Td [(i)]TJ/F56 8.9664 Tf 5.577 0.996 Td [(in)-269(the)-270(rele)25(v)25(ant)-269(subset)-270(of)]TJ/F34 8.9664 Tf 88.328 0 Td [(d)]TJ/F56 8.9664 Tf 7.191 0 Td [(di-)]TJ -235.12 -10.461 Td [(mensions,)]TJ/F34 8.9664 Tf 39.096 0 Td [(C)]TJ/F37 5.9776 Tf 7.216 3.809 Td [(0)]TJ/F31 8.9664 Tf 2.684 -3.809 Td [([)]TJ/F34 8.9664 Tf 2.56 0 Td [(i)]TJ/F31 8.9664 Tf 3.153 0 Td [(])]TJ/F56 8.9664 Tf 5.392 0 Td [(is)-316(set)-316(to)-316(be)-315(the)-316(minimum)-316(attrib)20(ute)-316(v)25(alue)-316(among)-315(all)]TJ -60.101 -10.46 Td [(positi)25(v)15(e)-333(points)-334(in)]TJ/F34 8.9664 Tf 65.904 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(C)]TJ/F31 8.9664 Tf 7.215 0 Td [(\051)]TJ/F56 8.9664 Tf 3.584 0 Td [(.)-560(Note)-334(that)]TJ/F34 8.9664 Tf 44.124 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.318 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(C)]TJ/F37 5.9776 Tf 7.216 3.809 Td [(0)]TJ/F36 8.9664 Tf 5.301 -3.809 Td [(\000)]TJ ET q 1 0 0 1 246.732 405.14 cm []0 d 0 J 0.379 w 0 0 m 3.734 0 l S Q BT /F34 8.9664 Tf 246.732 399.955 Td [(\017)]TJ/F31 8.9664 Tf 3.734 0 Td [(\051)]TJ/F56 8.9664 Tf 6.573 0 Td [(contains)-333(all)]TJ -203.241 -10.461 Td [(positi)25(v)15(e)-370(points)-371(in)]TJ/F34 8.9664 Tf 66.902 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.318 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(C)]TJ/F31 8.9664 Tf 7.216 0 Td [(\051)]TJ/F56 8.9664 Tf 6.905 0 Td [(b)20(ut)-371(t)1(here)-371(does)-370(not)-371(e)15(xist)-370(another)-371(point)]TJ/F34 8.9664 Tf -105.925 -10.461 Td [(C)]TJ/F37 5.9776 Tf 7.216 3.809 Td [(00)]TJ/F56 8.9664 Tf 8.158 -3.809 Td [(which)-367(\050i\051)-366(dominates)]TJ/F34 8.9664 Tf 77.102 0 Td [(C)]TJ/F37 5.9776 Tf 7.216 3.809 Td [(0)]TJ/F56 8.9664 Tf 5.972 -3.809 Td [(and)-367(\050ii\051)-366(contains)-367(all)-367(positi)25(v)15(e)-366(points)-367(in)]TJ/F34 8.9664 Tf -105.664 -10.461 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(C)]TJ/F31 8.9664 Tf 7.215 0 Td [(\051)]TJ/F56 8.9664 Tf 3.584 0 Td [(.)-580(Intuiti)25(v)15(ely)65(,)]TJ/F34 8.9664 Tf 49.353 0 Td [(C)]TJ/F37 5.9776 Tf 7.216 3.809 Td [(0)]TJ/F56 8.9664 Tf 5.732 -3.809 Td [(de\002nes)-340(the)-340(corner)-340(until)-340(which)]TJ/F34 8.9664 Tf 112.857 0 Td [(C)]TJ/F56 8.9664 Tf 10.264 0 Td [(can)-340(be)]TJ -221.124 -10.46 Td [(pushed)-265(to)25(w)10(ards)-265(the)-265(positi)25(v)15(e)-266(points)-265(without)-265(reducing)-265(the)-265(co)15(v)15(erage)-265(of)]TJ/F34 8.9664 Tf 0 -10.461 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050)]TJ/F34 8.9664 Tf 3.583 0 Td [(C)]TJ/F31 8.9664 Tf 7.216 0 Td [(\051)]TJ/F56 8.9664 Tf 5.826 0 Td [(with)-250(respect)-250(to)]TJ/F31 8.9664 Tf 55.035 0 Td [(\001)]TJ/F33 5.9776 Tf 7.679 3.809 Td [(+)]TJ/F56 8.9664 Tf 6.088 -3.809 Td [(.)]TJ -97.779 -10.461 Td [(The)-334(ne)25(w)-334(adjusted)-334(corner)]TJ/F34 8.9664 Tf 93.417 0 Td [(C)]TJ/F35 5.9776 Tf 6.578 -0.996 Td [(new)]TJ/F56 8.9664 Tf 17.114 0.996 Td [(is)-334(the)-334(a)20(v)15(erage)-334(of)]TJ/F34 8.9664 Tf 63.946 0 Td [(C)]TJ/F56 8.9664 Tf 10.21 0 Td [(and)]TJ/F34 8.9664 Tf 15.942 0 Td [(C)]TJ/F37 5.9776 Tf 7.216 3.809 Td [(0)]TJ/F56 8.9664 Tf 2.684 -3.809 Td [(.)-562(W)80(e)]TJ -226.074 -10.461 Td [(note)-250(that)-250(other)-250(adjustment)-250(policies)-250(may)-250(be)-250(easily)-250(adopted.)]TJ 8.966 -10.461 Td [(In)-494(Figure)-494(4,)]TJ/F34 8.9664 Tf 51.439 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050[)]TJ/F34 8.9664 Tf 6.144 0 Td [(P)]TJ/F31 8.9664 Tf 7.163 0 Td [(2[)]TJ/F34 8.9664 Tf 7.168 0 Td [(X)]TJ/F31 8.9664 Tf 8.314 0 Td [(1])]TJ/F34 8.9664 Tf 7.167 0 Td [(;)-171(P)]TJ/F31 8.9664 Tf 11.26 0 Td [(3[)]TJ/F34 8.9664 Tf 7.167 0 Td [(X)]TJ/F31 8.9664 Tf 8.314 0 Td [(2]]\051)]TJ/F56 8.9664 Tf 17.74 0 Td [(w)10(ould)-494(be)-494(returned)-494(by)]TJ -162.161 -10.46 Td [(QuickCorners.)-642(And,)]TJ/F34 8.9664 Tf 79.458 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.318 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(C)]TJ/F37 5.9776 Tf 7.216 3.809 Td [(0)]TJ/F31 8.9664 Tf 2.684 -3.809 Td [(\051)]TJ/F56 8.9664 Tf 6.816 0 Td [(is)-361(the)-360(minimal)-361(rectangle)-360(touching)]TJ -121.076 -10.461 Td [(positi)25(v)15(e)-316(points)-316(in)]TJ/F34 8.9664 Tf 65.442 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.318 0 Td [(\050[)]TJ/F34 8.9664 Tf 6.144 0 Td [(P)]TJ/F31 8.9664 Tf 7.163 0 Td [(2[)]TJ/F34 8.9664 Tf 7.168 0 Td [(X)]TJ/F31 8.9664 Tf 8.314 0 Td [(1])]TJ/F34 8.9664 Tf 7.167 0 Td [(;)-171(P)]TJ/F31 8.9664 Tf 11.26 0 Td [(3[)]TJ/F34 8.9664 Tf 7.167 0 Td [(X)]TJ/F31 8.9664 Tf 8.314 0 Td [(2]]\051)]TJ/F56 8.9664 Tf 13.311 0 Td [(.)-509(W)80(e)-316(adjust)-316(the)-316(corner)]TJ -162.768 -10.461 Td [(to)-250(be)-250(the)-250(a)20(v)15(erage)-250(of)]TJ/F31 8.9664 Tf 72.636 0 Td [([)]TJ/F34 8.9664 Tf 2.56 0 Td [(P)]TJ/F31 8.9664 Tf 7.164 0 Td [(2[)]TJ/F34 8.9664 Tf 7.167 0 Td [(X)]TJ/F31 8.9664 Tf 8.314 0 Td [(1])]TJ/F34 8.9664 Tf 7.168 0 Td [(;)-171(P)]TJ/F31 8.9664 Tf 11.259 0 Td [(3[)]TJ/F34 8.9664 Tf 7.168 0 Td [(X)]TJ/F31 8.9664 Tf 8.314 0 Td [(2]])]TJ/F56 8.9664 Tf 11.969 0 Td [(and)]TJ/F34 8.9664 Tf 15.189 0 Td [(C)]TJ/F37 5.9776 Tf 7.215 3.809 Td [(0)]TJ/F56 8.9664 Tf 2.685 -3.809 Td [(.)]TJ/F53 8.9664 Tf -168.808 -14.496 Td [(Pruning)-278(Corner)15(s)-278(Optimization)]TJ/F56 8.9664 Tf 0 -10.46 Td [(In)-365(the)-366(QuickCorners)-365(algorithm,)-394(it)-365(is)-365(further)-366(possible)-365(to)-365(a)20(v)20(oid)-365(pro-)]TJ 0 -10.461 Td [(cessing)-311(a)-310(rectangle)]TJ/F34 8.9664 Tf 71.593 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(C)]TJ/F31 8.9664 Tf 7.216 0 Td [(\051)]TJ/F56 8.9664 Tf 6.368 0 Td [(for)-311(the)-310(best)-311(rectangle)-310(when)-311(we)-310(kno)25(w)]TJ -110.08 -10.461 Td [(that)-336(an)15(y)-336(rectangle)]TJ/F34 8.9664 Tf 68.161 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.318 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(C)]TJ/F37 5.9776 Tf 7.216 3.809 Td [(0)]TJ/F31 8.9664 Tf 2.684 -3.809 Td [(\051)]TJ/F56 8.9664 Tf 6.596 0 Td [(contained)-336(in)]TJ/F34 8.9664 Tf 47.861 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(C)]TJ/F31 8.9664 Tf 7.216 0 Td [(\051)]TJ/F56 8.9664 Tf 6.596 0 Td [(w)10(ould)-336(ha)20(v)15(e)-336(a)]TJ -196.135 -10.461 Td [(quality)-250(less)-250(than)-250(that)-250(of)-250(the)-250(current)-250(best)-250(h)5(yper)20(-rectangle.)]TJ 8.967 -10.46 Td [(An)-474(upper)-474(bound)-474(on)-475(the)-474(quality)-474(of)-474(an)15(y)-474(rectangle)-474(contained)-474(in)]TJ/F34 8.9664 Tf -8.967 -10.461 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.319 0 Td [(\050)]TJ/F34 8.9664 Tf 3.583 0 Td [(C)]TJ/F31 8.9664 Tf 7.216 0 Td [(\051)]TJ/F56 8.9664 Tf 6.128 0 Td [(is)-284(the)-283(total)-284(number)-284(of)-284(positi)25(v)15(e)-283(points)-284(in)]TJ/F34 8.9664 Tf 145.03 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.318 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(C)]TJ/F31 8.9664 Tf 7.216 0 Td [(\051)]TJ/F56 8.9664 Tf 3.584 0 Td [(.)-411(Thus,)]TJ -218.978 -10.461 Td [(we)-233(can)-234(prune)]TJ/F34 8.9664 Tf 49.592 0 Td [(C)]TJ/F56 8.9664 Tf 9.307 0 Td [(to)-233(be)-234(not)-233(useful)-233(when)-233(the)-234(upper)-233(bound)-233(on)-234(ma)1(ximum)]TJ -58.899 -10.461 Td [(quality)-250(is)-250(less)-250(than)-250(the)-250(current)-250(best)-250(quality)65(.)]TJ/F55 8.9664 Tf 0 -12.478 Td [(Analysis)]TJ/F56 8.9664 Tf 32.386 0 Td [(:)-345(W)80(e)-268(no)25(w)-268(st)1(ate)-268(that)-268(the)-267(QuickCorners)-268(algorithm)-267(terminates)]TJ -32.386 -10.461 Td [(and)-250(discuss)-250(its)-250(comple)15(xity)65(.)]TJ 10.187 -18.386 Td [(T)]TJ/F56 7.1731 Tf 5.927 0 Td [(H)-62(E)-61(O)-62(R)-62(E)-61(M)]TJ/F56 8.9664 Tf 37.699 0 Td [(2.)]TJ/F57 8.9664 Tf 13.673 0 Td [(The)-375(Quic)20(kCorner)10(s)-375(algorithm)-375(terminates)-375(and)-375(r)37(e-)]TJ -67.486 -10.46 Td [(turns)-250(the)-250(maximum)]TJ/F34 8.9664 Tf 70.977 0 Td [(d)]TJ/F57 8.9664 Tf 4.775 0 Td [(-dimensional)-250(hyper)20(-r)37(ectangle)15(.)]TJ -75.752 -18.386 Td [(Comple)20(xity)-328(of)-327(Quic)20(kCorner)10(s)]TJ/F56 8.9664 Tf 104.049 0 Td [(:)-465(While)-328(processing)-328(each)-327(corner)]TJ/F34 8.9664 Tf 118.007 0 Td [(C)]TJ/F56 8.9664 Tf 7.216 0 Td [(,)-347(we)]TJ -229.272 -10.461 Td [(e)15(xamine)-333(each)-333(positi)25(v)15(e)-333(point)-333(to)-332(check)-333(whether)]TJ/F34 8.9664 Tf 170.802 0 Td [(C)]TJ/F56 8.9664 Tf 10.201 0 Td [(is)-333(v)25(alid.)-559(W)80(e)-332(may)]TJ -181.003 -10.461 Td [(then)-296(e)15(xamine)-297(each)-296(ne)15(g)5(ati)25(v)15(e)-297(sk)15(yline)-296(point)-297(to)-296(pick)-297(one)-296(at)-297(random)-296(for)]TJ 0 -10.46 Td [(recursing.)-527(The)-323(reduction)-322(in)-323(problem)-322(sizes)-323(depends)-322(on)-323(the)-322(distrib)20(u-)]TJ 0 -10.461 Td [(tion)-242(of)-242(sk)15(yline)-243(points.)-307(F)15(or)-242(instance)-242(when)]TJ/F34 8.9664 Tf 148.265 0 Td [(D)]TJ/F31 8.9664 Tf 10.414 0 Td [(=)-286(2)]TJ/F56 8.9664 Tf 14.335 0 Td [(,)-244(the)-242(number)-242(of)-242(sk)15(y-)]TJ 84.022 653.549 Td [(line)-323(points)-323(which)-324(dominate)-323(a)-323(ne)25(w)-323(corner)-323(is)-324(e)15(xpected)-323(to)-323(be)-323(half)-323(the)]TJ 0 -10.461 Td [(original)-313(num)1(ber)-313(of)-313(sk)15(yline)-312(points.)-498(Ho)25(we)25(v)15(er)40(,)-328(as)-312(for)-313(the)-312(randomized)]TJ 0 -10.461 Td [(con)40(v)15(e)15(x)-305(hull)-305(algorithms,)-318(it)-305(is)-305(hard)-304(to)-305(analyze)-305(the)-305(e)15(xpected)-304(reduction)]TJ 0 -10.46 Td [(especially)-224(for)-225(higher)-224(v)25(alues)-224(of)]TJ/F34 8.9664 Tf 109.429 0 Td [(D)]TJ/F56 8.9664 Tf 9.866 0 Td [(and)-224(we)-225(lea)20(v)15(e)-224(the)-224(analysis)-224(for)-225(future)]TJ -119.295 -10.461 Td [(w)10(ork.)-581(W)80(e)-340(demonstrate)-340(empirically)-340(that)-340(QuickCorners)-340(algorithm)-340(is)]TJ 0 -10.461 Td [(ef)25(\002cient)-260(e)25(v)15(en)-260(for)-260(lar)18(ge)]TJ/F34 8.9664 Tf 83.272 0 Td [(D)]TJ/F56 8.9664 Tf 10.187 0 Td [(v)25(alues)-260(\050up)-260(to)]TJ/F31 8.9664 Tf 48.608 0 Td [(30)]TJ/F56 8.9664 Tf 9.216 0 Td [(\051)-260(under)-260(the)-260(typical)-260(scenar)20(-)]TJ -151.283 -10.461 Td [(ios)-279(when)]TJ/F34 8.9664 Tf 34.891 0 Td [(d)]TJ/F56 8.9664 Tf 4.775 0 Td [(,)-286(the)-280(number)-279(of)-279(similarity)-279(functions)-279(allo)25(wed)-279(in)-280(similar)1(ity)]TJ -39.666 -10.46 Td [(joins,)-272(is)-268(sma)1(ll.)-363(Ev)15(en)-268(though)-267(we)-268(prefer)-268(that)-267(training)-268(time)-267(be)-268(not)-267(v)15(ery)]TJ 0 -10.461 Td [(lar)18(ge,)-271(our)-267(main)-267(performance)-267(and)-267(design)-267(criterion)-267(is)-267(that)-267(the)-266(time)-267(for)]TJ 0 -10.461 Td [(e)15(x)15(ecuting)-231(the)-231(resulting)-231(operator)-231(trees)-231(be)-231(less.)-304(As)-231(sho)25(wn)-231(in)-231(Section)-231(7,)]TJ 0 -10.461 Td [(e)15(x)15(ecution)-273(times)-274(are)-273(usually)-274(much)-273(lar)18(ger)-274(than)-273(training)-273(times)-274(for)-273(v)15(ery)]TJ 0 -10.461 Td [(lar)18(ge)-250(datasets.)]TJ/F55 11.9552 Tf 0 -18.901 Td [(4.3)-1000(Union)-250(of)-250(Similarity)-250(J)15(oins)]TJ/F56 8.9664 Tf 8.966 -12.951 Td [(As)-223(di)1(scussed)-223(earlier)40(,)-228(a)-222(single)-223(h)5(yper)20(-rectangle)]TJ/F31 8.9664 Tf 160.576 0 Td [(|)]TJ/F56 8.9664 Tf 9.216 0 Td [(equi)25(v)25(alently)65(,)-228(oper)20(-)]TJ -178.758 -10.461 Td [(ator)-214(tree)]TJ/F31 8.9664 Tf 29.301 0 Td [(|)]TJ/F56 8.9664 Tf 9.215 0 Td [(may)-214(not)-214(be)-214(able)-214(t)1(o)-214(co)15(v)15(er)-214(all)-214(the)-214(positi)25(v)15(e)-214(points.)-298(Therefore,)]TJ -38.516 -10.461 Td [(se)25(v)15(eral)-245(rectangles)-245(may)-246(ha)20(v)15(e)-245(to)-245(be)-245(used)-245(to)-246(impro)15(v)15(e)-245(the)-245(co)15(v)15(erage)-245(with)]TJ 0 -10.461 Td [(respect)-285(to)]TJ/F31 8.9664 Tf 37.473 0 Td [(\001)]TJ/F33 5.9776 Tf 7.679 3.809 Td [(+)]TJ/F56 8.9664 Tf 6.088 -3.809 Td [(.)-414(W)80(e)-285(no)25(w)-284(discuss)-285(an)-285(algori)1(thm)-285(to)-285(identify)-284(a)-285(good)-285(op-)]TJ -51.24 -10.46 Td [(erator)-250(tree)-250(\050in)]TJ/F34 8.9664 Tf 51.036 0 Td [(S)-57(J)-95(U)]TJ/F31 8.9664 Tf 19.308 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(d;)-171(K)]TJ/F31 8.9664 Tf 17.312 0 Td [(\051)]TJ/F56 8.9664 Tf 3.584 0 Td [(\051)-250(with)-250(at)-250(most)]TJ/F34 8.9664 Tf 51.807 0 Td [(K)]TJ/F56 8.9664 Tf 10.683 0 Td [(similarity)-250(joins.)]TJ -148.348 -10.461 Td [(W)80(e)-360(\002rst)-360(observ)15(e)-360(that)-361(this)-360(problem)-360(is)-360(similar)-360(to)-360(the)-360(set)-360(co)15(v)15(erage)]TJ -8.966 -10.461 Td [(problem)-223([26].)-300(Gi)25(v)15(en)-223(a)-223(collection)-222(of)-223(sets)]TJ/F36 8.9664 Tf 143.554 0 Td [(S)]TJ/F56 8.9664 Tf 8.242 0 Td [(and)-223(an)-222(inte)15(ger)]TJ/F34 8.9664 Tf 52.164 0 Td [(K)]TJ/F56 8.9664 Tf 8.442 0 Td [(,)-228(the)-223(goal)]TJ -212.402 -10.461 Td [(in)-213(the)-213(se)1(t)-213(co)15(v)15(erage)-213(problem)-213(is)-212(to)-213(pick)]TJ/F34 8.9664 Tf 133.527 0 Td [(K)]TJ/F56 8.9664 Tf 10.35 0 Td [(sets)]TJ/F36 8.9664 Tf 15.357 0 Td [(f)]TJ/F34 8.9664 Tf 4.608 0 Td [(S)]TJ/F33 5.9776 Tf 5.629 -0.996 Td [(1)]TJ/F34 8.9664 Tf 4.151 0.996 Td [(;)-171(:)-172(:)-171(:)-171(;)-171(S)]TJ/F35 5.9776 Tf 26.108 -0.996 Td [(K)]TJ/F36 8.9664 Tf 7.043 0.996 Td [(g)]TJ/F56 8.9664 Tf 6.516 0 Td [(such)-213(that)]TJ -213.289 -11.584 Td [(the)-267(total)-266(number)-267(of)-267(elements)-267(in)]TJ/F38 8.9664 Tf 114.962 6.725 Td [(S)]TJ/F35 5.9776 Tf 7.679 -2.463 Td [(K)]TJ 0 -7.002 Td [(i)]TJ/F33 5.9776 Tf 2.664 0 Td [(=1)]TJ/F34 8.9664 Tf 11.277 2.74 Td [(S)]TJ/F35 5.9776 Tf 5.629 -0.996 Td [(i)]TJ/F56 8.9664 Tf 5.554 0.996 Td [(is)-267(maximized.)-360(In)-267(our)-266(prob-)]TJ -147.765 -10.461 Td [(lem,)-246(by)-245(vie)25(wing)-245(each)]TJ/F31 8.9664 Tf 78.547 0 Td [(0)]TJ/F56 8.9664 Tf 4.608 0 Td [(-ne)15(g)-245(h)5(yper)20(-rectangle)-245(as)-245(a)-245(set)-245(in)-245(the)-245(collection)]TJ -83.155 -10.461 Td [(of)-362(sets,)-390(our)-362(problem)-362(of)-361(choosing)]TJ/F34 8.9664 Tf 124.564 0 Td [(K)]TJ/F56 8.9664 Tf 11.687 0 Td [(\050)]TJ/F31 8.9664 Tf 2.985 0 Td [(0)]TJ/F56 8.9664 Tf 4.608 0 Td [(-ne)15(g\051)-362(h)5(yper)20(-rectangles)-362(such)]TJ -143.844 -10.461 Td [(that)-278(their)-277(co)15(v)15(erage)-278(with)-278(respect)-278(to)]TJ/F31 8.9664 Tf 125.227 0 Td [(\001)]TJ/F33 5.9776 Tf 7.68 3.809 Td [(+)]TJ/F56 8.9664 Tf 8.578 -3.809 Td [(is)-278(maximized)-277(reduces)-278(to)-278(that)]TJ -141.485 -10.46 Td [(of)-254(choosing)-254(the)-254(best)]TJ/F34 8.9664 Tf 74.363 0 Td [(K)]TJ/F56 8.9664 Tf 10.721 0 Td [(sets.)-322(This)-255(relationship)-254(is)-254(the)-254(intuition)-254(behind)]TJ -85.084 -10.461 Td [(the)-250(follo)25(wing)-250(result.)]TJ 10.187 -20.332 Td [(T)]TJ/F56 7.1731 Tf 5.927 0 Td [(H)-62(E)-61(O)-62(R)-62(E)-61(M)]TJ/F56 8.9664 Tf 37.699 0 Td [(3.)]TJ/F57 8.9664 Tf 10.311 0 Td [(The)-250(oper)15(ator)-250(tr)37(ee)-250(design)-250(pr)45(oblem)-250(is)-250(NP-har)37(d.)]TJ/F56 8.9664 Tf -55.158 -20.332 Td [(W)80(e)-228(adapt)-228(the)-227(greedy)-228(algorithm)-228(for)-228(the)-227(set)-228(co)15(v)15(erage)-228(problem)-228(to)-227(our)]TJ -8.966 -10.461 Td [(scenario.)-382(Our)-274(main)-275(observ)25(ation)-274(is)-274(that)-274(we)-274(can)-274(e)15(xploit)-274(our)-274(algorithm)]TJ 0 -10.461 Td [(\050in)-289(Section)-290(4.2\051)-289(to)-290(identify)-289(the)-289(best)-290(h)5(yper)20(-rectangle)-289(o)15(v)15(er)-290(a)-289(gi)25(v)15(en)-289(set)]TJ 0 -10.461 Td [(of)-215(e)15(xamples,)-222(and)-216(a)20(v)20(oid)-215(the)-215(enumeration)-216(of)-215(all)-215(v)25(alid)-215(h)5(yper)20(-rectangles,)]TJ 0 -10.46 Td [(which)-246(can)-245(be)-246(v)15(ery)-246(lar)18(ge.)-308(W)80(e)-246(can)-245(greedily)-246(pick)-246(the)-245(best)-246(rectangle,)-246(re-)]TJ 0 -10.461 Td [(mo)15(v)15(e)-320(the)-321(positi)25(v)15(e)-320(\050and)-321(ne)15(g)5(ati)25(v)15(e\051)-320(points)-320(contained)-321(in)-320(this)-320(rectangle,)]TJ 0 -10.461 Td [(and)-270(repeat)-269(the)-270(procedure)-270(on)-269(the)-270(remaining)-270(e)15(xamples.)-369(W)80(e)-270(stop)-269(when)]TJ 0 -10.461 Td [(we)-313(ha)20(v)15(e)-313(pick)10(ed)]TJ/F34 8.9664 Tf 59.306 0 Td [(K)]TJ/F56 8.9664 Tf 11.249 0 Td [(rectangles)-313(or)-313(when)-313(all)-313(positi)25(v)15(e)-313(e)15(xamples)-313(are)-313(re-)]TJ -70.555 -10.46 Td [(mo)15(v)15(ed.)-504(W)80(e)-315(no)25(w)-314(sho)25(w)-315(that)-315(this)-314(greedy)-315(strate)15(gy)-314(yields)-315(a)-315(good)-314(solu-)]TJ 0 -10.461 Td [(tion,)-253(which)-252(is)-253(within)-252(a)-252(f)10(actor)-253(of)-252(the)-252(optimal.)-317(The)-253(proof)-252(follo)25(ws)-252(from)]TJ 0 -10.461 Td [(the)-250(set)-250(co)15(v)15(erage)-250(problem)-250([26].)]TJ 10.187 -15.351 Td [(L)]TJ/F56 7.1731 Tf 5.927 0 Td [(E)-61(M)-63(M)-62(A)]TJ/F56 8.9664 Tf 28.849 0 Td [(4.)]TJ/F57 8.9664 Tf 9.565 0 Td [(Given)]TJ/F34 8.9664 Tf 23.405 0 Td [(K)]TJ/F57 8.9664 Tf 8.441 0 Td [(,)-228(the)-222(gr)37(eedy)-222(algorithm)-223(pic)20(ks)-222(an)-222(oper)15(ator)-222(tr)37(ee)]TJ -86.374 -10.461 Td [(whose)-285(co)10(ver)15(a)10(g)10(e)-284(with)-285(r)37(espect)-285(to)]TJ/F31 8.9664 Tf 115.626 0 Td [(\001)]TJ/F33 5.9776 Tf 7.679 3.809 Td [(+)]TJ/F57 8.9664 Tf 8.642 -3.809 Td [(is)-285(within)-284(a)-285(factor)-285(of)]TJ/F31 8.9664 Tf 74.049 0 Td [(\0501)]TJ/F36 8.9664 Tf 10.476 0 Td [(\000)]TJ/F33 5.9776 Tf 10.648 3.674 Td [(1)]TJ ET q 1 0 0 1 537.954 275.362 cm []0 d 0 J 0.379 w 0 0 m 3.653 0 l S Q BT /F35 5.9776 Tf 538.02 270.078 Td [(e)]TJ/F31 8.9664 Tf 4.783 3.043 Td [(\051)]TJ/F57 8.9664 Tf 6.137 0 Td [(of)]TJ -238.106 -10.461 Td [(the)-319(optimal)]TJ/F31 8.9664 Tf 44.083 0 Td [(0)]TJ/F57 8.9664 Tf 4.607 0 Td [(-ne)40(g)-319(oper)15(ator)-319(tr)37(ee)-320(containing)-319(a)-319(union)-319(of)]TJ/F34 8.9664 Tf 150.711 0 Td [(K)]TJ/F57 8.9664 Tf 11.304 0 Td [(similarity)]TJ -210.705 -10.461 Td [(joins.)]TJ/F55 11.9552 Tf 0 -15.721 Td [(4.4)]TJ/F34 8.9664 Tf 26.899 0 Td [(\014)]TJ/F55 11.9552 Tf 5.662 0 Td [(\255neg)-250(Operator)-250(T)74(r)18(ees)]TJ/F56 8.9664 Tf -23.594 -12.952 Td [(Often,)-371(allo)25(wing)-346(rectangles)-346(to)-347(contain)-346(a)-347(fe)25(w)-346(ne)15(g)5(ati)25(v)15(e)-347(points)-346(may)]TJ -8.967 -10.461 Td [(signi\002cantly)-207(impro)15(v)15(e)-207(the)-207(co)15(v)15(erage)-207(of)-207(the)-207(positi)25(v)15(e)-207(points.)-295(In)-207(this)-207(case,)]TJ 0 -10.46 Td [(the)-259(o)15(v)15(erall)-260(outline)-259(of)-259(the)-260(algorithm)-259(remains)-259(the)-259(same)-260(e)15(xcept)-259(the)-259(v)25(al-)]TJ 0 -10.461 Td [(idation.)-527(The)-322(outline)-322(of)-322(the)-322(modi\002ed)-323(v)25(alidation)-322(function)-322(is)-322(gi)25(v)15(en)-322(in)]TJ 0 -10.461 Td [(Figure)-338(7.)-575(The)-338(intuition)-338(is)-338(that)-339(a)-338(rectangle)]TJ/F34 8.9664 Tf 157.126 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.318 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(C)]TJ/F31 8.9664 Tf 7.216 0 Td [(\051)]TJ/F56 8.9664 Tf 6.616 0 Td [(is)-338(v)25(alid)-338(if)-339(the)]TJ -195.86 -10.461 Td [(number)-250(of)-250(ne)15(g)5(ati)25(v)15(es)-250(it)-250(contains)-250(is)-250(less)-250(than)-250(or)-250(equal)-250(to)]TJ/F34 8.9664 Tf 196.452 0 Td [(\014)]TJ/F36 8.9664 Tf 5.661 0 Td [(j)]TJ/F31 8.9664 Tf 2.559 0 Td [(\001)]TJ/F37 5.9776 Tf 7.68 3.809 Td [(\000)]TJ/F36 8.9664 Tf 6.254 -3.809 Td [(j)]TJ/F56 8.9664 Tf 2.56 0 Td [(.)]TJ -212.199 -10.46 Td [(Note)-318(that)-318(the)-318(modi\002ed)-318(algorithm)-318(when)-318(rectangles)-318(are)-318(allo)25(wed)-318(to)]TJ -8.967 -10.461 Td [(contain)-314(a)-314(small)-314(number)-313(of)-314(ne)15(g)5(ati)25(v)15(e)-314(points)-314(may)-314(not)-314(return)-314(the)-313(max-)]TJ 0 -10.461 Td [(imum)-307(v)25(alid)-307(rectangle.)-481(Ho)25(we)25(v)15(er)40(,)-321(in)-307(Section)-306(7,)-322(we)-307(empiric)1(ally)-307(sho)25(w)]TJ 0 -10.461 Td [(that)-392(the)-392(quality)-393(of)-392(the)-392(resulting)-392(h)5(yper)20(-rectangles)-392(is)-392(comparable)-392(to)]TJ 0 -10.461 Td [(some)-250(of)-250(the)-250(best)-250(kno)25(wn)-250(machine)-250(learning)-250(results.)]TJ/F55 11.9552 Tf 0 -20.816 Td [(5.)-1000(INCLUDING)-250(REN)20(AME)-250(OPERA)95(T)18(ORS)]TJ/F56 8.9664 Tf 8.967 -12.951 Td [(W)80(e)-410(no)25(w)-410(consider)-410(a)-410(more)-410(general)-410(class)-410(of)-410(operator)-410(trees,)-450(those)]TJ -8.967 -10.461 Td [(containing)-387(attrib)20(ute)-387(v)25(alue)-387(transformation)-388(operators,)-421(which)-387(we)-387(call)]TJ ET Q 1 0 0 1 295.992 36 cm 0 Tr /QQAPFce02551e 12 Tf 0 0 0 rg 100 Tz 0 Ts 0 Tw 0 Tc BT 1 0 0 1 0 0 Tm (333)Tj ET 1 0 0 1 0 0 cm 1 0 0 1 -295.992 -36 cm endstream endobj 89 0 obj << /Type /Page /Resources 88 0 R /MediaBox [ 0 0 612 792 ] /Parent 91 0 R /Contents [ 90 0 R ] >> endobj 86 0 obj << /Type /XObject /Subtype /Form /FormType 1 /PTEX.FileName (figures/UnionRect.pdf) /PTEX.PageNumber 1 /PTEX.InfoDict 92 0 R /BBox [0 0 183 143] /Resources << /ProcSet [ /PDF /Text ] /ExtGState << /R7 93 0 R >>/Font << /R11 94 0 R/R9 95 0 R/R8 96 0 R>> >> /Length 97 0 R /Filter /FlateDecode >> stream xZK\ F+r=ѓ]@PM.灹nR I3FwDE=moNx/Oϧo??b㻓=PvȺ3FNߩTKZ6@V0?@3 +H Ir 6o_MtO1a>l0oT@&=ٸS;O>ţbk4t HUWjl8Pj wQ.; ]|;!cQ#2ґ]߃,ԫNԞI]߁,35"oGFmDLdF;nC0iQfrUD,\7#̞^LL 4ZLd&\GtΎ^k ^ND=xb YF>'Pf{39Ɛro]y9sZ/3ܜ/yڛ2:=RI#'Zko/s90_S3%%M}; J$_zz@z*I>e] ֤ LcxƗ_6G9`(qN.CR,L.eç,$ )kȅOIu%,7!4lsۤEn=/Z =CiY#*O u%]W>dʣcv^/J!oOߕ vW?1t<# {-|;2Z'a*+)/hۢMԽЖU$:~QD it*)uRY,V>Mz{*o $ \lI_T)kZUkZ;ߐzWd}dUsV%szrܐ%?!:GKpVE-u(,ĂQ[|Fí W~%\H,32ixJ]0 #˩Rzܾ".Crl.۾NWmL(D7^#:NJފe1[+lʦ3`1Rkv@ 1IRΡFb︾CIҘ~ YzFmkRI LqbAeCa!Ԏ٧#./yNN+LfDsfʹğ~ *9[%\fY^i :qV;NW9+:2%v?0ZW7GR\4kR8O/J fD 6-fotE/r!܂H]nAϧ~τ$νyFt/n6;qCAZԅ! "o5[74.4*IӬ]zͨKH(I*=F*SaAPY jER//jGc8V0Z;0qNʲ-[?i97ʄَrve[R<³0#wްYy xކegĚMXP4;fCAXC<7␏DxWOv~clz䖨;ڏF endstream endobj 92 0 obj << /Producer (AFPL Ghostscript 8.53) /CreationDate (D:20070709232320) /ModDate (D:20070709232320) /Title (Microsoft Word - UnionRect.doc) /Creator (PScript5.dll Version 5.2.2) /Author (vganti) >> endobj 93 0 obj << /Type /ExtGState /OPM 1 >> endobj 94 0 obj << /BaseFont /KPSHBO#2BTimesNewRoman /FontDescriptor 98 0 R /ToUnicode 99 0 R /Type /Font /FirstChar 1 /LastChar 1 /Widths [ 420] /Encoding 100 0 R /Subtype /TrueType >> endobj 95 0 obj << /BaseFont /Courier /Type /Font /Subtype /Type1 >> endobj 96 0 obj << /BaseFont /Times-Roman /Type /Font /Subtype /Type1 >> endobj 97 0 obj 2994 endobj 98 0 obj << /Type /FontDescriptor /FontName /KPSHBO#2BTimesNewRoman /FontBBox [ 34 -13 638 625] /Flags 4 /Ascent 625 /CapHeight 625 /Descent -13 /ItalicAngle 0 /StemV 95 /MissingWidth 777 /FontFile2 101 0 R >> endobj 99 0 obj << /Filter /FlateDecode /Length 154 >> stream x]0C|ЪbKVe0KtNWM\=:1_"NTs"8_<頪@kV5[4#jںZk;1^lMR򇓫y1>%FH*X#8<[J}̠M endstream endobj 100 0 obj << /Type /Encoding /BaseEncoding /WinAnsiEncoding /Differences [ 1/epsilon] >> endobj 101 0 obj << /Filter /FlateDecode /Length1 13056 /Length 5807 >> stream xZ xTյ^{sf& C&!q2!0&(F2yLx!<͠ !Lb`-*QP Rr2 h%ZUVRS_ms}f@~w}kkgB촎Θ] *2qeCKRѸQ~%+kz2zɊ5Ë{Kd wP[DLjV476p*se-vOH +KA-ͭmz`Է\rlV JN#'0Wl"C 2>jP/'qT BGH;h;QMR/M]TN&!Ki {Ҩv9S5 a*Mҥt%}LGj~B4#h m0**t`|yKCxxcgtd@i4:ǔN%CF$Cl-#)J1Jq9M}&A"ZVՃl5 &CcrQ>]Hөлl-B¸҇ /+[~D-:F_v>խvyu=Bh6C!4Bvbn:jXgN0:x_b`mpM 3\Daz ~|MgxqIh&ͧfZMWXg9+'zg܆S|{#V)F=04,Ʊl[6;X{-Wτ.^+Q2i8bZѾ MӋl0g[h C^lVN7SF'YevzQe‡l9ke-11P8&b brGyO6{ Wf?B,YYlt=uҭȗhҋ& 0Jdzv+n{=^do$p_x%KzV~?QtumqBj0Yݨ>dyZ`l]h{NFN~OL'N/+34dV&)L\l>-dKl!~b]Ns8 v&;>c_p$1f/x̴O3, hWXx7WJ-~!o(\+EJP,QnP))(ߪN5.UZr,c,s--wYZ>Zօֵ7͋ט>:*bjr5?"K7+ĭwb'\=)ˍE5hfANT,Md=CD? ,*E VnP?%oS) TncGm5r)G :&~'/N~KW#6Jlƿd}Jg{d8[E-'bO߳blxMZ:x* L#Y-sS|ưKa#wN]t|0vYN_?%wlu#~YTL T{c@H:@.Zkc_S[NE,ցE&`/ǨvpgR"50v(ߍE{6>u)߆,.3#MA7WڅyZ?BeZ<y2;rpQL|wR%nqKi 6vc]mIyO=EG6bߞLa?, 4MTNme&Mxxxm襒˨-xBC%RcvާhU޳;;'T6^p Q# F{4>,7'{h֐̌Aiԁ)I6EUgkQՕ|mBY h8C]Uml,P2tڒ9\A ]aͥZzu(RE\q|Yb(h g-r, իvU+%RlJ.SWr )(C.6d"3 |Hl*ժ3U9nwЯFmNZ3MFTVs29vnq¨o"mQåuh1|Jrͱ<393%73Ժ%DЇνj !X|}Ng1KC)>&-,%.=IЖv.ba;u7Rv9Nse9Z*+:gr =[Sr505Q`?tZgLsYu:LzMA:F<0q4q0ah/z,ӓ*Rzkk|!!x_,,9hП*>>jLk%V>N4Wp]kq>El"E-wcOYhaNBEΣR{J3xԬ;9KWͪZsUwF;zu 5C/D]gK8zj{sMLb)+Ejs؆]!a6̩q+py& 엊XvnC^e昚bQ#f}vR9{y+п$^[lb̞@Of_[0^>B!n* gH#ϝh Zln*4G< 咊b9N &x6$G]=Rӄn3J;!<;Oբlז;DklQ>z(PڊVn+jz <2kcn\k @HEEE%lm ZجZجETE+kł Ľqrxؔt pǑfP42@cU@E4tZi@gJW"@6BJB `>FZ% G+8)T6`Y(ebj&YJKHSzSrrgQ]bKRkZZ,,[,;,I[,[<Ғ.E8R\))ie;׋u[[ b\K\j#ANx*jK]*BJRS [Ziͩ6ҾOj#@(h,fG͎V xuk”"k@O(bLSlOFdHc$2e偐$==^TfosANe6;`NL+T"oQANũ9NeN;4MtA9Aef:> 4XTQ::)ndIYz?+-Q>[n=p;PGĴr)aʝlpmn>nTU:$.#@ 1p? x?"!Nģ%=(w;mһLzIL8TS7N@gg[M+(,!&;lRO&nR(mW>}~[Žk&MGlI4?ⴿ_촏ulTa&͑}XjU*%=ɾ*bN)'N_6GOa~PW6%~󐿇ywV{|^s{lPpم q^磚ݩA,tޣwE=tVb':8= PڕaS8GHWǞǝ0bf2w~>YY{om.γδNX .0k5Önsؒm6Ŧظl=ѐOeX4"b\RqD ]SXY8_n[#|^/!Ah}<'Ɗߒ#D"Fm.٘G2^U"2WeOL_]=$,ߙW0u"z@a};K=RRY4zaJ^tyǚ=ߩ5oܝyq,bw6qdA†`*ƬEBT 7Ku ]E'6G6.I_kiUQ7JuVE9u]XC!5TEwuT֜5ͧǪ:dgr]5ߣ]r9VkWh9Vͬ VS[eN&)ɸ9HEeysLpg]s@!FCm IIrveO; ^t2He(;N.vӼ ,W.{"ҷRzI1Q*z;]==7:> /XObject << /Im6 86 0 R >> /ProcSet [ /PDF /Text ] >> endobj 104 0 obj << /Length 20077 /LC /QQAP >> stream q BT /F55 7.9701 Tf 53.798 731.57 Td [(V)92(alidCor)15(nerBeta\050C,)]TJ/F67 7.9701 Tf 70.424 0 Td [(\001)]TJ/F37 5.9776 Tf 7.057 2.813 Td [(\000)]TJ/F55 7.9701 Tf 6.254 -2.813 Td [(,)]TJ/F68 7.9701 Tf 3.985 0 Td [(\014)]TJ/F55 7.9701 Tf 5.161 0 Td [(\051)]TJ/F56 7.9701 Tf -92.881 -8.966 Td [(\0501\051)-250(Initialization:)]TJ/F68 7.9701 Tf 56.707 0 Td [(P)]TJ/F37 5.9776 Tf 5.369 -1.074 Td [(\000)]TJ/F67 7.9701 Tf 8.606 1.074 Td [(=)-295(0)]TJ/F56 7.9701 Tf 13.173 0 Td [(;)]TJ/F68 7.9701 Tf 4.208 0 Td [(B)]TJ/F67 7.9701 Tf 9.133 0 Td [(=)]TJ/F68 7.9701 Tf 8.939 0 Td [(\014)]TJ/F69 7.9701 Tf 7.043 0 Td [(\001)-236(j)]TJ/F67 7.9701 Tf 6.586 0 Td [(\001)]TJ/F37 5.9776 Tf 7.057 2.812 Td [(\000)]TJ/F69 7.9701 Tf 6.255 -2.812 Td [(j)]TJ/F56 7.9701 Tf -133.076 -8.967 Td [(\0502\051)-250(foreach)]TJ/F68 7.9701 Tf 37.173 0 Td [(p)]TJ/F69 7.9701 Tf 6.615 0 Td [(2)]TJ/F67 7.9701 Tf 7.998 0 Td [(\001)]TJ/F37 5.9776 Tf 7.057 2.813 Td [(\000)]TJ/F56 7.9701 Tf -58.843 -11.779 Td [(\0503\051)-2508(if)]TJ/F68 7.9701 Tf 36.148 0 Td [(p)]TJ/F56 7.9701 Tf 6.255 0 Td [(strongly)-250(dominates)]TJ/F68 7.9701 Tf 62.876 0 Td [(C)]TJ -67.286 -8.967 Td [(P)]TJ/F37 5.9776 Tf 5.369 -1.073 Td [(\000)]TJ/F67 7.9701 Tf 8.136 1.073 Td [(+)-236(+)]TJ/F56 7.9701 Tf -13.505 -8.966 Td [(if)]TJ/F68 7.9701 Tf 6.862 0 Td [(P)]TJ/F37 5.9776 Tf 5.369 -1.074 Td [(\000)]TJ/F68 7.9701 Tf 8.606 1.074 Td [(>)-295(B)]TJ/F56 7.9701 Tf 17.712 0 Td [(return)-250(f)10(alse)]TJ -56.549 -8.966 Td [(endif)]TJ -19.993 -8.967 Td [(\0504\051)-250(return)-250(true)]TJ/F55 8.9664 Tf 16.733 -25.803 Td [(Figur)18(e)-250(7:)-310(Generalization)-250(to)-250(\002nd)]TJ/F34 8.9664 Tf 123.662 0 Td [(\014)]TJ/F55 8.9664 Tf 5.661 0 Td [(-neg)-250(h)15(yper)37(-r)18(ectangles)]TJ ET 1 0 0 1 89.938 513.496 cm q 0.98183 0 0 0.80562 0 0 cm q 1 0 0 1 0 0 cm /Im7 Do Q Q 1 0 0 1 -89.938 -513.496 cm BT /F55 8.9664 Tf 126.594 500.273 Td [(Figur)18(e)-250(8:)-310(Rename)-250(bene\002t)]TJ/F57 8.9664 Tf -72.796 -24.039 Td [(r)37(ename)-253(oper)15(ator)10(s)]TJ/F56 8.9664 Tf 63.477 0 Td [(,)-254(in)-254(addition)-253(to)-254(similarity)-253(join)-254(and)-253(the)-253(union)-254(opera-)]TJ -63.477 -10.461 Td [(tors.)-325(F)15(or)-255(instance,)-256(the)-255(operator)-255(tree)-255(in)-255(Figure)-255(1)-255(illustrates)-255(a)-254(tree)-255(with)]TJ 0 -10.46 Td [(these)-250(operators.)-311(A)-251(rename)-250(operator)-250(is)-250(bene\002cial)-251(for)-250(record)-250(matching)]TJ 0 -10.461 Td [(if)-229(pairs)-229(of)-229(matching)-229(records)-229(become)-229(closer)-229(while)-229(non-matching)-229(pairs)]TJ 0 -10.461 Td [(mo)15(v)15(e)-215(f)10(arther)-215(a)15(w)10(ay)-215(according)-215(to)-216(one)-215(or)-215(more)-215(similarity)-215(functions.)-298(W)80(e)]TJ 0 -10.461 Td [(\002rst)-273(characterize)-273(the)-273(rename)-273(operators)-273(which)-273(can)-273(be)-273(included)-273(in)-273(our)]TJ 0 -10.461 Td [(frame)25(w)10(ork,)-263(gi)25(v)15(e)-260(a)-260(fe)25(w)-260(e)15(xample)-260(rename)-260(operators,)-263(and)-260(then)-260(describe)]TJ 0 -10.46 Td [(our)-250(algorithm.)]TJ/F55 8.9664 Tf 8.967 -10.461 Td [(Pr)18(operties)-225(of)-224(r)18(ename)-225(operators)]TJ/F56 8.9664 Tf 118.756 0 Td [(:)-297(An)15(y)-225(unary)-225(operator)]TJ/F34 8.9664 Tf 76.798 0 Td [(\032)]TJ/F56 8.9664 Tf 6.761 0 Td [(that)-225(tak)10(es)]TJ -211.282 -10.461 Td [(a)-274(threshold)-274(parameter)]TJ/F34 8.9664 Tf 80.566 0 Td [(\022)]TJ/F56 8.9664 Tf 7.025 0 Td [(as)-274(input)-274(and)-273(which)-274(\050i\051)-274(produces)-274(e)15(xactly)-274(one)]TJ -87.591 -10.461 Td [(output)-309(tuple)-310(for)-309(each)-310(input)-309(tuple,)-324(and)-310(\050ii\051)-309(commutes)-310(with)-309(the)-309(union)]TJ 0 -10.46 Td [(operator)-225(can)-226(be)-225(implemented)-225(as)-226(a)-225(ne)25(w)-225(rename)-225(operator)-226(in)-225(our)-225(frame-)]TJ 0 -10.461 Td [(w)10(ork.)-668(That)-369(is,)-399(applying)-369(the)-369(operator)-370(to)-369(a)-369(relation)]TJ/F34 8.9664 Tf 188.538 0 Td [(R)]TJ/F56 8.9664 Tf 10.347 0 Td [(is)-369(equi)25(v)25(alent)]TJ -198.885 -10.461 Td [(to)-330(applying)-330(the)-331(operator)-330(to)-330(each)-330(indi)25(vidual)-330(record)]TJ/F34 8.9664 Tf 185.322 0 Td [(r)]TJ/F36 8.9664 Tf 8.342 0 Td [(2)]TJ/F34 8.9664 Tf 10.073 0 Td [(R)]TJ/F56 8.9664 Tf 9.996 0 Td [(and)-330(then)]TJ -213.733 -10.461 Td [(taking)-250(the)-250(union)-250(o)15(v)15(er)-250(the)-250(results)-250(of)-250(each)-250(application.)]TJ/F55 8.9664 Tf 0 -14.495 Td [(Example)-324(r)18(ename)-323(operators)]TJ/F56 8.9664 Tf 105.251 0 Td [(:)-457(W)80(e)-324(no)25(w)-324(illustrate)-324(that)-323(se)25(v)15(eral)-324(useful)]TJ -105.251 -10.461 Td [(data)-192(cleaning)-192(operations)-192(can)-193(be)-192(instantiated)-192(from)-192(the)-192(rename)-192(operator)]TJ 0 -10.461 Td [(thus)-250(demonstrating)-250(the)-250(generality)-250(of)-250(its)-250(abstraction.)]TJ/F57 8.9664 Tf 8.967 -10.461 Td [(Fuzzy)-477(Lookup)-478(Oper)15(ator)]TJ/F56 8.9664 Tf 89.615 0 Td [(:)-765(Consider)-477(the)-477(use)-477(of)-478(domain-speci\002c)]TJ -98.582 -10.461 Td [(lookup)-301(tables)-300(for)-301(standardizing)-300(attrib)20(ute)-301(v)25(alues.)-462(F)15(or)-300(e)15(xample,)-313(State)]TJ 0 -10.46 Td [(v)25(alues)-388(in)-387(USA)-388(may)-388(be)-387(abbre)25(viated)-388(to)]TJ/F31 8.9664 Tf 144.408 0 Td [(2)]TJ/F56 8.9664 Tf 4.608 0 Td [(-character)-388(codes)-387(based)-388(on)]TJ -149.016 -10.461 Td [(a)-318(translation)-319(table)-318(obtained)-319(from)-318(the)-318(US)-319(postal)-318(service)-318(department.)]TJ 0 -10.461 Td [(Ho)25(we)25(v)15(er)40(,)-285(due)-278(to)-278(errors)-279(the)-278(input)-278(v)25(alues)-278(may)-278(not)-278(match)-278(e)15(xactly)-278(with)]TJ 0 -10.461 Td [(the)-263(non-abbre)25(viated)-262(state)-263(names.)-347(The)-263(fuzzy)-263(lookup)-262(operator)-263(may)-262(be)]TJ 0 -10.46 Td [(used)-250(in)-250(such)-250(scenarios)-250([13,)-250(35].)]TJ 8.967 -10.461 Td [(Gi)25(v)15(en)-388(an)-388(input)-389(re)1(lation)]TJ/F34 8.9664 Tf 89.768 0 Td [(R)]TJ/F56 8.9664 Tf 7.036 0 Td [(,)-423(a)-388(lookup)-388(table)]TJ/F34 8.9664 Tf 62.794 0 Td [(L)]TJ/F56 8.9664 Tf 6.271 0 Td [(,)-423(a)-388(sequence)-388(of)-388(at-)]TJ -174.836 -10.461 Td [(trib)20(utes)]TJ/F34 8.9664 Tf 28.951 0 Td [(A)]TJ/F56 8.9664 Tf 6.911 0 Td [(,)-249(a)-249(similarity)-249(function)]TJ/F34 8.9664 Tf 79.413 0 Td [(f)]TJ/F56 8.9664 Tf 7.68 0 Td [(o)15(v)15(er)]TJ/F34 8.9664 Tf 17.897 0 Td [(A)]TJ/F56 8.9664 Tf 6.91 0 Td [(,)-249(and)-249(a)-249(threshold)-249(parameter)]TJ/F34 8.9664 Tf -147.762 -10.461 Td [(\022)]TJ/F56 8.9664 Tf 4.57 0 Td [(,)-301(the)-291(fuzzy)-291(lookup)-291(operator)-291(joins)-291(for)-291(each)-291(record)]TJ/F34 8.9664 Tf 178.693 0 Td [(r)]TJ/F36 8.9664 Tf 7.673 0 Td [(2)]TJ/F34 8.9664 Tf 9.404 0 Td [(R)]TJ/F56 8.9664 Tf 7.035 0 Td [(,)-301(the)-291(v)25(alue)]TJ/F34 8.9664 Tf -207.375 -10.461 Td [(r)28(:)1(A)]TJ/F56 8.9664 Tf 15.354 0 Td [(with)-221(the)-221(most)-221(similar)-221(v)25(alue)]TJ/F34 8.9664 Tf 98.355 0 Td [(l)-17(:A)]TJ/F56 8.9664 Tf 14.351 0 Td [(if)]TJ/F34 8.9664 Tf 7.461 0 Td [(f)]TJ/F31 8.9664 Tf 5.448 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(r)29(:A;)-172(l)-16(:A)]TJ/F31 8.9664 Tf 29.836 0 Td [(\051)]TJ/F34 8.9664 Tf 6.144 0 Td [(>)-285(\022)]TJ/F56 8.9664 Tf 14.297 0 Td [(.)-300(When)-221(multi-)]TJ -194.83 -10.46 Td [(ple)]TJ/F34 8.9664 Tf 12.881 0 Td [(L:A)]TJ/F56 8.9664 Tf 17.665 0 Td [(v)25(alues)-215(ha)20(v)15(e)-214(the)-215(same)-214(highest)-215(similarity)-214(v)25(alue,)-222(an)15(y)-215(consistent)]TJ -30.546 -10.461 Td [(tie-breaking)-368(mechanism)-369(may)-368(be)-369(adopted.)-665(Note)-369(that)-368(we)-369(may)-368(vie)25(w)]TJ 0 -10.461 Td [(the)-255(fuzzy)-255(lookup)-256(operator)-255(as)-255(a)-255(similarity)-255(join)-256(operator)-255(follo)25(wed)-255(by)-255(a)]TJ 0 -10.461 Td [(T)80(op-)]TJ/F31 8.9664 Tf 16.713 0 Td [(1)]TJ/F56 8.9664 Tf 7.378 0 Td [(operator)55(.)-487(W)80(e)-309(encapsulate)-309(these)-309(together)-309(so)-309(that)-309(the)-309(encapsu-)]TJ -24.091 -10.46 Td [(lation)-315(\050i\051)-315(can)-315(be)-315(implemented)-315(as)-316(a)-315(rename)-315(operator)40(,)-331(and)-315(\050ii\051)-315(can)-315(be)]TJ 0 -10.461 Td [(implemented)-250(more)-250(ef)25(\002ciently)-250([13,)-250(34].)]TJ/F57 8.9664 Tf 8.966 -10.461 Td [(Column)-343(Se)40(gmentation)-342(and)-343(Concatenation)]TJ/F56 8.9664 Tf 152.32 0 Td [(:)-495(Consider)-343(an)-343(ope)1(rator)]TJ -161.286 -10.461 Td [(which)-374(tak)10(es)-374(an)-374(attrib)20(ute)-374(v)25(alue)-374(and)-374(se)15(gments)-374(it)-374(into)-373(constituent)-374(at-)]TJ 0 -10.461 Td [(trib)20(ute)-221(v)25(alues)-220(based)-221(on)-220(re)15(gular)-221(e)15(xpressions)-220([31,)-227(11,)-226(1].)-300(Such)-221(an)-220(oper)20(-)]TJ 0 -10.46 Td [(ator)-281(is)-281(e)15(xtremely)-280(useful)-281(for)-281(identifying)-281(tar)18(get)-281(attrib)20(ute)-281(v)25(alues)-280(across)]TJ 257.036 653.549 Td [(a)-361(v)25(ariety)-361(of)-361(domai)1(ns:)-532(addresses,)-389(media)-360(databases,)-389(etc.)-643(F)15(or)-360(e)15(xam-)]TJ 0 -10.461 Td [(ple,)-398(commercial)-368(address)-368(cleansing)-368(tools)-368(\050e.g.,)-398(T)35(rillium\051)-368(rely)-368(hea)20(v-)]TJ 0 -10.461 Td [(ily)-356(on)-356(this)-357(operat)1(or)39(,)-382(which)-356(the)15(y)-357(call)-356(\223parsing\224.)-628(The)-356(concatenation)]TJ 0 -10.46 Td [(operator)]TJ/F31 8.9664 Tf 29.876 0 Td [(|)]TJ/F56 8.9664 Tf 9.215 0 Td [(which)-272(is)-272(the)-272(i)1(n)39(v)15(ers)1(e)-272(of)-272(se)15(gmentation)]TJ/F31 8.9664 Tf 131.591 0 Td [(|)]TJ/F56 8.9664 Tf 9.216 0 Td [(concatenates)-272(mul-)]TJ -179.898 -10.461 Td [(tiple)-366(columns)-366(together)55(.)-658(Note)-366(that)-366(both)-366(these)-366(opera)1(tors)-366(modify)-366(the)]TJ 0 -10.461 Td [(schema)-251(of)-251(the)-251(input)-251(relations.)-313(Ev)15(en)-251(though)-251(the)-251(discussi)1(on)-251(in)-251(this)-251(pa-)]TJ 0 -10.461 Td [(per)-298(assumes,)-311(for)-299(re)1(asons)-299(of)-298(clarity)65(,)-311(that)-298(schema)-299(is)-298(not)-299(modi\002ed,)-310(we)]TJ 0 -10.461 Td [(note)-258(that)-257(our)-258(approach)-257(is)-258(general)-257(enough)-258(to)-257(handle)-258(the)-257(se)15(gmentation)]TJ 0 -10.46 Td [(and)-250(concatenation)-250(operators.)]TJ/F57 8.9664 Tf 8.967 -10.461 Td [(FD-Corr)37(ection)-448(Oper)15(ator)]TJ/F56 8.9664 Tf 91.211 0 Td [(:)-706(The)]TJ/F57 8.9664 Tf 26.777 0 Td [(FD-corr)37(ection)]TJ/F56 8.9664 Tf 55.974 0 Td [(operator)-448(e)15(xploits)]TJ -182.929 -10.461 Td [(reference)-400(tables)-400(and)-400(the)-400(kno)25(wledge)-400(of)-400(functional)-399(dependencies)-400(to)]TJ 0 -10.461 Td [(correct)-231(missing)-231(and)-231(incorrect)-231(v)25(alues)-231(in)-231(a)-231(record,)-235(e)25(v)15(en)-231(when)-231(the)-231(func-)]TJ 0 -10.46 Td [(tional)-223(dependenc)15(y)-223(is)]TJ/F57 8.9664 Tf 75.088 0 Td [(soft)]TJ/F56 8.9664 Tf 14.954 0 Td [(in)-223(that)-223(it)-222(holds)-223(for)-223(a)-223(lar)18(ge)-223(subset)-223(of)-222(the)-223(data,)]TJ -90.042 -10.461 Td [(or)-250(when)-250(we)-250(do)-250(not)-250(ha)20(v)15(e)-250(a)-250(perfect)-250(reference)-250(table.)]TJ 8.967 -10.461 Td [(The)-300(functional)-301(dependenc)15(y)]TJ/F34 8.9664 Tf 101.069 0 Td [(Z)-71(ip)]TJ/F36 8.9664 Tf 18.106 0 Td [(!)]TJ/F34 8.9664 Tf 12.635 0 Td [(C)-71(ity)]TJ/F56 8.9664 Tf 21.251 0 Td [(is)-300(an)-301(e)15(xample)-300(of)-300(a)-301(soft)]TJ -162.028 -10.461 Td [(functional)-205(dependenc)15(y)-205(because)-204(a)-205(fe)25(w)-205(zip)-205(codes)-205(may)-205(actually)-205(be)-204(asso-)]TJ 0 -10.461 Td [(ciated)-213(with)-213(multiple)-214(cities.)-297(In)-214(a)-213(group)-213(of)-213(records)-214(sharing)-213(the)-213(same)-213(zip)]TJ 0 -10.46 Td [(v)25(alue,)-297(if)-287(a)-287(lar)18(ge)-288(percentage)-287(\050greater)-287(than)-288(a)-287(threshold)-287(abo)15(v)15(e)]TJ/F31 8.9664 Tf 215.155 0 Td [(50%)]TJ/F56 8.9664 Tf 16.895 0 Td [(\051)-287(of)]TJ -232.05 -10.461 Td [(City)-278(v)25(alues)-277(ha)20(v)15(e)-278(the)-278(s)1(ame)-278(City)-278(v)25(alue,)-284(we)-278(may)-278(the)1(n)-278(rename)-278(the)-277(City)]TJ 0 -10.461 Td [(v)25(alues)-267(of)-268(other)-267(records)-268(in)-267(the)-268(group)-267(to)-268(this)-267(dominant)-268(v)25(al)1(ue.)-363(In)-267(order)]TJ 0 -10.461 Td [(to)-298(a)20(v)20(oid)-299(con\003icts)-298(while)-298(determining)-299(the)-298(dominant)-298(v)25(alue)-299(in)-298(a)-298(group,)]TJ 0 -10.46 Td [(we)-351(restrict)-351(the)-351(threshold)-351(on)-351(the)-351(percentage)-352(to)-351(be)-351(abo)15(v)15(e)]TJ/F31 8.9664 Tf 206.503 0 Td [(50%)]TJ/F56 8.9664 Tf 16.895 0 Td [(.)-613(The)]TJ -223.398 -10.461 Td [(FD-Correction)-229(operator)-230(can)-229(in)-230(f)10(act)-229(be)-230(generalized)-229(to)-229(that)-230(of)-229(applying)]TJ 0 -10.461 Td [(high)-250(con\002dence)-250(\050greater)-250(than)]TJ/F31 8.9664 Tf 107.067 0 Td [(50%)]TJ/F56 8.9664 Tf 16.895 0 Td [(\051)-250(association)-250(rules.)]TJ/F55 8.9664 Tf -123.962 -14.496 Td [(RJU)-250(Operator)-250(T)74(r)18(ees)]TJ/F56 8.9664 Tf 0 -10.46 Td [(Introducing)-334(rename)-334(operators)-335(int)1(o)-335(the)-334(design)-334(space)-334(generalizes)-334(the)]TJ 0 -10.461 Td [(class)-486(of)-487(operator)-486(trees.)-1019(An)15(y)-486(operator)-487(tree)-486(which)-486(is)-487(a)-486(union)-486(of)]TJ 0 -10.461 Td [(\223rename-join\224)-199(blocks)-198(belongs)-199(to)-199(our)-198(generalized)-199(class.)-293(Each)]TJ/F57 8.9664 Tf 215.537 0 Td [(r)37(ename-)]TJ -215.537 -10.461 Td [(join)-236(\050RJ\051)]TJ/F56 8.9664 Tf 33.611 0 Td [(block)-236(is)-235(an)-236(operator)-236(tree)-236(o)15(v)15(er)-236(both)-235(input)-236(relations)-236(in)40(v)20(olving)]TJ -33.611 -10.461 Td [(a)-266(series)-266(of)-266(rename)-266(operators)-266(follo)25(wed)-266(by)-266(one)-266(similarity)-266(j)1(oin.)-358(An)-266(e)15(x-)]TJ 0 -10.46 Td [(ample)-328(is)-327(sho)25(wn)-328(on)-327(the)-328(right)-328(side)-327(in)-328(Figure)-327(1.)-543(W)80(e)-328(call)-327(this)-328(class)-327(of)]TJ 0 -10.461 Td [(operator)-250(trees)-250(the)]TJ/F57 8.9664 Tf 64.486 0 Td [(RJU)-250(class)]TJ/F56 8.9664 Tf 36.107 0 Td [(.)]TJ -91.626 -10.461 Td [(A)-230(rename)-229(operator)-230(may)-230(be)-230(applied)-229(to)-230(both)-230(input)-230(relations)]TJ/F34 8.9664 Tf 205.871 0 Td [(R)]TJ/F56 8.9664 Tf 9.096 0 Td [(and)]TJ/F34 8.9664 Tf 15.008 0 Td [(S)]TJ/F56 8.9664 Tf -238.942 -10.461 Td [(or)-245(to)-244(only)-245(one)-245(of)-245(the)-244(tw)10(o.)-308(F)15(or)-245(the)-245(sak)10(e)-245(of)-244(simplicity)65(,)-246(we)-245(only)-244(discuss)]TJ 0 -10.46 Td [(the)-248(restricted)-248(case)-248(where)-248(we)-249(apply)-248(the)-248(rename)-248(operator)-248(to)-248(both)-248(input)]TJ 0 -10.461 Td [(relations.)-295(Our)-205(techniques)-206(can)-205(be)-205(applied)-205(to)-206(the)-205(more)-205(general)-205(v)25(ariants.)]TJ/F55 8.9664 Tf 0 -14.496 Td [(Algorithm)]TJ/F56 8.9664 Tf 0 -10.461 Td [(Since)-195(we)-195(consider)-195(the)-194(class)-195(of)-195(thresholded)-195(rename)-195(operators,)-206(we)-194(ha)20(v)15(e)]TJ 0 -10.46 Td [(to)-260(decide)-260(whether)-260(or)-259(not)-260(to)-260(include)-260(a)-260(rename)-260(operator)-260(in)-260(an)-259(operator)]TJ 0 -10.461 Td [(tree,)-281(and)-275(also)-275(determine)-275(the)-275(threshold)-275(v)25(alue.)-385(F)15(or)-275(ease)-274(of)-275(e)15(xposition,)]TJ 0 -10.461 Td [(we)-229(\002rst)-228(consider)-229(the)-228(restricted)-229(case)-228(where)-229(the)-228(thresholds)-229(for)-228(renames)]TJ 0 -10.461 Td [(are)-250(\002x)15(ed.)]TJ 8.967 -10.46 Td [(Consider)-320(a)-319(rename)-320(operator)]TJ/F34 8.9664 Tf 104.084 0 Td [(\032)]TJ/F56 8.9664 Tf 4.747 0 Td [(.)-519(The)-319(bene\002t)-320(of)-319(a)-320(rename)-320(operator)]TJ -117.798 -10.461 Td [(depends)-249(on)-250(the)-249(operator)-250(tree)-249(follo)25(wing)-250(it.)-310(W)80(e)-249(may)-249(consider)-250(both)-249(op-)]TJ 0 -10.461 Td [(tions:)-310(design)-250(the)-249(best)-250(similarity)-250(join)-249(preceded)-250(by)]TJ/F34 8.9664 Tf 176.851 0 Td [(\032)]TJ/F56 8.9664 Tf 6.986 0 Td [(and)-250(not)-249(preceded)]TJ -183.837 -10.461 Td [(by)]TJ/F34 8.9664 Tf 11.407 0 Td [(\032)]TJ/F56 8.9664 Tf 4.747 0 Td [(,)-278(and)-272(choose)-272(the)-272(better)-272(of)-273(the)-272(tw)10(o)-272(operator)-272(trees.)-377(This)-272(approach)]TJ -16.154 -10.461 Td [(could)-307(be)-306(inef)25(\002cient)-307(if)-307(the)-306(number)-307(of)-307(re)1(name)-307(operators)-307(is)-306(lar)18(ge.)-480(W)80(e)]TJ 0 -10.46 Td [(adopt)-379(a)-378(heuristic)-379(where)-379(we)-378(\002rst)-379(design)-379(a)-378(similarity)-379(join,)-411(and)-378(then)]TJ 0 -10.461 Td [(e)25(v)25(aluate)-271(whether)-270(or)-271(not)-270(preceding)-271(it)-270(with)]TJ/F34 8.9664 Tf 150.501 0 Td [(\032)]TJ/F56 8.9664 Tf 7.173 0 Td [(applied)-271(to)-270(both)-271(input)-270(re-)]TJ -157.674 -10.461 Td [(lations)-251(w)10(ould)-252(impro)15(v)15(e)-251(the)-252(quality)65(.)-314(W)80(e)-251(choose)-252(the)-251(rename)-252(operat)1(or)]TJ/F34 8.9664 Tf 240.334 0 Td [(\032)]TJ/F56 8.9664 Tf -240.334 -10.461 Td [(with)-204(the)-204(highest)]TJ/F57 8.9664 Tf 58.292 0 Td [(bene\002t)]TJ/F56 8.9664 Tf 25.734 0 Td [(v)25(alue)]TJ/F34 8.9664 Tf 21.027 0 Td [(benef)-109(it)]TJ/F35 5.9776 Tf 30.006 -1.394 Td [(T)]TJ/F33 5.9776 Tf 5.339 0 Td [(\050)]TJ/F35 5.9776 Tf 2.878 0 Td [(R)-4(;S)]TJ/F33 5.9776 Tf 12.643 0 Td [(\051)]TJ/F31 8.9664 Tf 3.377 1.394 Td [(\050)]TJ/F34 8.9664 Tf 3.583 0 Td [(\032;)]TJ/F31 8.9664 Tf 8.843 0 Td [(\001\051)]TJ/F56 8.9664 Tf 11.263 0 Td [(,)-213(which)-204(we)-204(de\002ne)]TJ -182.985 -10.46 Td [(belo)25(w)65(.)-312(This)-251(al)1(gorithm)-251(can)-251(be)-250(generalized)-251(to)-251(also)-250(iterate)-251(o)15(v)15(er)-250(v)25(arious)]TJ 0 -10.461 Td [(alternate)-250(threshold)-250(v)25(alues,)-250(and)-250(choose)-250(the)-250(best)-250(one.)]TJ 8.967 -10.461 Td [(Let)]TJ/F34 8.9664 Tf 14.95 0 Td [(\032)]TJ/F56 8.9664 Tf 7.746 0 Td [(precede)-334(an)-335(operator)-334(tree)]TJ/F34 8.9664 Tf 91.651 0 Td [(T)]TJ/F56 8.9664 Tf 9.655 0 Td [(with)-334(one)-335(similarity)-334(join)-335(opera-)]TJ -132.969 -10.461 Td [(tor)55(.)-567(Consider)-336(the)-335(rectangle)-336(equi)25(v)25(alent)-336(to)]TJ/F34 8.9664 Tf 151.921 0 Td [(T)]TJ/F56 8.9664 Tf 9.666 0 Td [(in)-336(the)-335(similarity)-336(space.)]TJ -161.587 -10.461 Td [(A)-383(measure)-383(of)-383(bene\002t)-383(of)]TJ/F34 8.9664 Tf 92.87 0 Td [(\032)]TJ/F56 8.9664 Tf 8.183 0 Td [(is)-383(the)-383(sum)-383(of)-384(the)-383(increase)-383(in)-383(the)-383(num-)]TJ -101.053 -10.46 Td [(ber)-314(of)-314(positi)25(v)15(e)-314(points)-314(in)-314(the)-314(rectangle)-314(and)-314(the)-314(decrea)1(se)-314(in)-314(the)-314(num-)]TJ 0 -10.461 Td [(ber)-388(of)-388(ne)15(g)5(ati)25(v)15(e)-389(points.)-724(Figure)-388(8)-389(illustrates)-388(an)-388(e)15(xample)-388(where)-388(the)]TJ 0 -10.461 Td [(bene\002t)-476(is)]TJ/F31 8.9664 Tf 38.924 0 Td [(2)]TJ/F56 8.9664 Tf 4.608 0 Td [(.)-988(The)-476(positi)25(v)15(e)-476(point)]TJ/F34 8.9664 Tf 84.323 0 Td [(P)]TJ/F31 8.9664 Tf 7.163 0 Td [(1)]TJ/F56 8.9664 Tf 8.877 0 Td [(mo)15(v)15(es)-476(inside)-476(the)-476(rectangle)]TJ -143.895 -10.461 Td [(\050)]TJ/F34 8.9664 Tf 2.986 0 Td [(ur)-29(ect)]TJ/F31 8.9664 Tf 21.318 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(P)]TJ/F31 8.9664 Tf 7.164 0 Td [(2[)]TJ/F34 8.9664 Tf 7.167 0 Td [(X)]TJ/F31 8.9664 Tf 8.314 0 Td [(1])]TJ/F34 8.9664 Tf 7.168 0 Td [(;)-171(P)]TJ/F31 8.9664 Tf 11.259 0 Td [(3[)]TJ/F34 8.9664 Tf 7.168 0 Td [(X)]TJ/F31 8.9664 Tf 8.314 0 Td [(2]\051)]TJ/F56 8.9664 Tf 10.751 0 Td [(\051)-404(and)-404(the)-404(ne)15(g)5(ati)25(v)15(e)-404(point)]TJ/F34 8.9664 Tf 93.283 0 Td [(P)]TJ/F31 8.9664 Tf 7.163 0 Td [(4)]TJ/F56 8.9664 Tf 8.232 0 Td [(mo)15(v)15(es)-404(out-)]TJ -203.871 -10.46 Td [(side)-336(it.)-569(This)-336(intuition)-336(can)-336(in)-336(f)10(act)-337(be)-336(e)15(xtended)-336(to)-336(an)15(y)-336(operator)-336(tree,)]TJ 0 -10.461 Td [(as)-250(follo)25(ws.)]TJ ET Q 1 0 0 1 295.992 36 cm 0 Tr /QQAPFce02551e 12 Tf 0 0 0 rg 100 Tz 0 Ts 0 Tw 0 Tc BT 1 0 0 1 0 0 Tm (334)Tj ET 1 0 0 1 0 0 cm 1 0 0 1 -295.992 -36 cm endstream endobj 103 0 obj << /Type /Page /Resources 102 0 R /MediaBox [ 0 0 612 792 ] /Parent 91 0 R /Contents [ 104 0 R ] >> endobj 87 0 obj << /Type /XObject /Subtype /Form /FormType 1 /PTEX.FileName (figures/renameEg.pdf) /PTEX.PageNumber 1 /PTEX.InfoDict 105 0 R /BBox [0 0 176 143] /Resources << /ProcSet [ /PDF /Text ] /ExtGState << /R7 106 0 R >>/Font << /R9 107 0 R/R8 108 0 R>> >> /Length 109 0 R /Filter /FlateDecode >> stream x[ˎ\We"Z5@ Z-'qu;`Խ B7OUSj__~?l_iQôPְuNn{<ooRKr`m^CHq!/ZχH3~o\>@~=s Mk:ovJ9:cH={;ګ8 A`e狍WD{9k!4lU^3[VOg28f_>ܽ~:hٴ36Z5v5&FS1}ٝ/tfx4[L/X&Ve>~{:O\Ng*joNvu>tט դ*|>j]oQӱe T+X߅LD~_'"uf@.d 5%5 -?=ax8Kmߑb$D^V.- !E,lcH;I]=ב4#r$ьdAs>s.}mΛ'c>p F HvuNNtudJi>r;G]16`h#N_bԤ:Ri2L<-8J}n'7}W,2ۻ2Gև||l€\1M5Nð,hf3qU ,&mM]bïK AlDd+BgpxXU|'qWavLtZWibLY J~-ym[4 .;[̪8$P'=*Dh_M4ѝ fW_&EHd fj_gZhM=`C3{bcDK"Hj2퍌ȹPM/L;y&~-QMx'ƯA3pyh Ka@Iɼ=*D_O4 u :\W' QcFH}) ׉W`ve٤9ݽʗiÔkp~;R( g\b * Alن ju:s6:Z|} iJtIH-9$oMGO!o2(ЦٽU褃ܞdi?vt^w4"@+s)o9RosϼDSt rN4PPG3at1u%?EP NH/,:U3i߶CMܫ)Yl Gk9eƆjJd-:&5L%t0",XBc9ر]^]bs=BXa,dY:RhcʭI@`DXr*|(C@〫G)kFZf(K4֐gz,7EXvLG+/odnrx7+1c$a (#Ά1*ku M# JBbE\C|E|C\EdP6nuW'UӮ:#% R.rcVǣ iC8&!jn%~t'9Q#OuOr3q.{X$7(~{10؍ endstream endobj 105 0 obj << /Producer (AFPL Ghostscript 8.53) /CreationDate (D:20070710065911) /ModDate (D:20070710065911) /Title (Microsoft Word - RenameEg.doc) /Creator (PScript5.dll Version 5.2.2) /Author (vganti) >> endobj 106 0 obj << /Type /ExtGState /OPM 1 >> endobj 107 0 obj << /BaseFont /Courier /Type /Font /Subtype /Type1 >> endobj 108 0 obj << /BaseFont /Times-Roman /Type /Font /Encoding 110 0 R /Subtype /Type1 >> endobj 109 0 obj 2640 endobj 110 0 obj << /Type /Encoding /Differences [ 146/quoteright] >> endobj 102 0 obj << /Font << /F55 9 0 R /F67 82 0 R /F37 55 0 R /F68 83 0 R /F56 10 0 R /F69 84 0 R /F34 12 0 R /F57 11 0 R /F36 8 0 R /F31 18 0 R /F35 49 0 R /F33 51 0 R /QQAPFce02551e 232 0 R >> /XObject << /Im7 87 0 R >> /ProcSet [ /PDF /Text ] >> endobj 119 0 obj << /Length 27256 /LC /QQAP >> stream q BT /F57 8.9664 Tf 63.761 728.239 Td [(De\002nition)-250(9.)]TJ/F56 8.9664 Tf 49.315 0 Td [(Let)]TJ/F34 8.9664 Tf 15.358 0 Td [(\032)]TJ/F31 8.9664 Tf 4.747 0 Td [(\050\001\051)]TJ/F56 8.9664 Tf 18.253 0 Td [(denote)-380(the)-380(transformed)-379(e)15(xamples)-380(where)]TJ -97.636 -10.461 Td [(the)-316(rename)-316(operator)-315(is)-316(applied)-316(to)-316(each)-316(e)15(xample)-316(in)]TJ/F34 8.9664 Tf 185.706 0 Td [(x)]TJ/F36 8.9664 Tf 8.907 0 Td [(2)]TJ/F31 8.9664 Tf 9.827 0 Td [(\001)]TJ/F56 8.9664 Tf 7.68 0 Td [(,)-332(on)-316(both)]TJ -212.12 -10.46 Td [(projections)]TJ/F34 8.9664 Tf 42.151 0 Td [(x)]TJ/F31 8.9664 Tf 5.224 0 Td [([)]TJ/F34 8.9664 Tf 2.56 0 Td [(R)]TJ/F31 8.9664 Tf 7.035 0 Td [(])]TJ/F56 8.9664 Tf 4.865 0 Td [(and)]TJ/F34 8.9664 Tf 15.252 0 Td [(x)]TJ/F31 8.9664 Tf 5.224 0 Td [([)]TJ/F34 8.9664 Tf 2.56 0 Td [(S)]TJ/F31 8.9664 Tf 6.139 0 Td [(])]TJ/F56 8.9664 Tf 4.865 0 Td [(of)-257(the)-257(e)15(xample.)-331(F)15(ormally)65(,)-259(the)]TJ/F57 8.9664 Tf 108.476 0 Td [(bene\002t)]TJ/F56 8.9664 Tf 26.209 0 Td [(of)]TJ/F34 8.9664 Tf 9.774 0 Td [(\032)]TJ/F56 8.9664 Tf -240.334 -10.461 Td [(with)-250(respect)-250(to)]TJ/F34 8.9664 Tf 55.035 0 Td [(T)]TJ/F56 8.9664 Tf 8.898 0 Td [(o)15(v)15(er)]TJ/F31 8.9664 Tf 17.906 0 Td [(\001)]TJ/F56 8.9664 Tf 9.921 0 Td [(is)-250(de\002ned)-250(as:)]TJ/F34 8.9664 Tf 49.601 0 Td [(benef)-109(it)]TJ/F35 5.9776 Tf 30.006 -1.395 Td [(T)]TJ/F33 5.9776 Tf 5.339 0 Td [(\050)]TJ/F35 5.9776 Tf 2.878 0 Td [(R)-4(;S)]TJ/F33 5.9776 Tf 12.643 0 Td [(\051)]TJ/F31 8.9664 Tf 3.377 1.395 Td [(\050)]TJ/F34 8.9664 Tf 3.583 0 Td [(\032;)]TJ/F31 8.9664 Tf 8.843 0 Td [(\001\051)-285(=)]TJ/F36 8.9664 Tf -208.03 -11.514 Td [(f)]TJ/F34 8.9664 Tf 4.608 0 Td [(C)-71(ov)-36(er)-29(ag)-36(e)]TJ/F31 8.9664 Tf 39.055 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(T)]TJ/F31 8.9664 Tf 6.656 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(R)-7(;)-171(S)]TJ/F31 8.9664 Tf 17.27 0 Td [(\051)]TJ/F34 8.9664 Tf 3.584 0 Td [(;)-171(\032)]TJ/F31 8.9664 Tf 8.843 0 Td [(\050\001)]TJ/F33 5.9776 Tf 11.263 3.809 Td [(+)]TJ/F31 8.9664 Tf 6.088 -3.809 Td [(\051\051)]TJ/F36 8.9664 Tf 9.216 0 Td [(\000)]TJ/F34 8.9664 Tf 9.215 0 Td [(C)-71(ov)-36(er)-29(ag)-36(e)]TJ/F31 8.9664 Tf 39.055 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(T)]TJ/F31 8.9664 Tf 6.656 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(R)-7(;)-171(S)]TJ/F31 8.9664 Tf 17.271 0 Td [(\051)]TJ/F34 8.9664 Tf 3.583 0 Td [(;)]TJ/F31 8.9664 Tf 4.096 0 Td [(\001)]TJ/F33 5.9776 Tf 7.68 3.809 Td [(+)]TJ/F31 8.9664 Tf 6.088 -3.809 Td [(\051)]TJ/F36 8.9664 Tf 3.584 0 Td [(g)]TJ/F31 8.9664 Tf 4.607 0 Td [(+)]TJ/F36 8.9664 Tf -222.754 -10.46 Td [(f)]TJ/F34 8.9664 Tf 4.608 0 Td [(C)-71(ov)-36(er)-29(ag)-36(e)]TJ/F31 8.9664 Tf 39.055 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(T)]TJ/F31 8.9664 Tf 6.656 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(R)-7(;)-171(S)]TJ/F31 8.9664 Tf 17.27 0 Td [(\051)]TJ/F34 8.9664 Tf 3.584 0 Td [(;)]TJ/F31 8.9664 Tf 4.096 0 Td [(\001)]TJ/F37 5.9776 Tf 7.679 3.809 Td [(\000)]TJ/F31 8.9664 Tf 6.255 -3.809 Td [(\051)]TJ/F36 8.9664 Tf 5.631 0 Td [(\000)]TJ/F34 8.9664 Tf 9.216 0 Td [(C)-71(ov)-36(er)-29(ag)-35(e)]TJ/F31 8.9664 Tf 39.055 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(T)]TJ/F31 8.9664 Tf 6.656 0 Td [(\050)]TJ/F34 8.9664 Tf 3.583 0 Td [(R)-7(;)-171(S)]TJ/F31 8.9664 Tf 17.271 0 Td [(\051)]TJ/F34 8.9664 Tf 3.584 0 Td [(;)-171(\032)]TJ/F31 8.9664 Tf 8.843 0 Td [(\050\001)]TJ/F37 5.9776 Tf 11.263 3.809 Td [(\000)]TJ/F31 8.9664 Tf 6.254 -3.809 Td [(\051\051)]TJ/F36 8.9664 Tf 7.168 0 Td [(g)]TJ/F56 8.9664 Tf -209.512 -24.306 Td [(The)-220(abo)15(v)15(e)-220(discussion)-221(focuses)-220(on)-220(the)-220(addition)-221(of)-220(a)-220(rename)-220(operator)]TJ -8.967 -10.46 Td [(before)-395(an)-394(operator)-395(tree)-395(with)-394(only)-395(a)-395(similarity)-394(join.)-745(Ho)25(we)26(v)14(e)1(r)39(,)-430(the)]TJ 0 -10.461 Td [(procedure)-280(straightforw)10(ardly)-280(generalizes)-280(to)-280(an)-280(operator)-280(tree)-280(which)-280(is)]TJ 0 -10.461 Td [(an)15(y)-203(member)-204(of)-203(the)-203(RJU)-204(cl)1(ass.)-295(Thus,)-213(we)-203(are)-203(able)-203(to)-204(greedily)-203(add)-203(more)]TJ 0 -10.461 Td [(rename)-250(operators)-250(if)-250(the)15(y)-250(impro)15(v)15(e)-250(the)-250(o)15(v)15(erall)-250(quality)65(.)]TJ/F55 8.9664 Tf 8.967 -10.461 Td [(Implementing)-373(RJU)-374(Class)]TJ/F56 8.9664 Tf 98.35 0 Td [(:)-557(The)-374(rename)-373(operators)-374(that)-373(we)-374(con-)]TJ -107.317 -10.46 Td [(sider)-413(in)-413(this)-412(paper)-413(\050fuzzy)-413(lookup)-413([34,)-453(13]\051,)-454(column)-412(se)15(gmentation)]TJ 0 -10.461 Td [(\050[31,)-327(11,)-326(1]\051,)-327(and)-311(FD-correction)-311(\050as)-312(discussed)-311(abo)15(v)15(e\051)-311(ha)20(v)15(e)-311(ef)25(\002cient)]TJ 0 -10.461 Td [(implementations.)-310(By)-250(de\002nition,)-250(the)-250(rename)-250(operators)-250(commute)-250(o)15(v)15(er)]TJ 0 -10.461 Td [(unions.)-448(Therefore,)-307(a)-296(sequence)-295(of)-296(these)-296(rename)-296(operators)-296(can)-296(be)-295(ef-)]TJ 0 -10.46 Td [(\002ciently)-350(implemented)-349(using)-350(the)-350(pull-)1(based)-350(get)-350(ne)15(xt)-349(interf)10(ace.)-609(The)]TJ 0 -10.461 Td [(similarity)-333(joins)-334(are)-333(implemented)-333(using)-334(the)-333(same)-334(get)-333(ne)15(xt)-333(interf)10(ace,)]TJ 0 -10.461 Td [(and)-367(if)-367(the)-367(input)-368(relations)-367(are)-367(v)15(ery)-367(lar)18(ge)-367(we)-367(spool)-367(the)-367(intermediate)]TJ 0 -10.461 Td [(relations)-348(to)-348(disk.)-603(A)-348(signi\002cant)-348(number)-348(of)-348(ef)25(\002cient)-348(similarity)-347(joins)]TJ 0 -10.461 Td [(algorithms)-260(are)-260(de)25(v)15(eloped)-261(earlier)-260(for)-260(a)-260(broad)-261(class)-260(of)-260(similarity)-260(func-)]TJ 0 -10.46 Td [(tions)-365([23,)-395(2,)-394(28].)-656(W)80(e)-366(adopt)-365(these)-366(algorithms)-365(in)-366(our)-365(frame)25(w)10(ork)-365(to)]TJ 0 -10.461 Td [(ef)25(\002ciently)-250(and)-250(scalably)-250(implement)-250(the)-250(RJU)-250(operator)-250(trees.)]TJ/F55 11.9552 Tf 0 -21.194 Td [(6.)-1000(DISCUSSION)]TJ/F56 8.9664 Tf 8.967 -12.952 Td [(W)80(e)-208(no)25(w)-208(discuss)-208(\050i\051)-208(e)15(xtensions)-208(to)-208(handle)-208(lar)18(ge)-208(e)15(xample)-208(sets,)-216(\050ii\051)-208(the)]TJ -8.967 -10.46 Td [(v)25(ariants)-248(of)-247(the)-248(operator)-248(tree)-247(design)-248(formulation,)-248(and)-248(\050i)1(ii\051)-248(the)-248(issue)-247(of)]TJ 0 -10.461 Td [(g)5(athering)-250(e)15(xamples.)]TJ/F55 11.9552 Tf 0 -18.082 Td [(6.1)-1000(Lar)10(ge)-250(Example)-250(Sets)]TJ/F56 8.9664 Tf 8.967 -12.951 Td [(W)80(e)-318(no)25(w)-319(discuss)-318(a)-318(sampling-based)-319(technique)-318(to)-318(deal)-319(with)-318(a)-318(lar)18(ge)]TJ -8.967 -10.461 Td [(number)-196(of)-196(e)15(xamples.)-292(This)-196(strate)15(gy)-196(also)-196(sets)-196(the)-196(ground)-196(for)-196(e)25(v)25(aluating)]TJ 0 -10.461 Td [(the)-262(quality)-262(of)-263(our)-262(algorithm)-262(o)15(v)15(er)-262(real)-262(data)-263(where)-262(the)-262(ground)-262(truth)-262(as)]TJ 0 -10.46 Td [(to)-250(which)-250(record)-250(pairs)-250(match)-250(is)-250(not)-250(a)20(v)25(ailable.)]TJ 8.967 -10.461 Td [(Our)-268(idea)-268(is)-268(that)-268(running)-268(our)-268(algorithm)-268(on)-267(a)-268(uniform)-268(random)-268(sam-)]TJ -8.967 -10.461 Td [(ple)-338(of)-338(e)15(xamples)-337(w)10(ould)-338(return)-338(high)-338(quality)-337(operator)-338(trees.)-574(The)-337(dif-)]TJ 0 -10.461 Td [(ference)-324(in)-324(quality)-325(between)-324(the)-324(result)-324(o)15(v)15(er)-325(t)1(he)-325(sample)-324(and)-324(that)-324(o)15(v)15(er)]TJ 0 -10.46 Td [(the)-215(entire)-215(e)15(xample)-214(set)-215(can)-215(be)-215(probabilistically)-215(bound)-215(\050using)-214(Chernof)25(f)]TJ 0 -10.461 Td [(bounds\051.)-336(The)-259(intuition)-258(is)-259(similar)-258(to)-259(that)-259(of)-258(estimating)-259(selecti)25(vities)-258(of)]TJ 0 -10.461 Td [(predicates)-250(using)-250(uniform)-250(random)-250(samples.)]TJ 10.187 -12.898 Td [(L)]TJ/F56 7.1731 Tf 5.927 0 Td [(E)-61(M)-63(M)-62(A)]TJ/F56 8.9664 Tf 28.849 0 Td [(5.)]TJ/F57 8.9664 Tf 11.618 0 Td [(Let)]TJ/F34 8.9664 Tf 14.135 0 Td [(D)]TJ/F31 8.9664 Tf 11.244 0 Td [(=)]TJ/F34 8.9664 Tf 10.555 0 Td [(D)]TJ/F33 5.9776 Tf 7.855 3.809 Td [(+)]TJ/F36 8.9664 Tf 8.468 -3.809 Td [([)]TJ/F34 8.9664 Tf 8.523 0 Td [(D)]TJ/F37 5.9776 Tf 7.855 3.809 Td [(\000)]TJ/F57 8.9664 Tf 8.931 -3.809 Td [(be)-299(a)-298(set)-299(of)-298(e)20(xamples.)-456(Let)]TJ/F34 8.9664 Tf 94.239 0 Td [(S)]TJ/F31 8.9664 Tf 9.528 0 Td [(=)]TJ -237.914 -10.461 Td [(\001)]TJ/F33 5.9776 Tf 7.68 3.809 Td [(+)]TJ/F36 8.9664 Tf 8.112 -3.809 Td [([)]TJ/F31 8.9664 Tf 8.168 0 Td [(\001)]TJ/F37 5.9776 Tf 7.68 3.809 Td [(\000)]TJ/F57 8.9664 Tf 8.489 -3.809 Td [(be)-249(a)-250(uniform)-249(r)15(andom)-249(sample)-250(of)]TJ/F34 8.9664 Tf 114.894 0 Td [(D)]TJ/F57 8.9664 Tf 7.855 0 Td [(,)-249(and)]TJ/F34 8.9664 Tf 20.163 0 Td [(T)]TJ/F57 8.9664 Tf 8.891 0 Td [(be)-249(an)-250(oper)15(ator)]TJ -191.932 -10.461 Td [(tr)37(ee)-263(in)-262(the)-263(RJU)-262(class.)-348(Let)-262(the)-263(co)10(ver)15(a)10(g)10(e)-262(of)]TJ/F34 8.9664 Tf 151.45 0 Td [(T)]TJ/F57 8.9664 Tf 9.01 0 Td [(with)-263(r)37(espect)-262(to)]TJ/F31 8.9664 Tf 55.05 0 Td [(\001)]TJ/F33 5.9776 Tf 7.679 3.809 Td [(+)]TJ/F57 8.9664 Tf 8.443 -3.809 Td [(and)]TJ/F31 8.9664 Tf -231.632 -10.46 Td [(\001)]TJ/F37 5.9776 Tf 7.68 3.809 Td [(\000)]TJ/F57 8.9664 Tf 9.128 -3.809 Td [(be)]TJ/F34 8.9664 Tf 11.338 0 Td [(\014)]TJ/F33 5.9776 Tf 5.194 -0.997 Td [(+)]TJ/F57 8.9664 Tf 8.962 0.997 Td [(and)]TJ/F34 8.9664 Tf 16.323 0 Td [(\014)]TJ/F37 5.9776 Tf 5.194 -0.997 Td [(\000)]TJ/F57 8.9664 Tf 6.254 0.997 Td [(,)-338(r)37(espectively)55(.)-522(Then)-320(the)-321(co)10(ver)15(a)10(g)10(es,)-338(denoted)]TJ/F34 8.9664 Tf 161.308 0 Td [(X)]TJ/F33 5.9776 Tf 7.612 -0.997 Td [(+)]TJ/F57 8.9664 Tf -238.993 -9.464 Td [(and)]TJ/F34 8.9664 Tf 15.711 0 Td [(X)]TJ/F37 5.9776 Tf 7.612 -0.996 Td [(\000)]TJ/F57 8.9664 Tf 6.254 0.996 Td [(,)-253(of)]TJ/F34 8.9664 Tf 13.745 0 Td [(T)]TJ/F57 8.9664 Tf 8.918 0 Td [(with)-252(r)37(espect)-252(to)-252(the)-253(original)-252(e)20(xample)-252(sets)]TJ/F34 8.9664 Tf 146.816 0 Td [(D)]TJ/F33 5.9776 Tf 7.856 3.809 Td [(+)]TJ/F57 8.9664 Tf 8.349 -3.809 Td [(and)]TJ/F34 8.9664 Tf 15.711 0 Td [(D)]TJ/F37 5.9776 Tf 7.855 3.809 Td [(\000)]TJ/F57 8.9664 Tf -238.827 -14.27 Td [(ar)37(e)-354(with)-354(a)-354(high)-354(pr)45(obability)-355(close)-354(to)]TJ/F34 8.9664 Tf 134.574 0 Td [(\014)]TJ/F33 5.9776 Tf 5.193 -0.996 Td [(+)]TJ/F57 8.9664 Tf 9.264 0.996 Td [(and)]TJ/F34 8.9664 Tf 16.625 0 Td [(\014)]TJ/F37 5.9776 Tf 5.193 -0.996 Td [(\000)]TJ/F57 8.9664 Tf 6.254 0.996 Td [(,)-380(r)37(espectively)55(.)-622(F)105(or)]TJ -177.103 -10.461 Td [(constants)]TJ/F34 8.9664 Tf 36.116 0 Td [(\016)]TJ/F33 5.9776 Tf 4.088 -0.996 Td [(1)]TJ/F34 8.9664 Tf 6.711 0.996 Td [(>)]TJ/F31 8.9664 Tf 9.727 0 Td [(0)]TJ/F57 8.9664 Tf 6.849 0 Td [(and)]TJ/F34 8.9664 Tf 15.691 0 Td [(\016)]TJ/F33 5.9776 Tf 4.088 -0.996 Td [(2)]TJ/F34 8.9664 Tf 6.711 0.996 Td [(>)]TJ/F31 8.9664 Tf 9.727 0 Td [(0)]TJ/F57 8.9664 Tf 4.608 0 Td [(,)-250(we)-250(have)-250(the)-250(following)-250(bounds.)]TJ -93.108 -18.174 Td [(1.)]TJ/F34 8.9664 Tf 11.208 0 Td [(P)]TJ/F31 8.9664 Tf 7.164 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(X)]TJ/F33 5.9776 Tf 7.612 -0.996 Td [(+)]TJ/F34 8.9664 Tf 8.648 0.996 Td [(<)]TJ/F31 8.9664 Tf 9.727 0 Td [(\0501)]TJ/F36 8.9664 Tf 10.239 0 Td [(\000)]TJ/F34 8.9664 Tf 9.216 0 Td [(\016)]TJ/F33 5.9776 Tf 4.087 -0.996 Td [(1)]TJ/F31 8.9664 Tf 4.151 0.996 Td [(\051)]TJ/F34 8.9664 Tf 3.584 0 Td [(\014)]TJ/F33 5.9776 Tf 5.193 -0.996 Td [(+)]TJ/F36 8.9664 Tf 6.089 0.996 Td [(j)]TJ/F34 8.9664 Tf 2.559 0 Td [(D)]TJ/F33 5.9776 Tf 7.855 3.809 Td [(+)]TJ/F36 8.9664 Tf 6.089 -3.809 Td [(j)]TJ/F31 8.9664 Tf 2.56 0 Td [(\051)]TJ/F34 8.9664 Tf 6.143 0 Td [(<)-285(e)]TJ/F12 4.9813 Tf 15.207 8.174 Td [(\000)]TJ/F9 4.9813 Tf 5.397 0 Td [(\014)]TJ/F6 4.9813 Tf 3.938 -1.605 Td [(+)]TJ/F12 4.9813 Tf 5.618 1.605 Td [(j)]TJ/F9 4.9813 Tf 2.283 0 Td [(D)]TJ/F6 4.9813 Tf 5.702 2.01 Td [(+)]TJ/F12 4.9813 Tf 5.618 -2.01 Td [(j)]TJ/F9 4.9813 Tf 2.283 0 Td [(\016)]TJ/F6 4.9813 Tf 3.419 2.01 Td [(2)]TJ -0.161 -4.178 Td [(1)]TJ ET q 1 0 0 1 195.921 214.424 cm []0 d 0 J 0.29 w 0 0 m 38.146 0 l S Q BT /F6 4.9813 Tf 213.299 210.364 Td [(2)]TJ/F57 8.9664 Tf -148.293 -20.596 Td [(2.)]TJ/F34 8.9664 Tf 11.208 0 Td [(P)]TJ/F31 8.9664 Tf 7.164 0 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(X)]TJ/F37 5.9776 Tf 7.612 -0.996 Td [(\000)]TJ/F34 8.9664 Tf 8.814 0.996 Td [(>)]TJ/F31 8.9664 Tf 9.727 0 Td [(\0501)-228(+)]TJ/F34 8.9664 Tf 19.455 0 Td [(\016)]TJ/F33 5.9776 Tf 4.087 -0.996 Td [(2)]TJ/F31 8.9664 Tf 4.151 0.996 Td [(\051)]TJ/F34 8.9664 Tf 3.584 0 Td [(\014)]TJ/F37 5.9776 Tf 5.193 -0.996 Td [(\000)]TJ/F36 8.9664 Tf 6.255 0.996 Td [(j)]TJ/F34 8.9664 Tf 2.56 0 Td [(D)]TJ/F37 5.9776 Tf 7.855 3.809 Td [(\000)]TJ/F36 8.9664 Tf 6.254 -3.809 Td [(j)]TJ/F31 8.9664 Tf 2.56 0 Td [(\051)]TJ/F34 8.9664 Tf 6.143 0 Td [(<)]TJ/F31 8.9664 Tf 9.728 0 Td [(\050)]TJ/F35 5.9776 Tf 21.108 3.673 Td [(e)]TJ/F9 4.9813 Tf 3.52 2.509 Td [(\016)]TJ/F6 4.9813 Tf 3.259 -1.495 Td [(2)]TJ ET q 1 0 0 1 195.719 192.009 cm []0 d 0 J 0.379 w 0 0 m 43.823 0 l S Q BT /F33 5.9776 Tf 195.719 185.568 Td [(\0501+)]TJ/F35 5.9776 Tf 12.121 0 Td [(\016)]TJ/F6 4.9813 Tf 3.384 -1.152 Td [(2)]TJ/F33 5.9776 Tf 3.889 1.152 Td [(\051)]TJ/F6 4.9813 Tf 2.878 2.138 Td [(\0501+)]TJ/F9 4.9813 Tf 11.208 0 Td [(\016)]TJ/F6 4.9813 Tf 3.259 -1.495 Td [(2)]TJ 3.888 1.495 Td [(\051)]TJ/F31 8.9664 Tf 4.392 2.062 Td [(\051)]TJ/F35 5.9776 Tf 3.584 3.809 Td [(\014)]TJ/F12 4.9813 Tf 4.172 -1.262 Td [(\000)]TJ/F37 5.9776 Tf 5.895 1.262 Td [(j)]TJ/F35 5.9776 Tf 2.269 0 Td [(D)]TJ/F12 4.9813 Tf 6.161 2.508 Td [(\000)]TJ/F37 5.9776 Tf 5.895 -2.508 Td [(j)]TJ/F55 11.9552 Tf -214.916 -28.675 Td [(6.2)-1000(V)92(ariants)-128(of)-129(the)-128(Operator)-129(T)74(r)18(ee)-128(Design)-129(Pr)18(oblem)]TJ/F56 8.9664 Tf 8.967 -12.952 Td [(W)80(e)-232(no)25(w)-232(discuss)-232(a)-231(fe)25(w)-232(v)25(ariants)-232(of)-232(the)-232(operator)-232(tree)-231(design)-232(problem)]TJ -8.967 -10.461 Td [(that)-400(are)-400(potentially)-400(useful)-400(in)-401(s)1(e)25(v)15(eral)-401(scenarios,)-437(and)-400(w)10(ould)-400(greatly)]TJ 0 -10.46 Td [(bene\002t)-247(users)-247(of)-246(interacti)25(v)15(e)-247(data)-247(cleaning)-246(frame)25(w)10(orks)-247(\050e.g.,)-247([31,)-247(32]\051.)]TJ/F57 8.9664 Tf 0 -14.496 Td [(Constr)15(ained)-306(Co)10(ver)15(a)10(g)10(e)]TJ/F56 8.9664 Tf 81.406 0 Td [(:)-422(The)-306(dual)-306(formulation)-306(for)-306(the)-306(record)-306(match-)]TJ -81.406 -10.461 Td [(ing)-293(query)-293(des)1(ign)-293(problem)-293(is)-293(to)-292(\002nd)-293(the)-293(best)-293(operator)-292(tree)]TJ/F34 8.9664 Tf 209.67 0 Td [(T)]TJ/F37 5.9776 Tf 6.656 3.809 Td [(\003)]TJ/F31 8.9664 Tf 4.317 -3.809 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(R)-7(;)-171(S)]TJ/F31 8.9664 Tf 17.271 0 Td [(\051)]TJ/F56 8.9664 Tf -241.498 -10.461 Td [(which)-248(minimi)1(zes)-248(the)-247(co)15(v)14(e)1(rage)-248(of)]TJ/F34 8.9664 Tf 120.889 0 Td [(T)]TJ/F37 5.9776 Tf 6.656 3.809 Td [(\003)]TJ/F31 8.9664 Tf 4.317 -3.809 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(R)-7(;)-171(S)]TJ/F31 8.9664 Tf 17.271 0 Td [(\051)]TJ/F56 8.9664 Tf 5.803 0 Td [(with)-248(r)1(espect)-248(to)]TJ/F31 8.9664 Tf 54.968 0 Td [(\001)]TJ/F37 5.9776 Tf 7.68 3.809 Td [(\000)]TJ/F56 8.9664 Tf 8.473 -3.809 Td [(sub-)]TJ -229.641 -10.46 Td [(ject)-273(to)-273(the)-274(const)1(raint)-274(that)-273(the)-273(co)15(v)15(erage)-273(with)-273(respect)-273(to)]TJ/F31 8.9664 Tf 195.544 0 Td [(\001)]TJ/F33 5.9776 Tf 7.68 3.809 Td [(+)]TJ/F56 8.9664 Tf 8.537 -3.809 Td [(is)-273(greater)]TJ -211.761 -10.461 Td [(than)-250(a)-250(constant)]TJ/F34 8.9664 Tf 56.031 0 Td [(\013)]TJ/F56 8.9664 Tf 5.913 0 Td [(.)]TJ 204.059 653.549 Td [(W)80(e)-372(can)-372(still)-372(apply)-372(our)-372(algorithm)-372(for)-372(identifying)-371(the)-372(best)-372(h)5(yper)20(-)]TJ -8.966 -10.461 Td [(rectangle,)-241(and)-239(the)-238(greedy)-239(algorithm)-239(that)-238(we)-239(use)-239(for)-238(the)-239(union)-239(of)-238(sim-)]TJ 0 -10.46 Td [(ilarity)-284(joins.)-411(W)80(e)-284(stop)-284(when)-283(the)-284(desired)-284(positi)25(v)15(e)-284(co)15(v)15(erage)-283(thresholds)]TJ 0 -10.461 Td [(are)-319(met.)-518(Or)40(,)-336(return)-320(saying)-319(that)-319(we)-319(are)-319(unable)-320(to)-319(meet)-319(the)-319(speci\002ed)]TJ 0 -10.461 Td [(co)15(v)15(erage)-250(threshold)-250(with)-250(respect)-250(to)]TJ/F31 8.9664 Tf 124.981 0 Td [(\001)]TJ/F33 5.9776 Tf 7.679 3.809 Td [(+)]TJ/F56 8.9664 Tf 6.088 -3.809 Td [(.)]TJ/F57 8.9664 Tf -138.748 -14.496 Td [(Constr)15(ained)-384(Structur)37(e)]TJ/F56 8.9664 Tf 80.688 0 Td [(:)-578(Consider)-384(an)-384(incremental)-384(modi\002cation)-384(sce-)]TJ -80.688 -10.46 Td [(nario)-252(where)-253(the)-252(domain)-252(e)15(xpert)-253(has)-252(already)-252(designed)-253(an)-252(operator)-252(tree)]TJ 0 -10.461 Td [(\050either)-339(based)-340(upon)-340(a)-339(pre)25(vious)-340(set)-339(of)-340(e)15(xamples)-339(or)-340(upon)-339(e)15(xperience\051)]TJ 0 -10.461 Td [(and)-249(w)10(ants)-250(to)-249(adjust)-250(it)-249(to)-250(\002t)-249(a)-250(ne)25(w)-249(or)-250(a)-249(modi\002ed)-250(set)-249(of)-249(e)14(xa)1(mples.)-310(The)]TJ 0 -10.461 Td [(goal)-308(here)-307(is)-308(to)-307(b)20(uild)-308(an)-308(operator)-307(tree)-308(which)-308(i)1(s)-308(structurally)-308(the)-307(same)]TJ 0 -10.461 Td [(or)-293(v)15(ery)-293(similar)-292(to)-293(an)-293(input)-293(operator)-293(tree.)-438(Note)-293(that)-293(the)-292(language)-293(for)]TJ 0 -10.46 Td [(specifying)-241(such)-241(structural)-241(constraints)-241(can)-241(itself)-241(be)-241(f)10(airly)-241(general.)-307(W)80(e)]TJ 0 -10.461 Td [(only)-194(consider)-193(the)-194(case)-193(where)-194(a)-193(user)-194(speci\002es)-194(an)-193(operator)-194(tree)-193(sk)10(eleton)]TJ 0 -10.461 Td [(and)-253(w)10(ants)-252(to)-253(determine)-253(the)-252(best)-253(threshold)-253(parameters.)-318(W)80(e)-253(also)-252(sho)25(w)]TJ 0 -10.461 Td [(ho)25(w)-236(such)-236(functionality)-236(can)-236(be)-237(used)-236(in)-236(conjunction)-236(with)-236(the)-236(complete)]TJ 0 -10.46 Td [(operator)-250(tree)-250(design)-250(functionality)-250(to)-250(deri)25(v)15(e)-250(\223similar\224)-250(operator)-250(trees.)]TJ 8.966 -10.461 Td [(An)-311(operator)-312(tree)]TJ/F57 8.9664 Tf 62.652 0 Td [(sk)10(eleton)]TJ/F34 8.9664 Tf 32.085 0 Td [(T)]TJ/F35 5.9776 Tf 5.376 -1.063 Td [(sk)-21(eleton)]TJ/F56 8.9664 Tf 31.415 1.063 Td [(is)-311(an)-312(operator)-311(tree)-312(where)-311(the)]TJ -140.494 -10.461 Td [(threshold)-383(parameters)-383(of)-383(the)-384(similarit)1(y)-384(joins)-383(are)-383(left)-383(unspeci\002ed)-383(as)]TJ 0 -10.461 Td [(free)-263(v)25(ariable)1(s.)-348(F)15(ormally)65(,)-266(gi)25(v)15(en)-263(an)-262(operator)-263(tree)]TJ/F34 8.9664 Tf 171.342 0 Td [(T)]TJ/F35 5.9776 Tf 5.376 -1.062 Td [(sk)-21(eleton)]TJ/F31 8.9664 Tf 28.622 1.062 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(R)-7(;)-171(S)]TJ/F31 8.9664 Tf 17.271 0 Td [(\051)]TJ/F56 8.9664 Tf 5.938 0 Td [(and)]TJ -232.133 -10.461 Td [(sets)-276(of)-276(e)15(xamples)]TJ/F31 8.9664 Tf 62.08 0 Td [(\001)]TJ/F33 5.9776 Tf 7.679 3.809 Td [(+)]TJ/F56 8.9664 Tf 6.089 -3.809 Td [(,)]TJ/F31 8.9664 Tf 4.777 0 Td [(\001)]TJ/F37 5.9776 Tf 7.68 3.809 Td [(\000)]TJ/F56 8.9664 Tf 6.254 -3.809 Td [(,)-283(and)-276(a)-276(constant)]TJ/F31 8.9664 Tf 59.022 0 Td [(0)]TJ/F36 8.9664 Tf 7.615 0 Td [(\024)]TJ/F34 8.9664 Tf 10.176 0 Td [(\014)-388(<)]TJ/F31 8.9664 Tf 18.844 0 Td [(1)]TJ/F56 8.9664 Tf 4.608 0 Td [(,)-283(the)]TJ/F57 8.9664 Tf 18.211 0 Td [(structur)37(e)]TJ -213.035 -10.46 Td [(constr)15(ained)]TJ/F56 8.9664 Tf 45.765 0 Td [(operator)-397(tree)-397(design)-397(problem)-398(is)-397(to)-397(determine)-397(the)-397(best)]TJ -45.765 -10.461 Td [(threshold)-331(parameter)-331(settings)-331(for)-331(similarity)-331(joins)-331(in)]TJ/F34 8.9664 Tf 186.644 0 Td [(T)]TJ/F35 5.9776 Tf 5.376 -1.063 Td [(sk)-21(eleton)]TJ/F31 8.9664 Tf 28.622 1.063 Td [(\050)]TJ/F34 8.9664 Tf 3.584 0 Td [(R)-7(;)-171(S)]TJ/F31 8.9664 Tf 17.271 0 Td [(\051)]TJ/F56 8.9664 Tf -241.497 -10.461 Td [(which)-237(maximize)-238(the)-237(co)15(v)15(erage)-237(with)-238(respect)-237(to)]TJ/F31 8.9664 Tf 163.532 0 Td [(\001)]TJ/F33 5.9776 Tf 7.68 3.809 Td [(+)]TJ/F56 8.9664 Tf 8.216 -3.809 Td [(subject)-237(to)-238(the)-237(con-)]TJ -179.428 -10.461 Td [(straint)-250(that)-250(the)-250(co)15(v)15(erage)-250(with)-250(respect)-250(to)]TJ/F31 8.9664 Tf 142.913 0 Td [(\001)]TJ/F37 5.9776 Tf 7.679 3.809 Td [(\000)]TJ/F56 8.9664 Tf 8.496 -3.809 Td [(is)-250(less)-250(than)]TJ/F34 8.9664 Tf 41.595 0 Td [(\014)]TJ/F56 8.9664 Tf 5.661 0 Td [(.)]TJ -197.378 -10.46 Td [(Using)-287(the)-286(abo)15(v)15(e)-287(functionality)65(,)-295(we)-287(can)-287(b)20(uild)-286(slightly)-287(modi\002ed)-286(op-)]TJ -8.966 -10.461 Td [(erator)-338(trees)-337(by)-338(piping)-338(the)-337(\223residual\224)-338(e)15(xamples)-337(in)]TJ/F31 8.9664 Tf 181.955 0 Td [(\001)]TJ/F33 5.9776 Tf 7.68 3.809 Td [(+)]TJ/F36 8.9664 Tf 8.734 -3.809 Td [([)]TJ/F31 8.9664 Tf 8.79 0 Td [(\001)]TJ/F37 5.9776 Tf 7.679 3.809 Td [(\000)]TJ/F56 8.9664 Tf 9.282 -3.809 Td [(to)-338(the)]TJ -224.12 -10.461 Td [(\050original\051)-286(record)-287(matching)-286(operator)-286(tree)-287(design)-286(problem.)-419(The)-286(resid-)]TJ 0 -10.461 Td [(ual)-276(e)15(xample)-276(set)-277(is)-276(the)-276(set)-276(of)-277(all)-276(e)15(xamples)-276(which)-276(are)-277(not)-276(in)-276(the)-276(result)]TJ 0 -10.461 Td [(of)]TJ/F34 8.9664 Tf 10.974 0 Td [(T)]TJ/F37 5.9776 Tf 6.655 3.809 Td [(\003)]TJ/F35 5.9776 Tf -1.279 -5.665 Td [(sk)-21(eleton)]TJ/F56 8.9664 Tf 28.621 1.856 Td [(.)-733(That)-391(is,)]TJ/F34 8.9664 Tf 40.795 0 Td [(T)]TJ/F37 5.9776 Tf 6.655 3.809 Td [(\003)]TJ/F35 5.9776 Tf -1.279 -5.665 Td [(sk)-21(eleton)]TJ/F56 8.9664 Tf 32.126 1.856 Td [(cate)15(gorizes)-391(these)-391(e)15(xamples)-391(to)-390(be)]TJ -123.268 -10.46 Td [(non-matches.)-309(If)-247(there)-247(is)-247(a)-247(signi\002cant)-247(number)-247(of)-247(matching)-247(pairs)-247(from)]TJ/F31 8.9664 Tf 0 -10.461 Td [(\001)]TJ/F33 5.9776 Tf 7.679 3.809 Td [(+)]TJ/F56 8.9664 Tf 8.876 -3.809 Td [(in)-311(the)-311(residual)-311(set,)-326(then)-311(we)-311(may)-310(determine)-311(a)-311(ne)25(w)-311(operator)-311(tree)]TJ/F34 8.9664 Tf -16.555 -10.461 Td [(T)]TJ/F37 5.9776 Tf 6.655 3.809 Td [(\003)]TJ/F35 5.9776 Tf -1.279 -5.665 Td [(r)-32(esidual)]TJ/F56 8.9664 Tf 30.852 1.856 Td [(o)15(v)15(er)-260(the)-260(residual)-261(set.)-340(W)80(e)-261(can)-260(then)-260(union)-260(this)-261(ne)25(w)-260(operator)]TJ -36.228 -10.461 Td [(tree)]TJ/F34 8.9664 Tf 15.682 0 Td [(T)]TJ/F37 5.9776 Tf 6.655 3.809 Td [(\003)]TJ/F35 5.9776 Tf -1.279 -5.665 Td [(r)-32(esidual)]TJ/F56 8.9664 Tf 30.76 1.856 Td [(with)]TJ/F34 8.9664 Tf 18.183 0 Td [(T)]TJ/F37 5.9776 Tf 6.656 3.809 Td [(\003)]TJ/F35 5.9776 Tf -1.28 -5.665 Td [(sk)-21(eleton)]TJ/F56 8.9664 Tf 28.622 1.856 Td [(.)]TJ/F55 11.9552 Tf -103.999 -18.264 Td [(6.3)-1000(Gathering)-250(Mor)18(e)-250(Examples)]TJ/F56 8.9664 Tf 8.966 -12.952 Td [(Suppose)-333(we)-333(w)10(ant)-334(to)-333(add)-333(to)-333(a)-333(small)-334(set)-333(of)-333(ne)25(w)-333(labeled)-333(e)15(xamples)]TJ -8.966 -10.461 Td [(in)-306(order)-306(to)-305(obtain)-306(more)-306(accurate)-306(operator)-306(tr)1(ees.)-478(Instead)-306(of)-306(as)1(king)-306(a)]TJ 0 -10.46 Td [(programmer)-256(to)-256(label)-257(a)-256(random)-256(set)-256(of)-257(recor)1(d)-257(pairs)-256(in)]TJ/F34 8.9664 Tf 187.811 0 Td [(R)]TJ/F36 8.9664 Tf 9.127 0 Td [(\002)]TJ/F34 8.9664 Tf 9.258 0 Td [(S)]TJ/F56 8.9664 Tf 6.139 0 Td [(,)-258(we)-256(may)]TJ -212.335 -10.461 Td [(adopt)-340(acti)25(v)15(e)-340(learning)-340(approaches)-341(in)-340(machine)-340(learning)-340([3,)-363(32].)-580(The)]TJ 0 -10.461 Td [(idea)-288(is)-287(to)-288(identify)-288(a)-288(set)-287(of)-288(e)15(xamples)-288(which)-288(are)-287(lik)10(ely)-288(to)-288(result)-288(in)-287(the)]TJ 0 -10.461 Td [(best)-250(accurac)15(y)-250(impro)15(v)15(ement)-250(o)15(v)15(er)-250(the)-250(current)-250(operator)-250(tree.)]TJ 8.966 -10.461 Td [(The)-335(general)-336(approach)-335(is)-336(to)-335(identify)-336(e)15(xamples)-335(which)-335(are)-336(close)-335(to)]TJ -8.966 -10.46 Td [(the)-393(\223border\224)-393(separating)-393(positi)25(v)15(e)-393(from)-393(ne)15(g)5(ati)25(v)15(e)-393(points.)-739(Intuiti)25(v)15(ely)65(,)]TJ 0 -10.461 Td [(these)-218(are)-219(the)-218(points)-219(where)-218(the)-218(operator)-219(tree)-218(\050or)-219(the)-218(model\051)-218(is)-219(the)-218(most)]TJ 0 -10.461 Td [(unsure)-271(of)-271(while)-271(classifyi)1(ng)-271(them)-271(as)-271(matches)-271(or)-271(non-matches.)-372(In)-271(our)]TJ 0 -10.461 Td [(case,)-226(this)-220(border)-219(is)-220(easy)-220(to)-220(identify)-219(and)-220(corresponds)-220(to)-220(the)-220(planes)-219(that)]TJ 0 -10.46 Td [(de\002ne)-225(the)-226(rectangles)-225(equi)25(v)25(alent)-226(to)-225(the)-226(similarity)-225(joins.)-302(Therefore,)-230(we)]TJ 0 -10.461 Td [(may)-227(e)15(x)15(ecute)-228(the)-227(initial)-228(operator)-227(tree)-228(and)-227(sample)-227(a)-228(fe)25(w)-227(record)-228(pairs)-227(in)]TJ 0 -10.461 Td [(the)-224(output)-224(that)-224(are)-224(v)15(ery)-224(close)-224(to)-224(these)-224(planes)-223(and)-224(ask)-224(the)-224(programmer)]TJ 0 -10.461 Td [(to)-318(label)-318(them)-318(as)-318(matches)-318(or)-318(non-matches.)-514(W)80(e)-318(can)-318(add)-318(these)-318(ne)25(wly)]TJ 0 -10.461 Td [(labeled)-250(e)15(xamples)-250(to)-250(the)-250(original)-250(set)-250(and)-250(redesign)-250(the)-250(operator)-250(tree.)]TJ/F55 11.9552 Tf 0 -19.543 Td [(7.)-1000(EXPERIMENT)90(AL)-250(EV)135(ALU)60(A)95(TION)]TJ/F56 8.9664 Tf 8.966 -12.951 Td [(W)80(e)-213(no)25(w)-213(present)-213(a)-212(thorough)-213(e)25(v)25(aluation)-213(of)-213(our)-213(techniques.)-297(W)80(e)-213(com-)]TJ -8.966 -10.461 Td [(pare)-207(our)-207(techniques)-207(with)-207(domain-speci\002c)-207(address)-206(cleansing)-207(solutions)]TJ 0 -10.461 Td [(as)-275(well)-275(as)-276(with)-275(currently)-275(best)-275(kno)25(wn)-276(machine)-275(learning)-275(\050SVM\051)-275(tech-)]TJ 0 -10.461 Td [(niques)-300(for)-300(record)-300(matching.)-460(In)-300(both)-300(cases,)-312(we)-300(demonstrate)-300(that)-300(our)]TJ 0 -10.461 Td [(techniques)-264(yield)-265(operator)-265(trees)-264(with)-265(comparable)-264(and)-265(sometimes)-264(bet-)]TJ 0 -10.46 Td [(ter)-258(accurac)15(y)65(.)-334(W)80(e)-259(also)-258(sho)25(w)-258(that)-258(similarity)-258(joins)-258(can)-258(be)-258(e)15(x)15(ecuted)-258(sig-)]TJ 0 -10.461 Td [(ni\002cantly)-234(more)-233(ef)25(\002ciently)-234(than)-233(e)15(x)15(ecuting)-234(a)-234(join)-233(based)-234(on)-234(SVM)-233(pred-)]TJ 0 -10.461 Td [(icates,)-324(which)-308(require)-309(a)-309(cross)-309(product.)-487(Thus,)-324(we)-309(are)-308(able)-309(to)-309(pro)15(vide)]TJ 0 -10.461 Td [(accurate)-312(operator)-311(trees)-312(which)-312(are)-312(interpretable,)-327(ef)25(\002cient)-312(to)-311(e)15(x)15(ecute,)]TJ 0 -10.46 Td [(and)-250(can,)-250(if)-250(required,)-250(be)-250(modi\002ed)-250(by)-250(a)-250(programmer)55(.)]TJ ET Q 1 0 0 1 295.992 36 cm 0 Tr /QQAPFce02551e 12 Tf 0 0 0 rg 100 Tz 0 Ts 0 Tw 0 Tc BT 1 0 0 1 0 0 Tm (335)Tj ET 1 0 0 1 0 0 cm 1 0 0 1 -295.992 -36 cm endstream endobj 118 0 obj << /Type /Page /Resources 117 0 R /MediaBox [ 0 0 612 792 ] /Parent 91 0 R /Contents [ 119 0 R ] >> endobj 117 0 obj << /Font << /F57 11 0 R /F56 10 0 R /F34 12 0 R /F31 18 0 R /F36 8 0 R /F35 49 0 R /F33 51 0 R /F37 55 0 R /F55 9 0 R /F12 85 0 R /F9 50 0 R /F6 120 0 R /QQAPFce02551e 232 0 R >> /ProcSet [ /PDF /Text ] >> endobj 123 0 obj << /Length 14707 /LC /QQAP >> stream q 1 0 0 1 59.182 630.204 cm q 0.18181 0 0 0.17647 0 0 cm q 1 0 0 1 0 0 cm /Im8 Do Q Q 1 0 0 1 -59.182 -630.204 cm BT /F55 8.9664 Tf 102.602 616.981 Td [(Figur)18(e)-250(9:)-310(Cora)]TJ ET 1 0 0 1 213.942 630.204 cm q 0.18181 0 0 0.17647 0 0 cm q 1 0 0 1 0 0 cm /Im9 Do Q Q 1 0 0 1 -213.942 -630.204 cm BT /F55 8.9664 Tf 243.415 616.981 Td [(Figur)18(e)-250(10:)-310(Restaurant)]TJ ET 1 0 0 1 368.701 630.204 cm q 0.18181 0 0 0.17647 0 0 cm q 1 0 0 1 0 0 cm /Im10 Do Q Q 1 0 0 1 -368.701 -630.204 cm BT /F55 8.9664 Tf 410.871 616.981 Td [(Figur)18(e)-250(11:)-310(Bird)]TJ ET 1 0 0 1 59.182 510.599 cm q 0.18181 0 0 0.17647 0 0 cm q 1 0 0 1 0 0 cm /Im11 Do Q Q 1 0 0 1 -59.182 -510.599 cm BT /F55 8.9664 Tf 86.118 497.376 Td [(Figur)18(e)-250(12:)-310(Design)-250(T)18(ime)]TJ ET 1 0 0 1 213.942 510.599 cm q 0.18181 0 0 0.17647 0 0 cm q 1 0 0 1 0 0 cm /Im12 Do Q Q 1 0 0 1 -213.942 -510.599 cm BT /F55 8.9664 Tf 215.144 497.376 Td [(Figur)18(e)-250(13:)-310(Design)-250(time)-250(vs)-250(#Examples)]TJ ET 1 0 0 1 368.701 510.599 cm q 0.18181 0 0 0.17647 0 0 cm q 1 0 0 1 0 0 cm /Im13 Do Q Q 1 0 0 1 -368.701 -510.599 cm BT /F55 8.9664 Tf 388.334 497.376 Td [(Figur)18(e)-250(14:)-310(Design)-250(time)-250(vs)-250(d)]TJ/F57 8.9664 Tf -325.569 -29.72 Td [(Evaluation)-306(Metrics)]TJ/F56 8.9664 Tf 69.492 0 Td [(:)-423(W)80(e)-306(use)]TJ/F57 8.9664 Tf 35.461 0 Td [(pr)37(ecision)]TJ/F56 8.9664 Tf 35.788 0 Td [(and)]TJ/F57 8.9664 Tf 15.696 0 Td [(r)37(ecall)]TJ/F56 8.9664 Tf 23.334 0 Td [(metrics)-306(to)-307(e)25(v)25(al-)]TJ -188.738 -10.461 Td [(uate)-300(an)15(y)-300(record)-300(matching)-300(program)]TJ/F34 8.9664 Tf 127.854 0 Td [(Q)]TJ/F56 8.9664 Tf 9.959 0 Td [([10].)-460(Recall)-300(is)-300(the)-300(fraction)-300(of)]TJ -137.813 -10.461 Td [(true)-383(matching)-384(record)-383(pairs)-383(identi\002ed)-383(by)]TJ/F34 8.9664 Tf 151.108 0 Td [(Q)]TJ/F56 8.9664 Tf 7.268 0 Td [(.)-710(And,)-417(prec)1(ision)-384(is)-383(the)]TJ -158.376 -10.46 Td [(fraction)-352(of)-351(record)-352(pairs)]TJ/F34 8.9664 Tf 88.3 0 Td [(Q)]TJ/F56 8.9664 Tf 10.422 0 Td [(returns)-352(which)-351(are)-352(true)-352(matches.)-615(Higher)]TJ -98.722 -10.461 Td [(recall)-252(and)-252(precision)-252(v)25(alues)-252(are)-252(better)55(.)-316(Comparing)-252(recall)-252(v)25(alues)-252(at)-252(the)]TJ 0 -10.461 Td [(same)-314(precision)-313(\050or)-314(vice)-314(v)15(ersa\051)-314(w)10(ould)-313(allo)25(w)-314(us)-314(to)-314(compare)-313(dif)25(ferent)]TJ 0 -10.461 Td [(record)-241(matching)-242(program)1(s.)-308(Note)-241(that)-241(we)-241(can)-242(control)-241(the)-241(precision)-241(of)]TJ 0 -10.461 Td [(the)-250(resulting)-250(operator)-250(trees)-250(by)-250(v)25(arying)]TJ/F34 8.9664 Tf 138.727 0 Td [(\014)]TJ/F56 8.9664 Tf 5.661 0 Td [(.)]TJ -135.421 -10.46 Td [(W)80(e)-256(implemented)-256(the)-257(similarity)-256(join)-256(and)-256(rename)-257(operators)-256(and)-256(our)]TJ -8.967 -10.461 Td [(operator)-254(tree)-255(design)-254(techniques)-255(as)-254(client)-255(applications)-254(o)15(v)15(er)-254(Microsoft)]TJ 0 -10.461 Td [(SQL)-272(Serv)15(er)-271(2005.)-376(W)80(e)-271(ran)-272(all)-272(our)-272(e)15(xperiments)-271(on)-272(a)-272(desktop)-272(PC)-271(run-)]TJ 0 -10.461 Td [(ning)-344(W)40(indo)25(ws)-343(XP)-344(SP2)-343(o)15(v)15(er)-344(a)-343(2.2)-344(GHz)-343(Pentium)-344(4)-343(CPU)-344(with)-343(2GB)]TJ 0 -10.46 Td [(main)-303(memory)65(.)-471(Unless)-303(otherwise)-303(e)15(xplicitly)-304(mentioned,)-317(we)-303(allo)25(w)-303(all)]TJ 0 -10.461 Td [(similarity)-231(joins)-230(to)-231(in)40(v)20(olv)15(e)-230(at)-231(most)]TJ/F31 8.9664 Tf 121.338 0 Td [(4)]TJ/F56 8.9664 Tf 6.675 0 Td [(\050i.e.,)]TJ/F34 8.9664 Tf 18.287 0 Td [(d)]TJ/F31 8.9664 Tf 7.334 0 Td [(=)-286(4)]TJ/F56 8.9664 Tf 14.335 0 Td [(\051)-231(similarity)-230(functions.)]TJ -167.969 -10.461 Td [(Further)40(,)-295(we)-287(only)-286(consider)-286(the)-286(union)-287(of)-286(at)-286(most)]TJ/F31 8.9664 Tf 171.003 0 Td [(4)]TJ/F56 8.9664 Tf 7.175 0 Td [(\050i.e.,)]TJ/F34 8.9664 Tf 18.833 0 Td [(K)]TJ/F31 8.9664 Tf 11.621 0 Td [(=)-355(4)]TJ/F56 8.9664 Tf 14.954 0 Td [(\051)-286(sim-)]TJ -223.586 -10.461 Td [(ilarity)-277(joins)-277(in)-277(the)-277(resulting)-277(operator)-277(tree.)-391(W)80(e)-277(also)-277(e)25(v)25(aluate)]TJ/F57 8.9664 Tf 215.197 0 Td [(baseline)]TJ/F56 8.9664 Tf -215.197 -10.461 Td [(operator)-372(trees,)-403(which)-372(contain)-372(one)-372(similarity)-373(join)-372(with)-372(at)-372(most)-372(one)]TJ 0 -10.46 Td [(similarity)-250(function)-250(predicate)-250(\050i.e.,)]TJ/F34 8.9664 Tf 122.273 0 Td [(K)]TJ/F31 8.9664 Tf 11.002 0 Td [(=)-285(1)]TJ/F56 8.9664 Tf 16.576 0 Td [(and)]TJ/F34 8.9664 Tf 15.189 0 Td [(d)]TJ/F31 8.9664 Tf 7.335 0 Td [(=)-285(1)]TJ/F56 8.9664 Tf 14.335 0 Td [(\051.)]TJ/F55 11.9552 Tf -186.71 -19.367 Td [(7.1)-1000(Comparison)-250(with)-250(T)74(rillium)]TJ/F56 8.9664 Tf 8.967 -12.952 Td [(T)35(rillium)-292(is)-291(a)-292(domain-speci\002c)-291(address)-292(cleansing)-292(tool,)-302(which)-291(relies)]TJ -8.967 -10.461 Td [(on)-210(an)-211(e)15(xtensi)25(v)15(e)-210(set)-210(of)-211(domain-speci\002c)-210(rules)-210(\050e.g.,)-218(the)-211(w)10(ord)-210(\223street\224)-210(at)]TJ 0 -10.46 Td [(the)-214(end)-213(of)-214(the)-214(address)-213(attrib)20(ute)-214(may)-214(be)-213(replaced)-214(with)-214(\223st\224,)-220(etc.\051,)-221(or)18(g)5(a-)]TJ 0 -10.461 Td [(nization)-274(and)-275(address)-274(reference)-275(tables.)-383(T)35(rillium)-275(e)15(xploit)1(s)-275(a)-274(signi\002cant)]TJ 0 -10.461 Td [(amount)-309(of)-308(domain)-309(kno)25(wledge)-309(\050e)15(xpressed)-308(in)-309(the)-309(form)-309(of)-308(rules\051.)-486(W)80(e)]TJ 0 -10.461 Td [(demonstrate)-362(that)-361(operator)-362(trees)-362(designed)-361(using)-362(our)-362(domain)-361(neutral)]TJ 0 -10.46 Td [(techniques)-356(are)-356(able)-356(to)-356(achie)25(v)15(e)-356(accurac)15(y)-356(comparable)-355(with)-356(T)35(rillium.)]TJ 0 -10.461 Td [(Therefore,)-431(our)-394(packages)-394(are)-395(already)-394(v)15(ery)-395(accurate)-394(starting)-394(points,)]TJ 0 -10.461 Td [(which)-250(programmers)-250(can)-250(further)-250(enhance.)]TJ/F55 8.9664 Tf 8.967 -15.442 Td [(Dataset:)]TJ/F56 8.9664 Tf 38.386 0 Td [(Our)-459(\002rst)-458(set)-459(of)-458(e)15(xperiments)-459(are)-458(based)-459(on)-459(a)-458(relation)]TJ/F57 8.9664 Tf -47.353 -10.461 Td [(GBR)40(Or)37(gs)]TJ/F56 8.9664 Tf 37.219 0 Td [(consisting)-284(of)-284(names)-284(and)-284(addresses)-284(of)-284(or)18(g)5(anizati)1(ons)-284(based)]TJ -37.219 -10.461 Td [(in)-258(Great)-259(Britain.)-335(The)-258(relation)-258(contains)-259(multiple)-258(records)-258(representing)]TJ 0 -10.46 Td [(the)-243(sa)1(me)-243(or)18(g)5(anization.)-307(The)-243(schema)-242(of)-243(the)-242(relation)-243(is)]TJ/F57 8.9664 Tf 189.024 0 Td [(Name)10(,)-244(Addr)37(ess,)]TJ -189.024 -10.461 Td [(City)55(,)-384(State)10(,)-383(P)80(ostalCode)]TJ/F56 8.9664 Tf 84.788 0 Td [(.)-631(Our)-357(goal)-357(here)-357(is)-356(to)-357(identify)-357(the)-357(matching)]TJ -84.788 -10.461 Td [(record)-349(pairs)-349(in)]TJ/F78 8.9664 Tf 56.696 0 Td [(G)]TJ/F34 8.9664 Tf 7.883 0 Td [(B)-50(R)-7(O)-28(r)-29(g)-36(s)]TJ/F36 8.9664 Tf 37.871 0 Td [(\002)]TJ/F78 8.9664 Tf 9.891 0 Td [(G)]TJ/F34 8.9664 Tf 7.883 0 Td [(B)-50(R)-7(O)-28(r)-29(g)-36(s)]TJ/F56 8.9664 Tf 38.277 0 Td [(and)-349(then)-349(compare)-349(them)]TJ -158.501 -10.461 Td [(with)-250(the)-250(set)-250(of)-250(pairs)-250(output)-250(by)-250(T)35(rillium.)]TJ 8.967 -10.46 Td [(W)80(e)-257(ha)20(v)15(e)]TJ/F31 8.9664 Tf 32.957 0 Td [(29)]TJ/F56 8.9664 Tf 11.523 0 Td [(similarity)-257(functions.)-332(W)80(e)-258(use)-257(\050e)15(xact\051)-257(equality)65(,)-260(jaccard,)]TJ -53.447 -10.461 Td [(edit,)-420(generalized)-386(edit)-387(similarity)-386(functions)-386(on)-386(se)25(v)15(eral)-386(combinations)]TJ 257.036 392.966 Td [(of)-358(attrib)20(utes)-358(in)-358(the)-358(GBR)40(Or)18(gs)-358(table.)-634(W)80(e)-358(also)-358(use)-358(the)-358(follo)25(wing)-358(re-)]TJ 0 -10.461 Td [(name)-358(operators:)-526(\0501\051)-359(Posta)1(lCode)-359(splitter:)-526(in)-358(Great)-358(Britain,)-385(a)-358(pre\002x)]TJ 0 -10.461 Td [(usually)-324(of)-324(length)-324(of)]TJ/F31 8.9664 Tf 74.88 0 Td [(3)]TJ/F56 8.9664 Tf 4.608 0 Td [(,)-343(called)-324(the)]TJ/F57 8.9664 Tf 43.492 0 Td [(out-code)]TJ/F56 8.9664 Tf 31.374 0 Td [(,)-343(determ)1(ines)-325(the)-324(city)-324(and)]TJ -154.354 -10.461 Td [(state,)-334(while)-317(the)-318(suf)25(\002x,)-334(called)-317(the)]TJ/F57 8.9664 Tf 121.74 0 Td [(in-code)]TJ/F56 8.9664 Tf 26.89 0 Td [(,)-334(determines)-317(a)-318(small)-317(block)]TJ -148.63 -10.46 Td [(of)-287(addresses.)-419(Therefore,)-296(we)-287(may)-286(use)-287(the)-287(in-codes)-286(to)-287(compare)-286(street)]TJ 0 -10.461 Td [(addresses.)-302(W)80(e)-226(implement)-227(the)-226(rename)-226(operator)-227(for)-226(splitting)-226(the)-226(postal)]TJ 0 -10.461 Td [(code)-319(into)]TJ/F57 8.9664 Tf 36.607 0 Td [(out-code)]TJ/F56 8.9664 Tf 34.237 0 Td [(and)]TJ/F57 8.9664 Tf 15.811 0 Td [(in-code)]TJ/F56 8.9664 Tf 26.89 0 Td [(.)-518(\0502\051)-320(W)80(e)-319(also)-319(use)-320(the)-319(FD-correction)]TJ -113.545 -10.461 Td [(operator)-204(based)-205(on)-204(the)-205(functional)-204(dependencies:)]TJ/F57 8.9664 Tf 169.109 0 Td [(Out-code)]TJ/F36 8.9664 Tf 35.196 0 Td [(!)]TJ/F57 8.9664 Tf 11.049 0 Td [(City)]TJ/F56 8.9664 Tf 16.78 0 Td [(and)]TJ/F57 8.9664 Tf -232.134 -10.46 Td [(Out-code)]TJ/F36 8.9664 Tf 35.387 0 Td [(!)]TJ/F57 8.9664 Tf 11.239 0 Td [(State)]TJ/F56 8.9664 Tf 17.932 0 Td [(.)-302(Note)-226(that)-225(these)-226(tw)10(o)-225(are)-226(deri)25(v)15(ed)-226(columns)-225(obtained)]TJ -64.558 -10.461 Td [(only)-343(after)-343(the)-343(PostalCode)-343(splitter)-343(is)-343(actually)-343(applied.)-588(W)80(e)-343(initialize)]TJ 0 -10.461 Td [(these)-260(attrib)20(ute)-260(v)25(alues)-260(to)-260(be)-260(null)-260(and)-260(only)-260(if)-260(the)-260(postal)-260(code)-260(splitter)-260(is)]TJ 0 -10.461 Td [(applied)-250(these)-250(w)10(ould)-250(be)-250(populated)-250(with)-250(non-null)-250(v)25(alues.)]TJ/F57 8.9664 Tf 8.967 -10.461 Td [(T)55(r)15(aining)-417(set)]TJ/F56 8.9664 Tf 44.466 0 Td [(:)-645(W)80(e)-417(obtained)-417(a)-418(training)-417(set)-417(from)-417(the)-418(data)-417(o)25(wners)]TJ -53.433 -10.46 Td [(which)-382(the)15(y)-382(generated)-382(for)-382(e)25(v)25(aluation)-382(while)-382(tuning)-382(the)-381(T)35(rillium)-382(ad-)]TJ 0 -10.461 Td [(dress)-315(cleansing)-315(tool.)-504(The)-315(set)-315(has)]TJ/F31 8.9664 Tf 122.978 0 Td [(957)]TJ/F56 8.9664 Tf 16.646 0 Td [(e)15(xamples)-315(with)-315(roughly)-314(equal)]TJ -139.624 -10.461 Td [(numbers)-250(of)-250(matching)-250(and)-250(non-matching)-250(pairs.)]TJ/F57 8.9664 Tf 8.966 -10.461 Td [(Evaluating)-322(Pr)37(ecision)]TJ/F56 8.9664 Tf 76.273 0 Td [(:)-453(W)80(e)-322(\002rst)-321(e)25(v)25(aluate)-322(the)-322(precision)-321(of)-322(T)35(rillium)]TJ -85.239 -10.46 Td [(as)-236(follo)25(ws.)-305(W)80(e)-236(choose)-236(multiple)-236(uniform)-235(random)-236(samples)-236(of)-236(size)]TJ/F31 8.9664 Tf 231.258 0 Td [(200)]TJ/F56 8.9664 Tf -231.258 -10.461 Td [(from)-311(the)-310(matching)-311(record)-310(pairs)-311(output)-311(by)-310(T)35(rillium,)-326(and)-311(then)-310(manu-)]TJ 0 -10.461 Td [(ally)-313(e)15(xamine)-313(each)-313(pair)-313(to)-313(check)-313(whether)-313(or)-313(not)-313(the)-312(tw)10(o)-313(records)-313(are)]TJ 0 -10.461 Td [(true)-381(matches.)-704(Therefore,)-414(the)-381(ratio)-381(between)-382(the)-381(number)-381(of)-381(correct)]TJ 0 -10.461 Td [(matches)-345(and)]TJ/F31 8.9664 Tf 48.518 0 Td [(200)]TJ/F56 8.9664 Tf 16.917 0 Td [(is)-345(a)-345(good)-345(unbiased)-345(estimate)-345(of)-345(the)-345(true)-346(precision)]TJ -65.435 -10.46 Td [(\050see)-276(Section)-276(6.1\051.)-388(W)80(e)-276(a)20(v)15(erage)-276(the)-276(precision)-276(v)25(alues)-275(o)15(v)14(e)1(r)-276(all)-276(samples.)]TJ 0 -10.461 Td [(W)80(e)-234(b)20(ui)1(ld)-234(an)-233(operator)-234(tree)-233(using)-234(our)-233(techniques)-234(such)-233(that)-234(our)-233(tar)18(geted)]TJ 0 -10.461 Td [(precision)-210(\050at)]TJ/F31 8.9664 Tf 46.092 0 Td [(100%)]TJ/F56 8.9664 Tf 23.383 0 Td [(recall\051)-210(is)-209(equal)-210(to)-210(that)-210(of)-210(T)35(rilli)1(um')55(s)-210(estimated)-210(pre-)]TJ -69.475 -10.461 Td [(cision)]TJ/F34 8.9664 Tf 23.473 0 Td [(p)]TJ/F56 8.9664 Tf 4.626 0 Td [(.)-303(W)80(e)-229(then)-229(e)25(v)25(aluate)-229(the)-229(precision)-229(of)-229(the)-229(resulting)-229(operator)-229(tree)]TJ -28.099 -10.46 Td [(ag)5(ain)-285(using)-286(multiple)-285(samples)-286(of)-285(size)]TJ/F31 8.9664 Tf 134.36 0 Td [(200)]TJ/F56 8.9664 Tf 13.823 0 Td [(,)-294(and)-286(a)20(v)15(erage)-285(the)-286(precision)]TJ -148.183 -10.461 Td [(estimates.)]TJ 8.966 -10.461 Td [(T)80(able)-255(1)-256(compares)-255(the)-256(results)-255(of)-256(our)-255(operator)-256(tree)-255(with)-255(that)-256(of)-255(T)35(ril-)]TJ -8.966 -10.461 Td [(lium.)-466(W)80(e)-301(observ)15(e)-302(that)-302(the)-302(precision)-302(obtained)-302(by)-302(using)-301(our)-302(operator)]TJ 0 -10.461 Td [(trees)-229(\050)]TJ/F31 8.9664 Tf 21.969 0 Td [(0)]TJ/F34 8.9664 Tf 4.608 0 Td [(:)]TJ/F31 8.9664 Tf 2.559 0 Td [(98)]TJ/F56 8.9664 Tf 9.216 0 Td [(\051)-229(is)-229(v)15(ery)-230(clos)1(e)-230(to)-229(that)-229(of)-229(T)35(rillium)-229(\050)]TJ/F31 8.9664 Tf 120.09 0 Td [(0)]TJ/F34 8.9664 Tf 4.607 0 Td [(:)]TJ/F31 8.9664 Tf 2.56 0 Td [(99)]TJ/F56 8.9664 Tf 9.216 0 Td [(\051.)-303(Further)40(,)-233(the)-230(num)1(-)]TJ -174.825 -10.46 Td [(ber)-302(of)-302(positi)25(v)15(e)-302(pairs)-303(t)1(hat)-303(our)-302(operator)-302(trees)-302(detected)-302(is)-302(much)-302(higher)]TJ 0 -10.461 Td [(\050by)-287(about)]TJ/F31 8.9664 Tf 37.016 0 Td [(10%)]TJ/F56 8.9664 Tf 16.895 0 Td [(\051)-287(than)-286(that)-287(returned)-287(by)-286(T)35(rillium)-287(suggesting)-286(that)-287(at)-287(al-)]TJ -53.911 -10.461 Td [(most)-382(the)-382(sam)1(e)-382(precision)-382(the)-382(recall)-382(of)-381(our)-382(operator)-382(trees)-382(is)-381(higher)55(.)]TJ 0 -10.461 Td [(Thus,)-311(operator)-299(trees)-298(designed)-299(by)-299(our)-298(domain)-299(neutral)-299(techniques)-298(are)]TJ 0 -10.46 Td [(at)-373(least)-373(of)-374(comparabl)1(e,)-404(and)-374(quite)-373(lik)10(ely)-373(higher)40(,)-404(accurac)15(y)-373(than)-373(that)]TJ 0 -10.461 Td [(of)-328(the)-327(domain)-328(speci\002c)-328(commercial)-327(address)-328(cleansing)-328(tool)-327(T)35(rillium.)]TJ 0 -10.461 Td [(Also,)-376(observ)15(e)-350(that)-351(the)-350(best)-351(base)1(line)-351(operator)-350(is)-351(only)-350(able)-351(to)-350(detect)]TJ ET Q 1 0 0 1 295.992 36 cm 0 Tr /QQAPFce02551e 12 Tf 0 0 0 rg 100 Tz 0 Ts 0 Tw 0 Tc BT 1 0 0 1 0 0 Tm (336)Tj ET 1 0 0 1 0 0 cm 1 0 0 1 -295.992 -36 cm endstream endobj 122 0 obj << /Type /Page /Resources 121 0 R /MediaBox [ 0 0 612 792 ] /Parent 91 0 R /Contents [ 123 0 R ] >> endobj 111 0 obj << /Type /XObject /Subtype /Form /FormType 1 /PTEX.FileName (Plots/Cora.pdf) /PTEX.PageNumber 1 /PTEX.InfoDict 125 0 R /Matrix [0 -1 1 0 0 612] /BBox [0 0 612 792] /Resources << /ProcSet [ /PDF /Text ] /ExtGState << /R7 126 0 R >>/Font << /R8 127 0 R/R9 128 0 R/R10 129 0 R>> >> /Length 130 0 R /Filter /FlateDecode >> stream x[Kdׯe.:;ddaT<#,aYY$./.̾Gk_ aƠȡw] !.s:pbAMGi$$jH$I6 J'K2( G`t2;Ўw$PI#c&:5=R,Hy:pТmBL|:h4=elFUjmxEY[%zxCn:4_г$8t1t`#uFȚFCۂ TJNhG&oz}/\])$R}Jd"=:"UX9742b6#*au_PZ?Ӣ4n~byg4BSg};I\xDX%2s:gITRrt@~2E% 4hP7j\Y!T\5t9j~iҋ9]uMC/۽QuwvͦR=k-ɳvʾB|phEdL8pQ)L7CFH6#b`7"Ue (YsҢyS^BD-1m 5ֆ:hcIA N2 1wkm6df@'!ډ/Kj٦inITثHEi*rKցDP 5m+4qﶣyMFK:h="ˣe@uٛӧ_8Rd(ppKg굌r˓k+ק+Ej_vpy̛6_eo1)Gu3i G7ޝOjyڽ_C;/.s0(UntПTvױs:in?U)9ˡүD\շs0gGkQW DK,$4ˬЋGmМ|, 3|\SN׏CX8u a#FPFvACCol—F˚]nԔM`VPљ9Aσ,j ʵBa_3T~q3Au&\%x,5t4O?3g3X_k>?&؂A sfΔi Ʃׇ3JIkLRWaL5Uj'aV/Oߎ2V;]o?-<ǾF{\[$7ܺ m8b{;OT0+)M$idЕb2pUN r X)h*97?n@FA!"Aww|ymE &Dzn:uv77Z1{?=ǟG|y30p`ӲF6'Ade +i$I7M!$HJdH\% $uCb޽[3Fb7:4btd:Z4l0z6{Y(=>; EwtHkzT1O'~*4n!A-zVS$[gg%B?1hZ;)kZlI0jzd$-O9/-ˈPV :#GyNQB#6`l˝%y?%~M@2"U&댄%^Zl[h+UDT52hz2DB^1tOt?zxYUM#3 0kw o6 V.!b1_ [Ox"Ē%dl2FK^Fw. I:F̬ix#ӯJ?2tL؆YHSEDX m/OxÒ9Rb O 7e(:1YFбytG--Ʋ>`]|3; uscl;Aױ M؅tnb]?g"/#׏KO2NE?̻ѐbˊջ.|y_>F×@Hutޤ=z:ӋJouDK\O\Ho 8 ӕv\gMgޏ V[)wt $8q_ xb2CQ&_*-SGB?L=|$㡲BϷF5$3V.bc iO}+콻ڭlj??~ _}5z_}F endstream endobj 125 0 obj << /Producer (AFPL Ghostscript 8.53) /CreationDate (D:20070710120831) /ModDate (D:20070710120831) /Title (Overall-Expts.xls) /Creator (PScript5.dll Version 5.2.2) /Author (vganti) >> endobj 126 0 obj << /Type /ExtGState /OPM 1 >> endobj 127 0 obj << /BaseFont /Helvetica /Type /Font /Subtype /Type1 >> endobj 128 0 obj << /BaseFont /Courier /Type /Font /Subtype /Type1 >> endobj 129 0 obj << /BaseFont /Helvetica-Bold /Type /Font /Subtype /Type1 >> endobj 130 0 obj 4109 endobj 112 0 obj << /Type /XObject /Subtype /Form /FormType 1 /PTEX.FileName (Plots/Restaurant.pdf) /PTEX.PageNumber 1 /PTEX.InfoDict 131 0 R /Matrix [0 -1 1 0 0 612] /BBox [0 0 612 792] /Resources << /ProcSet [ /PDF /Text ] /ExtGState << /R7 132 0 R >>/Font << /R8 133 0 R/R10 134 0 R/R9 135 0 R>> >> /Length 136 0 R /Filter /FlateDecode >> stream x\]\}_я34&_ XlCIJxoSUV:@lȂ# XSm_N_~tS}J)s׿_Ԑ|9R_8]9S8} {B~!RF©o>^;j^8 b#S({N@_()GT0J:_8zlTL: ϸ1O@ʆQA?O+㡑ĕo^bި"ثzjiA:+1n6qff68(vQDz]ˁrXNXiY @NDLuqXXu"vSۖ\Xyc%C/Dbn ҃ tkk=-ǁ`Eꐕ)NS{[le}J_U?0Τ h_[ojH-VU~mjLT[V`gZw:T/:ىӴQAʏF6o.f6Kux\ u+Uh_[@6p:e&*)ul32N)ؙV!r -ٜe'F~lBwv3Ge,tԔGVџ#D\mcek@ 0_%iÔN Z!S1ZxEMMVGr7ъR:GudgM[)3m]\@$Q:G.[Z5,\*_v6[Yz!sIqG$Q8`ۨ;R+q2i'RsM,4vBE.1jDA ]muGpUwl҉+:8;DRd{; B"s|m8Ͼ8($4vG$Ը.L9 Uڹ f2׃i>,t=LlDΖC-A1L/E|dK`$u`ۨ 'טl@c°%rhPWWutLic6dFaa]eb<Yq ;[ &5Н(5q Ӌ8^Pq^k]Q1p6A -JJM7_i!E ]m*ո %=Au;s*av sp+7tؾf@LН(58"Ο*8LI1E^O&PD]\=iRJnjV*1T*tEvU&@sɸ52@1lНS]q Ӌ8Wu]"1J`SLx[6,9#`6/[9(Qr+ = wZmQ"y^֣nU][S,n\Hs VD\46yH^d]FB@zn5rHDUkAdT[$jwd_]m ET=Ц4rHOڭ:6 bǎ=xOm[9։'n(_[$ˊ[ 5k ! TrsE OKHYB""4ÔTtzZl{R 2S!eԖ8sW}<+huU`. \R*JKf[Y=]q²Jٰ+RQW@YhE`zW1|Ҥz5DPWK']zIU)2j8sW*5YW p-0Dk.)mKf[YiI-'c(0GFȠi$Kה;V$QE<7 x_<@[0v/oK@|4U~फ़pX.on/Fԩ>X]|DK^V+$k_!b*?[J8,7W7מ%- ,yY6}Ak\K-x2͊q:E %- ,yY&gyvE,ZeMu*xNYVQO]xV?|]A6hVhgBT,bHE)qՓH9Mq. ihF]I=!>5KuFSՏ62wl2Mm4٤XD%/ڶI(ѭkDg (4 8ߑ'^cTF@FSՏ6*2wls)+Jo-R'AnF?> Vٟ__;}uiLno87a9O)p-5Ňcmqf?N1_N_Oyw )#uԁKg\&n>8 mJER3miCB}Mx=LJggtyOZZ%3:{>)舘ϛJ*L9tHSsH}+ffnoO5R<-}Ό3?6 ^Ur+_ݍ8M;?KȚQQƏtFDd8³)~>EȁL[q}\_}Gq2_ "Z OȆQA;b 7o^b?\lǞ%s.!}GD,2*>q:ԁňhR͈ȃ$,яZx;yd/G_󰧞&1jeog34{M7qׄ GyL{:~a=dP{IׅζC|1@q8{Mۤy 9$ K[l"8> *L3'K}M<|@+xtxN$ VH"XzzbF\Zeر/fx2kp=dtzbɗ;Vȍy|- bc.yT?ί~~366)|4}MhMT窠}M{) B%>j@9Xd'E ^IéZH{QN9XdQNӏb9)J/@? $IZ W) '":wܔs RoH6-q[hބۧ 7׏YxZJmy fc efo.,^]jb_s乳~N3j(swcqobs:?7?<γcL 3_J7rSԗZD}B_FJ/#YO"1xʭG Nsƥr#%[ZK?`* endstream endobj 131 0 obj << /Producer (AFPL Ghostscript 8.53) /CreationDate (D:20070710120831) /ModDate (D:20070710120831) /Title (Overall-Expts.xls) /Creator (PScript5.dll Version 5.2.2) /Author (vganti) >> endobj 132 0 obj << /Type /ExtGState /OPM 1 >> endobj 133 0 obj << /BaseFont /Helvetica /Type /Font /Subtype /Type1 >> endobj 134 0 obj << /BaseFont /Helvetica-Bold /Type /Font /Subtype /Type1 >> endobj 135 0 obj << /BaseFont /Courier /Type /Font /Subtype /Type1 >> endobj 136 0 obj 4765 endobj 113 0 obj << /Type /XObject /Subtype /Form /FormType 1 /PTEX.FileName (Plots/Birds.pdf) /PTEX.PageNumber 1 /PTEX.InfoDict 137 0 R /Matrix [0 -1 1 0 0 612] /BBox [0 0 612 792] /Resources << /ProcSet [ /PDF /Text ] /ExtGState << /R7 138 0 R >>/Font << /R10 139 0 R/R9 140 0 R/R8 141 0 R>> >> /Length 142 0 R /Filter /FlateDecode >> stream x\ˎd WԲk.;dda=n8 ҽ<|j #pXHQDI;g7Oߝk9S?)2oߞ~ߜBiWFrυ$^#yDs=F$WF'#"]=iCOȠ (=)FDoz6a!S!#+d2az}#Xi bA[䖹D$?݃D:LtLQRz._!j$u :(}ӂK`&3PsNHVt .=\mlzTd!j. ܭwMIK1H'rn*w׎v% P]9Ir7--ѝZF:hYZPs]kQI2vU/mG;aq@LtA&}KtDwCea1ѭ9sKtmfӣDBȹ H/{q}޳?b o{AWZP"pjϲ(8RJWs*NAtŹtBc$.' NN<T(C=ۜ_襾eLKBׅ _ ܫ@/@o36+ϞZ,FB(J#8iS!#[DȽE*lTH@v>ڷ0H):h)#AI]rcA TuЬ ފn$R< ܅:Z UJ#Tӣ K֌pE>BFܐr6uzhdA20uuqɴ+vV /tSF Ѕ9A"d^+ޠ xPAe2yPwx*phBvj|>T6=BSnFx+qYIԂV=ę[+ !\kfE3%]9[#ӊ9`nEDž XtBfB/)@o2x9.ф.H+x=4SèB=^4%aC@6\wiA9t>->">bo)k6 +GC IN[,f_>Fԅ HfT554ƭep## #Iam#hi$kmCbjK"fiJ }4}Z|D|< (jN,k68#؆Xz{mEe |$U*EHik~S^%R*FeD$㣖d|F%d:lӈ$k\ҴQ[YȗQ!u\|G9%2 n8G((Yf&@ƛe 44b(4}4x82rbđAD$?Ǒ;qӀ>ӷO>ocdyF v{'wq6F>]ǯݘ7O26zSn헧'yHG/%nHϧp( :pM-Ovcܴ)q0sS~avsQ-?Xd{˦73"i׀j΍1rmJG)mldp#`γν5_ݝa8ckӽo߯ӹ֨PdBM#y#jN<9S|բ[ LGZM!tD2um  Y9HaFSzuU@< 48 Inr*,teY&4p| =<_BSOOD9dT`܊?Ht¡ea82F[.A O_Zj7ֆrg_F'ߙ])>ŨXG\9/kQ$UU%LD2BR4e<쯵v<{z/k+Lg>d)vM?Vmn&,7O 3vzC2-`$X[3pB&#>2Liu_\hϵf*H/7lIv")$ BjQZ^tidIKVM#JD$䚕dHI8IrE'A^t,.:4$;樌~ Oq./.iT%<804Bh:P]C?3^uH%tSFų z怯wd 2HXM%nxPNe &%hm7'Gw)k v27fڵ]mF#lRcx! PGۖ?*)*̍=l $uGn~\ب ojܘ-AtQݥ룋K]_e@ f&*-ߧq~?=0B3t~TBx+{~> endobj 138 0 obj << /Type /ExtGState /OPM 1 >> endobj 139 0 obj << /BaseFont /Helvetica-Bold /Type /Font /Subtype /Type1 >> endobj 140 0 obj << /BaseFont /Courier /Type /Font /Subtype /Type1 >> endobj 141 0 obj << /BaseFont /Helvetica /Type /Font /Subtype /Type1 >> endobj 142 0 obj 4752 endobj 114 0 obj << /Type /XObject /Subtype /Form /FormType 1 /PTEX.FileName (Plots/ModelBldTime.pdf) /PTEX.PageNumber 1 /PTEX.InfoDict 143 0 R /Matrix [0 -1 1 0 0 612] /BBox [0 0 612 792] /Resources << /ProcSet [ /PDF /Text ] /ExtGState << /R7 144 0 R >>/Font << /R8 145 0 R/R10 146 0 R/R9 147 0 R>> >> /Length 148 0 R /Filter /FlateDecode >> stream xZKo7أ@-RCC(VNb+j&3oRыA^<9to:DsZQƫ9ksmwTpziejA~)(wD!}sݭa;)l6"/*Bu뤖wVB>N2ǩ>M37V+[L8)G+]y'L1ZV2;^cm ng3\ޜnM;nw5oݤSxMKwY$@٥T?^m?.|-7܇(g ho,E&晤hf:@(}rGf Sv TTh$ jR!&LzVFƞ|ڡNf:iseֳ3@ك&}zzi=hϨ(ҘTe;4!y;R3*to+B,7ߺ 0jYRI ~/Tw_A CՀQ=LRN+C _SC~2[CR2Y2? Sb@~ wimo !}?ۛ#\FY(TiyP:ye(D*>#Þ1te}9m_*PzF_~H~_cFj9*Ub5(̔ƗDq{fef| .ƪ})N|9>n~66%XBB_b_)9؍e땼6ij=wǚBmx)GP+wdL|>0Q>ڤ};(LUFumdڥx07x9^˯teYº8 endstream endobj 143 0 obj << /Producer (AFPL Ghostscript 8.53) /CreationDate (D:20070709230708) /ModDate (D:20070709230708) /Title (Overall-Expts.xls) /Creator (PScript5.dll Version 5.2.2) >> endobj 144 0 obj << /Type /ExtGState /OPM 1 >> endobj 145 0 obj << /BaseFont /Helvetica-Bold /Type /Font /Subtype /Type1 >> endobj 146 0 obj << /BaseFont /Helvetica /Type /Font /Subtype /Type1 >> endobj 147 0 obj << /BaseFont /Courier /Type /Font /Subtype /Type1 >> endobj 148 0 obj 1921 endobj 115 0 obj << /Type /XObject /Subtype /Form /FormType 1 /PTEX.FileName (Plots/Scalability.pdf) /PTEX.PageNumber 1 /PTEX.InfoDict 149 0 R /Matrix [0 -1 1 0 0 612] /BBox [0 0 612 792] /Resources << /ProcSet [ /PDF /Text ] /ExtGState << /R7 150 0 R >>/Font << /R10 151 0 R/R9 152 0 R/R8 153 0 R>> >> /Length 154 0 R /Filter /FlateDecode >> stream xXn7+Hpf F' S,ɸKA3$;\ɒR!"iT3Q28-gWMhP68hxb4Yy$O_6W!X$],Z|}|/k/X0ɪUt#Ry,:Ȫc0}†"NoU"yeo֢9Z1GA&{ ML<E:8WhBMuVe^=~tz,V4mW/Df&jTN5d4j[aueh.ij~ފ$lڬzfeAvYM%٠^q*mx'*RNBp)6u(Q{6HOn^ky.A)DYSؚ;MRF%U,1lDhJiH|IY$pePu|If/ _ DlaR<\Y]8ʁET)FrA)D󧁵)/49>> endobj 150 0 obj << /Type /ExtGState /OPM 1 >> endobj 151 0 obj << /BaseFont /Helvetica /Type /Font /Subtype /Type1 >> endobj 152 0 obj << /BaseFont /Courier /Type /Font /Subtype /Type1 >> endobj 153 0 obj << /BaseFont /Helvetica-Bold /Type /Font /Subtype /Type1 >> endobj 154 0 obj 1523 endobj 116 0 obj << /Type /XObject /Subtype /Form /FormType 1 /PTEX.FileName (Plots/Scalability-dimns.pdf) /PTEX.PageNumber 1 /PTEX.InfoDict 155 0 R /Matrix [0 -1 1 0 0 612] /BBox [0 0 612 792] /Resources << /ProcSet [ /PDF /Text ] /ExtGState << /R7 156 0 R >>/Font << /R8 157 0 R/R10 158 0 R/R9 159 0 R>> >> /Length 160 0 R /Filter /FlateDecode >> stream xn$5_cJӸ6B!#8Pj&K)mwIh7v\oW{@0~}e$awg?tF  qL:)cc]w=vRX@BNqkH۰C2˱w/ȹ,*2}%#W! $Y!R@5} \m©@j *! fO p]NaL(t p;äq0["Z0|Ppn`M-  HJGb% Z-,P$aF7kʚV5. MTZi5s q-*>hfH) \Gn}rw_{6Y< ʭÖ2˔ %PZVn.{*H*lRm .M6lEgD/R)B))A~ أC^P7K<"ͤV9QH_Q4G>ԭyəOi+Z$eeel*4]jNG'H*S:HF_UY U%\zFTTKmܺl%N}bQjn-\]$g$UuYZV;=arT"f%[ަ-UuYuY*ٺ^U;VHm ^K߆e OWgǞ$ďsPL 1 %(m'b 9.dsľ׷,`H l Pv ?msx=ev:~-70p^m<5+~XA=>u[T1:[FonRJJaAJko!."9LzqvcQP\|"~DWośKEnzW+ub9-Hz l"D HP:L bJeF1b&'< A^؇\>ufD@B0Xg%zV|i#6jjym69lf0l f&ER&Jh@j?XTioL>Og< >jPXO|\Ec,> endobj 156 0 obj << /Type /ExtGState /OPM 1 >> endobj 157 0 obj << /BaseFont /Helvetica-Bold /Type /Font /Subtype /Type1 >> endobj 158 0 obj << /BaseFont /Helvetica /Type /Font /Subtype /Type1 >> endobj 159 0 obj << /BaseFont /Courier /Type /Font /Subtype /Type1 >> endobj 160 0 obj 1565 endobj 121 0 obj << /Font << /F55 9 0 R /F57 11 0 R /F56 10 0 R /F34 12 0 R /F31 18 0 R /F78 124 0 R /F36 8 0 R /QQAPFce02551e 232 0 R >> /XObject << /Im8 111 0 R /Im9 112 0 R /Im10 113 0 R /Im11 114 0 R /Im12 115 0 R /Im13 116 0 R >> /ProcSet [ /PDF /Text ] >> endobj 163 0 obj << /Length 30350 /LC /QQAP >> stream q BT /F55 8.9664 Tf 65.541 722.012 Td [(T)92(able)-250(1:)-310(Comparison)-250(with)-250(T)74(rillium:)]TJ/F34 8.9664 Tf 137.04 0 Td [(K)]TJ/F31 8.9664 Tf 11.002 0 Td [(=)-285(4)]TJ/F34 8.9664 Tf 14.335 0 Td [(;)-171(D)]TJ/F31 8.9664 Tf 14.511 0 Td [(=)-285(29)]TJ/F34 8.9664 Tf 18.942 0 Td [(;)-171(d)]TJ/F31 8.9664 Tf 11.431 0 Td [(=)-285(4)]TJ ET q 1 0 0 1 101.928 718.992 cm []0 d 0 J 0.398 w 0 0 m 148.821 0 l S Q q 1 0 0 1 101.928 709.827 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q q 1 0 0 1 140.734 709.827 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 146.114 712.517 Td [(Estimated)-250(precision)]TJ ET q 1 0 0 1 214.585 709.827 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 222.485 712.517 Td [(Recall)]TJ ET q 1 0 0 1 250.749 709.827 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q q 1 0 0 1 101.928 709.627 cm []0 d 0 J 0.398 w 0 0 m 148.821 0 l S Q q 1 0 0 1 101.928 700.462 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 108.185 703.152 Td [(T)35(rillium)]TJ ET q 1 0 0 1 140.734 700.462 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F67 7.9701 Tf 170.132 703.152 Td [(0)]TJ/F68 7.9701 Tf 4.234 0 Td [(:)]TJ/F67 7.9701 Tf 2.353 0 Td [(99)]TJ ET q 1 0 0 1 214.585 700.462 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F67 7.9701 Tf 219.964 703.152 Td [(144733)]TJ ET q 1 0 0 1 250.749 700.462 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q q 1 0 0 1 101.928 691.495 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 107.308 694.185 Td [(Op.)-250(T)35(ree)]TJ ET q 1 0 0 1 140.734 691.495 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F67 7.9701 Tf 170.132 694.185 Td [(0)]TJ/F68 7.9701 Tf 4.234 0 Td [(:)]TJ/F67 7.9701 Tf 2.353 0 Td [(98)]TJ ET q 1 0 0 1 214.585 691.495 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F67 7.9701 Tf 219.964 694.185 Td [(159354)]TJ ET q 1 0 0 1 250.749 691.495 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q q 1 0 0 1 101.928 682.529 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 107.607 685.219 Td [(Baseline)]TJ ET q 1 0 0 1 140.734 682.529 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F67 7.9701 Tf 170.132 685.219 Td [(0)]TJ/F68 7.9701 Tf 4.234 0 Td [(:)]TJ/F67 7.9701 Tf 2.353 0 Td [(98)]TJ ET q 1 0 0 1 214.585 682.529 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F67 7.9701 Tf 222.082 685.219 Td [(79600)]TJ ET q 1 0 0 1 250.749 682.529 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q q 1 0 0 1 101.928 682.33 cm []0 d 0 J 0.398 w 0 0 m 148.821 0 l S Q BT /F55 8.9664 Tf 102.591 643.952 Td [(T)92(able)-250(2:)-310(V)92(alue)-250(of)-250(thr)18(esholded-r)18(enames)]TJ ET q 1 0 0 1 90.031 642.59 cm []0 d 0 J 0.398 w 0 0 m 172.615 0 l S Q q 1 0 0 1 90.031 633.425 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 95.411 636.115 Td [(T)80(ar)18(get)-250(precision)]TJ ET q 1 0 0 1 152.022 633.425 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 157.402 636.115 Td [(No-Renames)]TJ ET q 1 0 0 1 204.393 633.425 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 209.773 636.115 Td [(W)40(ith-Renames)]TJ ET q 1 0 0 1 262.646 633.425 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q q 1 0 0 1 90.031 633.226 cm []0 d 0 J 0.398 w 0 0 m 172.615 0 l S Q q 1 0 0 1 90.031 624.06 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 116.045 626.75 Td [(0.8)]TJ ET q 1 0 0 1 152.022 624.06 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 171.234 626.75 Td [(0.53)]TJ ET q 1 0 0 1 204.393 624.06 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 226.546 626.75 Td [(0.60)]TJ ET q 1 0 0 1 262.646 624.06 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q q 1 0 0 1 90.031 615.094 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 114.053 617.784 Td [(0.85)]TJ ET q 1 0 0 1 152.022 615.094 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 171.234 617.784 Td [(0.48)]TJ ET q 1 0 0 1 204.393 615.094 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 226.546 617.784 Td [(0.55)]TJ ET q 1 0 0 1 262.646 615.094 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q q 1 0 0 1 90.031 606.127 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 114.053 608.817 Td [(0.90)]TJ ET q 1 0 0 1 152.022 606.127 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 171.234 608.817 Td [(0.46)]TJ ET q 1 0 0 1 204.393 606.127 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 226.546 608.817 Td [(0.48)]TJ ET q 1 0 0 1 262.646 606.127 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q q 1 0 0 1 90.031 597.161 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 114.053 599.851 Td [(0.95)]TJ ET q 1 0 0 1 152.022 597.161 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 171.234 599.851 Td [(0.42)]TJ ET q 1 0 0 1 204.393 597.161 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 226.546 599.851 Td [(0.45)]TJ ET q 1 0 0 1 262.646 597.161 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q q 1 0 0 1 90.031 588.194 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 114.053 590.884 Td [(0.95)]TJ ET q 1 0 0 1 152.022 588.194 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 171.234 590.884 Td [(0.39)]TJ ET q 1 0 0 1 204.393 588.194 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 226.546 590.884 Td [(0.39)]TJ ET q 1 0 0 1 262.646 588.194 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q q 1 0 0 1 90.031 587.995 cm []0 d 0 J 0.398 w 0 0 m 172.615 0 l S Q BT /F56 8.9664 Tf 53.798 548.821 Td [(less)-222(than)]TJ/F31 8.9664 Tf 32.867 0 Td [(50%)]TJ/F56 8.9664 Tf 18.884 0 Td [(of)-222(positi)25(v)15(e)-222(pa)1(irs.)-301(Thus)-222(it)-222(is)-221(important)-222(to)-222(consider)-222(more)]TJ -51.751 -10.461 Td [(comple)15(x)-250(operator)-250(trees.)]TJ/F57 8.9664 Tf 8.967 -10.46 Td [(Thr)37(esholded)-254(r)37(ename)-254(oper)15(ator)10(s)]TJ/F56 8.9664 Tf 110.259 0 Td [(:)-318(T)80(able)-254(2)-254(demonstrates)-254(the)-254(v)25(alue)-254(of)]TJ -119.226 -10.461 Td [(thresholded)-383(rename)-382(operators)-383(such)-382(as)-383(FD-Correction.)-708(W)80(e)-382(present)]TJ 0 -10.461 Td [(the)-362(co)15(v)15(erage)-362(of)-362(one)]TJ/F31 8.9664 Tf 76.449 0 Td [(4)]TJ/F56 8.9664 Tf 4.608 0 Td [(-dimensional)-362(rectangle)-362(\050i.e.,)]TJ/F34 8.9664 Tf 105.857 0 Td [(K)]TJ/F31 8.9664 Tf 12.914 0 Td [(=)-499(1)]TJ/F56 8.9664 Tf 16.247 0 Td [(\051)-362(v)15(ersus)]TJ -216.075 -10.461 Td [(the)-283(tar)18(get)-283(precision)-282(for)-283(the)-283(address)-283(dataset.)-408(At)-283(almost)-283(all)-283(tar)18(get)-282(pre-)]TJ 0 -10.461 Td [(cision)-384(le)25(v)15(els,)-418(the)-384(sequence)-384(of)-384(postal)-384(code)-384(splitter)-384(follo)25(wed)-384(by)-384(the)]TJ 0 -10.46 Td [(FD-correction)-295(operator)-296(\050with)-295(threshold)]TJ/F31 8.9664 Tf 143.568 0 Td [(0)]TJ/F34 8.9664 Tf 4.608 0 Td [(:)]TJ/F31 8.9664 Tf 2.56 0 Td [(82)]TJ/F56 8.9664 Tf 9.215 0 Td [(\051)-295(between)-296(out-code)-295(and)]TJ -159.951 -10.461 Td [(city)-253(attrib)20(utes)-253(w)10(as)-253(chosen.)-319(The)-253(operator)-253(trees)-253(with)-252(rename)-253(operators)]TJ 0 -10.461 Td [(ha)20(v)15(e)-308(a)-308(higher)-308(co)15(v)15(erage,)-323(often)-308(by)-308(upto)]TJ/F31 8.9664 Tf 140.633 0 Td [(5%)]TJ/F56 8.9664 Tf 12.288 0 Td [(.)-484(Thus,)-322(rename)-308(operators)]TJ -152.921 -10.461 Td [(are)-250(useful)-250(in)-250(impro)15(ving)-250(the)-250(co)15(v)15(erage)-250(at)-250(the)-250(same)-250(precision.)]TJ/F55 11.9552 Tf 0 -20.344 Td [(7.2)-1000(Comparison)-250(with)-250(SVMs)]TJ/F56 8.9664 Tf 8.967 -12.952 Td [(W)80(e)-287(no)25(w)-286(compare)-287(our)-287(techniques)-287(wi)1(th)-287(currently)-287(kno)25(wn)-287(best)-286(tech-)]TJ -8.967 -10.461 Td [(niques)-292(based)-292(on)-292(SVMs)-292(for)-292(learning)-292(ef)25(fecti)25(v)15(e)-292(record)-291(matching)-292(func-)]TJ 0 -10.46 Td [(tions)-358([9,)-386(6].)-634(T)70(echniques)-359(based)-358(on)-358(SVMs)-358(ha)20(v)15(e)-359(been)-358(sho)25(wn)-358(to)-358(sig-)]TJ 0 -10.461 Td [(ni\002cantly)-369(outperform)-368(those)-369(based)-369(on)-368(other)-369(machine)-369(learning)-368(tech-)]TJ 0 -10.461 Td [(niques)-377(such)-377(as)-377(dec)1(ision)-377(trees)-377([9,)-409(6].)-690(Therefore,)-409(we)-377(only)-376(consider)]TJ 0 -10.461 Td [(SVMs.)-291(W)80(e)-193(obtained)-192(the)-193(implementation)-193(of)-192(the)-193(SVM)-193(techniques)-192(from)]TJ 0 -10.46 Td [(Bilenk)10(o)-266(et)-265(al.)-357(W)80(e)-265(randomly)-266(split)-265(labeled)-266(e)15(xample)-265(pairs)-266(into)-265(roughly)]TJ 0 -10.461 Td [(equal)-256(numbers)-256(of)-257(training)-256(and)-256(test)-256(datasets.)-329(W)80(e)-256(use)-256(the)-256(training)-256(data)]TJ 0 -10.461 Td [(to)-250(design)-250(an)-250(operator)-250(tree/SVM)-250(and)-250(test)-250(data)-250(to)-250(e)25(v)25(aluate.)]TJ 8.967 -10.461 Td [(W)80(e)-347(\002rst)-348(discuss)-347(the)-347(results)-348(on)-347(the)-347(hurricane)-348(Katrina)-347(dataset)-347(that)]TJ -8.967 -10.461 Td [(we)-318(introduced)-319(in)-318(Section)-318(1.)-515(W)80(e)-319(obtained)-318(a)-318(set)-319(of)]TJ/F31 8.9664 Tf 183.731 0 Td [(1000)]TJ/F56 8.9664 Tf 21.286 0 Td [(labeled)-318(e)15(x-)]TJ -205.017 -10.46 Td [(amples,)-339(with)-321(around)]TJ/F31 8.9664 Tf 77.281 0 Td [(400)]TJ/F56 8.9664 Tf 16.703 0 Td [(matching)-321(pairs.)-523(W)80(e)-321(present)-321(the)-321(results)-322(in)]TJ -93.984 -10.461 Td [(T)80(able)-269(3.)-367(W)80(e)-269(\002rs)1(t)-269(note)-269(that)-269(no)-269(baseline)-269(operator)-269(tree)-269(satis\002es)-268(our)-269(tar)20(-)]TJ 0 -10.461 Td [(get)-331(precision)-331(constraint)-331(\050abo)15(v)15(e)]TJ/F31 8.9664 Tf 115.197 0 Td [(0)]TJ/F34 8.9664 Tf 4.608 0 Td [(:)]TJ/F31 8.9664 Tf 2.56 0 Td [(8)]TJ/F56 8.9664 Tf 4.607 0 Td [(\051;)-372(hence)-331(recall)-331(is)-331(set)-331(to)]TJ/F31 8.9664 Tf 87.401 0 Td [(0)]TJ/F34 8.9664 Tf 4.608 0 Td [(:)]TJ/F31 8.9664 Tf 2.559 0 Td [(0)]TJ/F56 8.9664 Tf 4.608 0 Td [(.)-554(W)80(e)]TJ -226.148 -10.461 Td [(observ)15(e)-229(that)-228(for)-229(this)-229(dataset,)-233(SVMs)-228(of)25(fer)-229(better)-228(recall)-229(at)-229(higher)-228(preci-)]TJ 0 -10.46 Td [(sion)-284(\050)]TJ/F31 8.9664 Tf 20.48 0 Td [(0)]TJ/F34 8.9664 Tf 4.608 0 Td [(:)]TJ/F31 8.9664 Tf 2.559 0 Td [(95)]TJ/F56 8.9664 Tf 9.216 0 Td [(\051.)-412(Ho)25(we)25(v)15(er)40(,)-293(the)-284(recall)-284(of)-284(operator)-284(trees)-284(at)-284(lo)25(wer)-284(precision)]TJ -36.863 -10.461 Td [(is)-259(close)-258(to)-259(that)-259(of)-258(SVMs.)-336(Therefore,)-261(as)-259(discussed)-258(earlier)40(,)-261(we)-259(can)-258(use)]TJ 0 -10.461 Td [(our)-202(operator)-202(trees)-202(as)-202(ef)25(\002cient)-202(\002lters)-202(\050with)-202(lo)25(w)-202(tar)18(get)-201(precision\051)-202(before)]TJ 0 -10.461 Td [(in)40(v)20(oking)-250(SVMs)-250(enabling)-250(ef)25(\002cient)-250(e)15(x)15(ecution)-250(of)-250(SVM)-250(models.)]TJ 8.967 -10.461 Td [(W)80(e)-347(study)-347(the)-347(comparison)-347(on)-348(other)-347(datasets)-347(belo)25(w)65(,)-371(where)-347(opera-)]TJ -8.967 -10.46 Td [(tor)-351(trees)-350(are)-351(i)1(n)-351(f)10(act)-351(c)1(omparable)-351(and)-350(sometimes)-351(outperform)-350(SVMs.)]TJ 0 -10.461 Td [(W)80(e)-224(consider)-225(three)-224(benchmark)-224(datasets)-224(dra)15(wn)-225(from)-224(dif)25(ferent)-224(domains)]TJ 0 -10.461 Td [(of)-449(the)-449(RIDDLE)-449(repository)-449([8]:)]TJ/F57 8.9664 Tf 123.051 0 Td [(Cor)15(a)]TJ/F56 8.9664 Tf 22.326 0 Td [(consisting)-449(of)-449(bibliographic)]TJ -145.377 -10.461 Td [(records,)]TJ/F57 8.9664 Tf 32.577 0 Td [(Restaur)15(ant)]TJ/F56 8.9664 Tf 42.825 0 Td [(consisting)-402(of)-402(restaurant)-403(names)-402(and)-402(addresses,)]TJ -75.402 -10.46 Td [(and)]TJ/F57 8.9664 Tf 15.189 0 Td [(Bir)37(d)]TJ/F56 8.9664 Tf 17.852 0 Td [(consisting)-250(of)-250(scienti\002c)-250(names)-250(of)-250(birds.)]TJ -24.074 -10.461 Td [(F)15(or)-284(these)-285(e)15(xperiments)1(,)-293(we)-285(only)-284(consider)-284(edit,)-293(jaccard,)-293(and)-284(gener)20(-)]TJ/F55 8.9664 Tf 23.909 -30.777 Td [(T)92(able)-250(3:)-310(Hurricane)-250(Katrina)-250(data:)]TJ/F34 8.9664 Tf 128.227 0 Td [(K)]TJ/F31 8.9664 Tf 11.002 0 Td [(=)-285(4)]TJ/F34 8.9664 Tf 14.335 0 Td [(;)-171(d)]TJ/F31 8.9664 Tf 11.43 0 Td [(=)-285(4)]TJ ET q 1 0 0 1 89.745 115.682 cm []0 d 0 J 0.398 w 0 0 m 173.187 0 l S Q q 1 0 0 1 89.745 106.517 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q q 1 0 0 1 159.674 106.517 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 196.471 109.207 Td [(Precision)]TJ ET q 1 0 0 1 262.932 106.517 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q q 1 0 0 1 89.745 106.318 cm []0 d 0 J 0.398 w 0 0 m 173.187 0 l S Q q 1 0 0 1 89.745 97.152 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q q 1 0 0 1 159.674 97.152 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F67 7.9701 Tf 165.054 99.842 Td [(0)]TJ/F68 7.9701 Tf 4.234 0 Td [(:)]TJ/F67 7.9701 Tf 2.353 0 Td [(80)]TJ ET q 1 0 0 1 185.489 97.152 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F67 7.9701 Tf 190.869 99.842 Td [(0)]TJ/F68 7.9701 Tf 4.234 0 Td [(:)]TJ/F67 7.9701 Tf 2.352 0 Td [(85)]TJ ET q 1 0 0 1 211.303 97.152 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F67 7.9701 Tf 216.683 99.842 Td [(0)]TJ/F68 7.9701 Tf 4.234 0 Td [(:)]TJ/F67 7.9701 Tf 2.353 0 Td [(90)]TJ ET q 1 0 0 1 237.118 97.152 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F67 7.9701 Tf 242.498 99.842 Td [(0)]TJ/F68 7.9701 Tf 4.234 0 Td [(:)]TJ/F67 7.9701 Tf 2.352 0 Td [(95)]TJ ET q 1 0 0 1 262.932 97.152 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q q 1 0 0 1 89.745 96.953 cm []0 d 0 J 0.398 w 0 0 m 173.187 0 l S Q q 1 0 0 1 89.745 87.787 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 95.125 81.511 Td [(Recall)]TJ ET q 1 0 0 1 120.868 87.787 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 126.248 90.477 Td [(Op.)-250(T)35(ree)]TJ ET q 1 0 0 1 159.674 87.787 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 165.608 90.477 Td [(0.78)]TJ ET q 1 0 0 1 185.489 87.787 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 191.422 90.477 Td [(0.78)]TJ ET q 1 0 0 1 211.303 87.787 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 217.237 90.477 Td [(0.76)]TJ ET q 1 0 0 1 237.118 87.787 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 243.051 90.477 Td [(0.53)]TJ ET q 1 0 0 1 262.932 87.787 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q q 1 0 0 1 89.745 78.821 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q q 1 0 0 1 120.868 78.821 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 126.547 81.511 Td [(Baseline)]TJ ET q 1 0 0 1 159.674 78.821 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 170.589 81.511 Td [(0)]TJ ET q 1 0 0 1 185.489 78.821 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 196.404 81.511 Td [(0)]TJ ET q 1 0 0 1 211.303 78.821 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 222.218 81.511 Td [(0)]TJ ET q 1 0 0 1 237.118 78.821 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 248.033 81.511 Td [(0)]TJ ET q 1 0 0 1 262.932 78.821 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q q 1 0 0 1 89.745 69.854 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q q 1 0 0 1 120.868 69.854 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 131.636 72.544 Td [(SVM)]TJ ET q 1 0 0 1 159.674 69.854 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 165.608 72.544 Td [(0.85)]TJ ET q 1 0 0 1 185.489 69.854 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 191.422 72.544 Td [(0.82)]TJ ET q 1 0 0 1 211.303 69.854 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 217.237 72.544 Td [(0.81)]TJ ET q 1 0 0 1 237.118 69.854 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q BT /F56 7.9701 Tf 243.051 72.544 Td [(0.70)]TJ ET q 1 0 0 1 262.932 69.854 cm []0 d 0 J 0.398 w 0 0 m 0 8.966 l S Q q 1 0 0 1 89.745 69.655 cm []0 d 0 J 0.398 w 0 0 m 173.187 0 l S Q BT /F55 8.9664 Tf 373.069 729.213 Td [(T)92(able)-250(4:)-310(V)92(arying)]TJ/F34 8.9664 Tf 66.387 0 Td [(K)]TJ/F31 8.9664 Tf 8.442 0 Td [(&)]TJ/F34 8.9664 Tf 7.167 0 Td [(d)]TJ/F55 8.9664 Tf 4.775 0 Td [(,)]TJ/F34 8.9664 Tf 4.483 0 Td [(D)]TJ/F31 8.9664 Tf 10.415 0 Td [(=)-285(29)]TJ ET q 1 0 0 1 338.44 726.193 cm []0 d 0 J 0.398 w 0 0 m 189.87 0 l S Q q 1 0 0 1 338.44 715.533 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F56 8.9664 Tf 353.345 718.671 Td [(V)111(arying)]TJ/F34 8.9664 Tf 30.629 0 Td [(K)]TJ/F56 8.9664 Tf 8.442 0 Td [(,)]TJ/F34 8.9664 Tf 4.483 0 Td [(d)]TJ/F31 8.9664 Tf 7.334 0 Td [(=)-286(4)]TJ ET q 1 0 0 1 433.473 715.533 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q q 1 0 0 1 435.267 715.533 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q q 1 0 0 1 435.267 715.533 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F56 8.9664 Tf 449.176 718.671 Td [(V)111(arying)]TJ/F34 8.9664 Tf 30.629 0 Td [(d)]TJ/F56 8.9664 Tf 4.775 0 Td [(,)]TJ/F34 8.9664 Tf 4.483 0 Td [(K)]TJ/F31 8.9664 Tf 11.002 0 Td [(=)-285(4)]TJ ET q 1 0 0 1 528.31 715.533 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q q 1 0 0 1 338.44 715.334 cm []0 d 0 J 0.398 w 0 0 m 189.87 0 l S Q q 1 0 0 1 338.44 713.54 cm []0 d 0 J 0.398 w 0 0 m 189.87 0 l S Q q 1 0 0 1 338.44 702.88 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F56 8.9664 Tf 343.82 706.018 Td [(K)]TJ ET q 1 0 0 1 355.673 702.88 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F56 8.9664 Tf 361.053 706.018 Td [(Precision)]TJ ET q 1 0 0 1 399.805 702.88 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F56 8.9664 Tf 405.185 706.018 Td [(Recall)]TJ ET q 1 0 0 1 433.473 702.88 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q q 1 0 0 1 435.267 702.88 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F56 8.9664 Tf 440.647 706.018 Td [(d)]TJ ET q 1 0 0 1 450.51 702.88 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F56 8.9664 Tf 455.889 706.018 Td [(Precision)]TJ ET q 1 0 0 1 494.642 702.88 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F56 8.9664 Tf 500.021 706.018 Td [(Recall)]TJ ET q 1 0 0 1 528.31 702.88 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q q 1 0 0 1 338.44 702.681 cm []0 d 0 J 0.398 w 0 0 m 189.87 0 l S Q q 1 0 0 1 338.44 692.021 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F56 8.9664 Tf 344.815 695.159 Td [(1)]TJ ET q 1 0 0 1 355.673 692.021 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F31 8.9664 Tf 369.548 695.159 Td [(0)]TJ/F34 8.9664 Tf 4.607 0 Td [(:)]TJ/F31 8.9664 Tf 2.56 0 Td [(95)]TJ ET q 1 0 0 1 399.805 692.021 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F31 8.9664 Tf 408.448 695.159 Td [(0)]TJ/F34 8.9664 Tf 4.608 0 Td [(:)]TJ/F31 8.9664 Tf 2.559 0 Td [(82)]TJ ET q 1 0 0 1 433.473 692.021 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q q 1 0 0 1 435.267 692.021 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F56 8.9664 Tf 440.647 695.159 Td [(1)]TJ ET q 1 0 0 1 450.51 692.021 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F31 8.9664 Tf 464.384 695.159 Td [(0)]TJ/F34 8.9664 Tf 4.608 0 Td [(:)]TJ/F31 8.9664 Tf 2.56 0 Td [(95)]TJ ET q 1 0 0 1 494.642 692.021 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F31 8.9664 Tf 503.284 695.159 Td [(0)]TJ/F34 8.9664 Tf 4.608 0 Td [(:)]TJ/F31 8.9664 Tf 2.56 0 Td [(89)]TJ ET q 1 0 0 1 528.31 692.021 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q q 1 0 0 1 338.44 681.56 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F56 8.9664 Tf 344.815 684.698 Td [(2)]TJ ET q 1 0 0 1 355.673 681.56 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F31 8.9664 Tf 369.548 684.698 Td [(0)]TJ/F34 8.9664 Tf 4.607 0 Td [(:)]TJ/F31 8.9664 Tf 2.56 0 Td [(96)]TJ ET q 1 0 0 1 399.805 681.56 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F31 8.9664 Tf 408.448 684.698 Td [(0)]TJ/F34 8.9664 Tf 4.608 0 Td [(:)]TJ/F31 8.9664 Tf 2.559 0 Td [(93)]TJ ET q 1 0 0 1 433.473 681.56 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q q 1 0 0 1 435.267 681.56 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F56 8.9664 Tf 440.647 684.698 Td [(2)]TJ ET q 1 0 0 1 450.51 681.56 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F31 8.9664 Tf 464.384 684.698 Td [(0)]TJ/F34 8.9664 Tf 4.608 0 Td [(:)]TJ/F31 8.9664 Tf 2.56 0 Td [(96)]TJ ET q 1 0 0 1 494.642 681.56 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F31 8.9664 Tf 503.284 684.698 Td [(0)]TJ/F34 8.9664 Tf 4.608 0 Td [(:)]TJ/F31 8.9664 Tf 2.56 0 Td [(93)]TJ ET q 1 0 0 1 528.31 681.56 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q q 1 0 0 1 338.44 671.099 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F56 8.9664 Tf 344.815 674.238 Td [(3)]TJ ET q 1 0 0 1 355.673 671.099 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F31 8.9664 Tf 369.548 674.238 Td [(0)]TJ/F34 8.9664 Tf 4.607 0 Td [(:)]TJ/F31 8.9664 Tf 2.56 0 Td [(96)]TJ ET q 1 0 0 1 399.805 671.099 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F31 8.9664 Tf 408.448 674.238 Td [(0)]TJ/F34 8.9664 Tf 4.608 0 Td [(:)]TJ/F31 8.9664 Tf 2.559 0 Td [(94)]TJ ET q 1 0 0 1 433.473 671.099 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q q 1 0 0 1 435.267 671.099 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F56 8.9664 Tf 440.647 674.238 Td [(3)]TJ ET q 1 0 0 1 450.51 671.099 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F31 8.9664 Tf 464.384 674.238 Td [(0)]TJ/F34 8.9664 Tf 4.608 0 Td [(:)]TJ/F31 8.9664 Tf 2.56 0 Td [(96)]TJ ET q 1 0 0 1 494.642 671.099 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F31 8.9664 Tf 503.284 674.238 Td [(0)]TJ/F34 8.9664 Tf 4.608 0 Td [(:)]TJ/F31 8.9664 Tf 2.56 0 Td [(94)]TJ ET q 1 0 0 1 528.31 671.099 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q q 1 0 0 1 338.44 660.639 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F56 8.9664 Tf 344.815 663.777 Td [(4)]TJ ET q 1 0 0 1 355.673 660.639 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F31 8.9664 Tf 369.548 663.777 Td [(0)]TJ/F34 8.9664 Tf 4.607 0 Td [(:)]TJ/F31 8.9664 Tf 2.56 0 Td [(95)]TJ ET q 1 0 0 1 399.805 660.639 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F31 8.9664 Tf 408.448 663.777 Td [(0)]TJ/F34 8.9664 Tf 4.608 0 Td [(:)]TJ/F31 8.9664 Tf 2.559 0 Td [(95)]TJ ET q 1 0 0 1 433.473 660.639 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q q 1 0 0 1 435.267 660.639 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F56 8.9664 Tf 440.647 663.777 Td [(4)]TJ ET q 1 0 0 1 450.51 660.639 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F31 8.9664 Tf 464.384 663.777 Td [(0)]TJ/F34 8.9664 Tf 4.608 0 Td [(:)]TJ/F31 8.9664 Tf 2.56 0 Td [(96)]TJ ET q 1 0 0 1 494.642 660.639 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F31 8.9664 Tf 503.284 663.777 Td [(0)]TJ/F34 8.9664 Tf 4.608 0 Td [(:)]TJ/F31 8.9664 Tf 2.56 0 Td [(95)]TJ ET q 1 0 0 1 528.31 660.639 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q q 1 0 0 1 338.44 660.439 cm []0 d 0 J 0.398 w 0 0 m 189.87 0 l S Q BT /F56 8.9664 Tf 310.834 629.702 Td [(alized)-265(edit)-265(similarity)-266(functions)-265(o)15(v)15(er)-265(multiple)-265(attrib)20(ute)-265(combinations,)]TJ 0 -10.46 Td [(and)-373(do)-373(not)-372(consider)-373(an)15(y)-373(rename)-372(operators.)-679(Figures)-372(9,)-373(10,)-404(and)-372(11)]TJ 0 -10.461 Td [(sho)25(w)-380(the)-380(results)-379(for)-380(both)-380(SVM-based)-380(techniques)-380(and)-380(the)-379(operator)]TJ 0 -10.461 Td [(trees)-447(our)-448(techniques)-447(return.)-903(On)-447(these)-448(datasets,)-497(the)-447(recall)-447(v)25(alues)]TJ 0 -10.461 Td [(achie)25(v)15(ed)-292(by)-293(our)-292(operator)-292(trees)-293(are)-292(comparable)-292(to)-292(that)-293(of)-292(the)-292(current)]TJ 0 -10.461 Td [(best)-255(SVM-based)-254(techniques)-255(at)-254(the)-255(same)-254(precision.)-324(Most)-254(of)-255(the)-254(time,)]TJ 0 -10.46 Td [(we)-306(obtain)-306(equal)-306(recall)-306(at)-306(the)-306(same)-306(precision)-306(and)-306(somet)1(imes)-306(signi\002-)]TJ 0 -10.461 Td [(cantly)-217(better)-216(recall)-217(v)25(alues)-216(\050e.g.,)-223(the)-217(Bird)-217(dat)1(aset\051.)-299(The)-217(recall)-216(obtained)]TJ 0 -10.461 Td [(is)-258(high)-258(e)25(v)15(en)-258(at)-257(high)-258(precision)-258(indicating)-258(that)-258(there)-258(e)15(xists)-258(an)-257(operator)]TJ 0 -10.461 Td [(tree)-295(and)-295(an)-295(SVM)-294(model)-295(which)-295(precisely)-295(identify)-295(all)-295(matching)-294(pairs)]TJ 0 -10.46 Td [(of)-241(records.)-307(Also)-241(observ)15(e)-241(that)-241(baseline)-241(operator)-241(trees)-241(may)-241(not)-240(be)-241(able)]TJ 0 -10.461 Td [(to)-309(obtain)-308(high)-309(recall)-309(\050e.g.,)-323(Cora\051)-309(thus)-308(indicating)-309(that)-309(more)-308(comple)15(x)]TJ 0 -10.461 Td [(operator)-250(trees)-250(are)-250(often)-250(required.)]TJ/F55 11.9552 Tf 0 -19.108 Td [(7.3)-1000(V)92(arying)]TJ/F34 8.9664 Tf 70.631 0 Td [(K)]TJ/F55 11.9552 Tf 11.431 0 Td [(and)]TJ/F34 8.9664 Tf 22.261 0 Td [(d)]TJ/F56 8.9664 Tf -95.356 -12.952 Td [(W)80(e)-228(no)25(w)-228(e)25(v)25(aluate)-229(the)-228(impact)-228(of)-228(operator)-228(tree)-229(comple)15(xity)-228(on)-228(the)-228(ac-)]TJ -8.967 -10.46 Td [(curac)15(y)-296(using)-295(the)-296(GBR)40(O)1(r)17(gs)-295(relation.)-446(Recall)-296(that)]TJ/F34 8.9664 Tf 175.386 0 Td [(K)]TJ/F56 8.9664 Tf 11.092 0 Td [(is)-295(the)-296(maximum)]TJ -186.478 -10.461 Td [(number)-245(of)-245(similarity)-245(joins)-245(in)-245(an)-245(operator)-246(tr)1(ee,)-247(and)]TJ/F34 8.9664 Tf 180.409 0 Td [(d)]TJ/F56 8.9664 Tf 6.973 0 Td [(is)-245(the)-245(maximum)]TJ -187.382 -10.461 Td [(number)-255(of)-255(similarity)-255(function)-255(predicates)-255(per)-255(similarity)-255(join.)-324(In)-255(order)]TJ 0 -10.461 Td [(to)-238(measure)-238(recall)-238(and)-239(pre)1(cision,)-241(we)-238(synthetically)-238(generate)-238(data)-238(using)]TJ 0 -10.46 Td [(error)-318(models)-317(similar)-318(to)-317(that)-318(of)-317([13,)-335(25])-317(and)-318(that)-317(a)20(v)25(ailable)-318(from)-317([8].)]TJ 0 -10.461 Td [(W)80(e)-342(introduce)-343(a)-342(v)25(ariety)-342(of)-343(errors)-342(\050e.g.,)-365(spelling)-343(errors,)-365(missing)-342(v)25(al-)]TJ 0 -10.461 Td [(ues,)-294(attrib)20(ute)-285(v)25(alue)-286(truncations,)-294(tok)10(en)-285(transpositions,)-294(etc.\051)-416(into)-285(a)-285(set)]TJ 0 -10.461 Td [(of)-359(distinct)-359(tuples)-358(from)-359(the)-359(GBR)40(Or)18(gs)-359(relation)-359(and)-359(create)-358(erroneous)]TJ 0 -10.461 Td [(v)15(ersions.)-599(The)-346(record)-346(matching)-347(task)-346(is)-346(to)-347(correctly)-346(match)-346(the)-346(erro-)]TJ 0 -10.46 Td [(neous)-254(tuples)-254(with)-255(the)-254(tuples)-254(from)-254(which)-254(the)15(y)-254(were)-255(deri)25(v)15(ed.)-322(The)-254(\002rst)]TJ 0 -10.461 Td [(three)-260(columns)-260(in)-260(T)80(able)-260(4)-260(sho)25(w)-260(precision)-260(and)-260(recall)-260(while)-260(v)25(arying)]TJ/F34 8.9664 Tf 236.639 0 Td [(K)]TJ/F56 8.9664 Tf -236.639 -10.461 Td [(and)-342(\002xing)]TJ/F34 8.9664 Tf 40.007 0 Td [(d)]TJ/F56 8.9664 Tf 7.841 0 Td [(at)]TJ/F31 8.9664 Tf 9.539 0 Td [(4)]TJ/F56 8.9664 Tf 4.608 0 Td [(.)-586(And,)-365(the)-342(last)-342(three)-341(columns)-342(sho)25(w)-342(precision)-342(and)]TJ -61.995 -10.461 Td [(recall)-296(when)-296(we)-295(\002x)]TJ/F34 8.9664 Tf 69.868 0 Td [(K)]TJ/F31 8.9664 Tf 11.783 0 Td [(=)-373(4)]TJ/F56 8.9664 Tf 17.769 0 Td [(and)-296(v)25(ary)]TJ/F34 8.9664 Tf 33.961 0 Td [(d)]TJ/F56 8.9664 Tf 7.427 0 Td [(between)]TJ/F31 8.9664 Tf 32.528 0 Td [(1)]TJ/F56 8.9664 Tf 7.26 0 Td [(and)]TJ/F31 8.9664 Tf 15.6 0 Td [(4)]TJ/F56 8.9664 Tf 4.608 0 Td [(.)-447(From)-296(both)]TJ -200.804 -10.46 Td [(tables,)-339(we)-321(obs)1(erv)15(e)-321(that)-321(\050i\051)-321(it)-321(is)-321(important)-321(to)-321(consider)-321(operator)-320(trees)]TJ 0 -10.461 Td [(which)-337(ha)20(v)15(e)-337(more)-336(than)-337(one)-337(similarity)-337(join)-336(and)-337(more)-337(than)-337(one)-336(simi-)]TJ 0 -10.461 Td [(larity)-318(predicate)-318(per)-318(join,)-335(and)-318(\050ii\051)-318(increasing)-318(the)-318(comple)15(xity)-318(initially)]TJ 0 -10.461 Td [(impro)15(v)15(es)-250(accurac)15(y)-250(b)20(ut)-250(the)-250(impro)15(v)15(ements)-250(start)-250(diminishing)-250(quickly)65(.)]TJ/F55 11.9552 Tf 0 -17.668 Td [(7.4)-1000(Ef\002ciency)-250(and)-250(Scalability)]TJ/F56 8.9664 Tf 8.967 -12.951 Td [(W)80(e)-454(no)25(w)-453(illustrate)-454(that)-453(similarity)-454(joins)-453(can)-454(be)-454(e)15(x)15(ecuted)-453(signif-)]TJ -8.967 -10.461 Td [(icantly)-438(more)-439(e)1(f)25(\002ciently)-439(than)-438(SVM)-438(models,)-485(e)25(v)15(en)-439(if)-438(we)-438(apply)-438(the)]TJ 0 -10.461 Td [(blocking)-301(approaches)-302(discussed)-301(in)-301([7,)-314(30].)-464(In)-301(T)80(able)-302(5,)-314(we)-301(report)-301(the)]TJ 0 -10.46 Td [(time)-332(for)-332(e)15(x)15(ecuting)-333(the)-332(similarity)-332(join)]TJ/F57 8.9664 Tf 138.145 0 Td [(jaccar)37(d\050Name)10(,)-353(Addr)37(ess,)-352(City)55(,)]TJ -138.145 -10.461 Td [(State)10(,)-342(P)80(ostalCode\051)]TJ/F34 8.9664 Tf 67.267 0 Td [(>)-426(\022)]TJ/F56 8.9664 Tf 18.459 0 Td [(on)-324(a)-324(subset)-323(of)-324(GBR)40(Or)18(gs)-324(relation)-324(consisting)]TJ -85.726 -10.461 Td [(of)]TJ/F31 8.9664 Tf 10.691 0 Td [(500)]TJ/F34 8.9664 Tf 13.823 0 Td [(K)]TJ/F56 8.9664 Tf 11.663 0 Td [(records)-359(with)-360(itself;)-413(we)-360(v)25(ary)]TJ/F34 8.9664 Tf 105.517 0 Td [(\022)]TJ/F56 8.9664 Tf 4.569 0 Td [(.)-638(W)80(e)-359(also)-359(report)-360(the)-359(times)]TJ -146.263 -10.461 Td [(for)-272(a)-271(cross)-272(product)-272(required)-271(when)-272(we)-272(ha)20(v)15(e)-271(to)-272(e)15(x)15(ecute)-272(SVM)-271(models,)]TJ 0 -10.461 Td [(and)-257(the)-257(time)-257(required)-257(for)-257(implementing)-257(the)-257(techni)1(ques)-257(for)-257(e)15(x)15(ecuting)]TJ 0 -10.46 Td [(blocking)-382(predicates)-382(proposed)-382(in)-381([7].)-706(It)-382(is)-382(clear)-382(that)-382(the)-381(similarity)]TJ 0 -10.461 Td [(join)-281(implementation)-280(is)-281(signi\002cantly)-281(more)-281(ef)25(\002c)1(ient)-281(than)-281(either)-281(of)-280(the)]TJ 0 -10.461 Td [(SVM)-402(implementations.)-765(A)-402(more)-402(comprehensi)25(v)15(e)-402(e)25(v)25(aluation)-401(of)-402(our)]TJ 0 -10.461 Td [(similarity)-250(join)-250(implementations)-250(is)-250(in)-250([2].)]TJ/F55 11.9552 Tf 0 -29.569 Td [(7.5)-1000(Operator)-250(T)74(r)18(ee)-250(Design)-250(T)18(ime)]TJ/F56 8.9664 Tf 8.967 -12.951 Td [(W)80(e)-354(no)25(w)-355(e)25(v)25(aluate)-354(the)-354(time)-355(required)-354(for)-355(designing)-354(operator)-354(trees.)]TJ -8.967 -10.461 Td [(In)-337(Figure)-337(12,)-359(we)-337(plot)-337(the)-337(operator)-337(tree)-337(des)1(ign)-337(times)-337(for)-337(GBR)40(Or)18(gs,)]TJ 0 -10.461 Td [(Cora,)-429(Restaurant,)-428(and)-394(B)1(ird)-393(datasets)-393(at)-393(dif)25(ferent)-393(tar)18(geted)-393(precision)]TJ 0 -10.46 Td [(v)25(alues)-336(while)-336(k)10(eeping)-337(the)-336(training)-336(data)-336(size)-336(constant.)-569(In)-336(Figure)-336(13,)]TJ ET Q 1 0 0 1 295.992 36 cm 0 Tr /QQAPFce02551e 12 Tf 0 0 0 rg 100 Tz 0 Ts 0 Tw 0 Tc BT 1 0 0 1 0 0 Tm (337)Tj ET 1 0 0 1 0 0 cm 1 0 0 1 -295.992 -36 cm endstream endobj 162 0 obj << /Type /Page /Resources 161 0 R /MediaBox [ 0 0 612 792 ] /Parent 91 0 R /Contents [ 163 0 R ] >> endobj 161 0 obj << /Font << /F55 9 0 R /F34 12 0 R /F31 18 0 R /F56 10 0 R /F67 82 0 R /F68 83 0 R /F57 11 0 R /QQAPFce02551e 232 0 R >> /ProcSet [ /PDF /Text ] >> endobj 166 0 obj << /Length 21549 /LC /QQAP >> stream q BT /F55 8.9664 Tf 116.278 729.262 Td [(T)92(able)-250(5:)-310(J)15(accard)-250(similarity)-250(join)]TJ ET q 1 0 0 1 80.099 726.242 cm []0 d 0 J 0.398 w 0 0 m 192.48 0 l S Q q 1 0 0 1 80.099 715.582 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F56 8.9664 Tf 85.479 718.72 Td [(Threshold)]TJ ET q 1 0 0 1 127.217 715.582 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F56 8.9664 Tf 132.597 718.72 Td [(SimJoin)]TJ ET q 1 0 0 1 167.377 715.582 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F56 8.9664 Tf 177.984 718.72 Td [(SVM)]TJ ET q 1 0 0 1 208.021 715.582 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F56 8.9664 Tf 213.401 718.72 Td [(SVM-blocking)]TJ ET q 1 0 0 1 272.579 715.582 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q q 1 0 0 1 80.099 715.382 cm []0 d 0 J 0.398 w 0 0 m 192.48 0 l S Q q 1 0 0 1 80.099 704.722 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F56 8.9664 Tf 98.054 707.861 Td [(0.9)]TJ ET q 1 0 0 1 127.217 704.722 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F56 8.9664 Tf 135.968 707.861 Td [(61)-250(sec)]TJ ET q 1 0 0 1 167.377 704.722 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F56 8.9664 Tf 174.998 707.861 Td [(10)-250(days)]TJ ET q 1 0 0 1 208.021 704.722 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F56 8.9664 Tf 224.488 707.861 Td [(3602)-250(sec)]TJ ET q 1 0 0 1 272.579 704.722 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q q 1 0 0 1 80.099 694.262 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F56 8.9664 Tf 95.812 697.4 Td [(0.85)]TJ ET q 1 0 0 1 127.217 694.262 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F56 8.9664 Tf 133.726 697.4 Td [(125)-250(sec)]TJ ET q 1 0 0 1 167.377 694.262 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F56 8.9664 Tf 174.998 697.4 Td [(10)-250(days)]TJ ET q 1 0 0 1 208.021 694.262 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F56 8.9664 Tf 224.488 697.4 Td [(3602)-250(sec)]TJ ET q 1 0 0 1 272.579 694.262 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q q 1 0 0 1 80.099 683.801 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F56 8.9664 Tf 95.812 686.939 Td [(0.80)]TJ ET q 1 0 0 1 127.217 683.801 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F56 8.9664 Tf 133.726 686.939 Td [(285)-250(sec)]TJ ET q 1 0 0 1 167.377 683.801 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F56 8.9664 Tf 174.998 686.939 Td [(10)-250(days)]TJ ET q 1 0 0 1 208.021 683.801 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q BT /F56 8.9664 Tf 224.488 686.939 Td [(3602)-250(sec)]TJ ET q 1 0 0 1 272.579 683.801 cm []0 d 0 J 0.398 w 0 0 m 0 10.461 l S Q q 1 0 0 1 80.099 683.602 cm []0 d 0 J 0.398 w 0 0 m 192.48 0 l S Q BT /F56 8.9664 Tf 53.798 653.538 Td [(we)-333(v)25(ary)-332(the)-333(number)-332(of)-333(training)-332(e)15(xamples)-333(for)-332(the)-333(GBR)40(Or)18(gs)-332(dataset)]TJ 0 -10.46 Td [(and)-331(plot)-332(the)-331(design)-332(time.)-554(In)-331(Figure)-332(14,)-352(we)-331(v)25(ary)-332(the)-331(number)-331(\050)]TJ/F34 8.9664 Tf 226.88 0 Td [(d)]TJ/F56 8.9664 Tf 4.775 0 Td [(\051)-331(of)]TJ -231.655 -10.461 Td [(similarity)-299(functions)-300(a)1(llo)25(wed)-300(in)-299(a)-299(similarity)-300(join)-299(using)-299(the)-299(GBR)40(Or)18(gs)]TJ 0 -10.461 Td [(dataset.)-709(Note)-383(that)-383(in)-383(the)-383(e)15(xperiments)-383(o)15(v)15(er)-383(the)-383(GBR)40(Or)18(gs)-383(relation,)]TJ/F34 8.9664 Tf 0 -10.461 Td [(D)]TJ/F31 8.9664 Tf 10.415 0 Td [(=)-285(29)]TJ/F56 8.9664 Tf 18.943 0 Td [(.)]TJ -20.391 -10.461 Td [(W)80(e)-222(obs)1(erv)15(e)-222(that)-222(the)-221(design)-222(time)-221(can)-222(increase)-221(\050as)-222(seen)-221(for)-222(Cora)-221(and)]TJ -8.967 -10.46 Td [(GBR)40(Or)18(gs)-338(datasets\051)-337(when)-338(the)-338(tar)18(get)-337(precision)-338(is)-338(high.)-573(The)-337(number)]TJ 0 -10.461 Td [(of)-316(ne)25(w)-315(sub-re)15(gions)-315(e)15(xplored)-316(by)-315(our)-316(algorithm)-315(increases)-316(when)-315(each)]TJ 0 -10.461 Td [(v)25(alid)-325(sub-re)15(gion)-325(is)-326(allo)25(wed)-325(to)-325(contain)-325(only)-325(a)-326(v)15(ery)-325(small)-325(\050)]TJ/F31 8.9664 Tf 210.737 0 Td [(5)]TJ/F56 8.9664 Tf 7.524 0 Td [(or)-325(less\051)]TJ -218.261 -10.461 Td [(ne)15(g)5(ati)25(v)15(e)-381(pairs.)-704(Second,)-414(the)-381(design)-381(time)-381(depends)-381(primarily)-381(on)-381(the)]TJ 0 -10.46 Td [(number)-275(of)-275(ne)15(g)5(ati)25(v)15(e)-274(sk)15(yline)-275(points)-275(\050as)-275(seen)-275(from)-274(Figure)-275(13\051.)-385(W)80(e)-274(an-)]TJ 0 -10.461 Td [(ticipate)-301(this)-302(dependence)-301(because)-302(the)-301(number)-302(of)-301(rectangles)-301(e)15(xplored)]TJ 0 -10.461 Td [(by)-283(our)-283(algori)1(thm)-283(depends)-283(on)-283(the)-282(number)-283(of)-283(ne)15(g)5(ati)25(v)15(e)-283(sk)15(yline)-282(points.)]TJ 0 -10.461 Td [(Finally)65(,)-318(we)-304(observ)15(e)-304(\050from)-305(Figure)-304(14\051)-304(that)-305(the)-304(design)-304(time)-304(increases)]TJ 0 -10.461 Td [(with)]TJ/F34 8.9664 Tf 18.184 0 Td [(d)]TJ/F56 8.9664 Tf 4.775 0 Td [(;)-250(we)-250(e)15(xplore)-250(a)-250(lar)18(ger)-250(number)-250(of)-250(sub-re)15(gions)-250(as)]TJ/F34 8.9664 Tf 168.638 0 Td [(d)]TJ/F56 8.9664 Tf 7.016 0 Td [(is)-250(increased.)]TJ/F55 11.9552 Tf -198.613 -23.917 Td [(8.)-1000(CONCLUSION)]TJ/F56 8.9664 Tf 8.967 -12.951 Td [(In)-471(this)-471(paper)40(,)-527(we)-471(proposed)-471(that)-471(record)-471(matching)-471(programs)-471(be)]TJ -8.967 -10.461 Td [(vie)25(wed)-286(as)-286(ef)25(\002ciently)-286(e)15(x)15(ecutabl)1(e)-286(operator)-286(trees)-286(b)20(uilt)-286(o)15(v)15(er)-286(a)-286(small)-285(set)]TJ 0 -10.461 Td [(of)-325(relational)-325(and)-326(data)-325(cleaning)-325(operators.)-536(Since)-325(designing)-325(accurate)]TJ 0 -10.461 Td [(operator)-244(trees)-245(is)-244(challenging,)-246(we)-244(propose)-245(techniques)-244(for)-245(creating)-244(op-)]TJ 0 -10.46 Td [(erator)-289(trees)-288(that)-289(best)-288(match)-289(a)-288(gi)25(v)15(en)-289(set)-289(of)-288(e)15(xamples.)-426(A)-288(programmer)]TJ 0 -10.461 Td [(is)-299(no)25(w)-299(a)1(ble)-299(to)-299(easily)-299(interpret,)-311(re)25(vie)25(w)65(,)-310(and)-299(modify)-299(the)-299(resulting)-298(op-)]TJ 0 -10.461 Td [(erator)-258(tr)1(ees.)-333(W)80(e)-258(dem)1(onstrated)-258(that)-257(operator)-258(trees)-257(designed)-258(using)-257(our)]TJ 0 -10.461 Td [(techniques)-292(compare)-291(f)10(a)20(v)20(orably)-292(in)-292(quality)-291(with)-292(a)-292(commercial)-291(address)]TJ 0 -10.46 Td [(cleansing)-330(tool)-331(and)-330(with)-331(current)-330(best)-331(kno)25(wn)-330(machine)-331(learning)-330(tech-)]TJ 0 -10.461 Td [(niques)-291(for)-290(record)-291(matching,)-300(while)-291(being)-290(signi\002cantly)-291(more)-290(ef)25(\002cient)]TJ 0 -10.461 Td [(to)-250(e)15(x)15(ecute.)]TJ/F55 11.9552 Tf 0 -23.917 Td [(9.)-1000(REFERENCES)]TJ/F56 7.9701 Tf 3.985 -6.979 Td [([1])-563(E.)-250(Agichtei)1(n)-250(and)-250(V)129(.)-250(Ganti.)-250(Mining)-250(reference)-250(tables)-250(for)-250(automatic)-250(te)15(xt)]TJ 13.777 -8.967 Td [(se)15(gmentation.)-250(In)]TJ/F57 7.9701 Tf 55.001 0 Td [(Pr)45(oceedings)-250(of)-250(A)30(CM)-250(SIGKDD)]TJ/F56 7.9701 Tf 97.466 0 Td [(,)-250(2004.)]TJ -166.244 -9.962 Td [([2])-563(A.)-250(Arasu,)-250(V)129(.)-250(Ganti)1(,)-250(and)-250(R.)-250(Kaushik.)-250(Ef)25(\002cient)-250(e)15(xact)-250(set-similarity)-250(joins.)]TJ 13.777 -8.967 Td [(In)]TJ/F57 7.9701 Tf 8.631 0 Td [(Pr)45(oceedings)-250(of)-250(VLDB)]TJ/F56 7.9701 Tf 69.595 0 Td [(,)-250(2006.)]TJ -92.003 -9.962 Td [([3])-563(S.)-250(Ar)18(g)5(amon-Engelson)-250(a)1(nd)-250(I.)-250(Dag)5(an.)-250(Committee-based)-250(sample)]TJ 13.777 -8.967 Td [(selection)-250(for)-250(probabilistic)-250(classi\002ers.)]TJ/F57 7.9701 Tf 118.872 0 Td [(J)25(ournal)-250(of)-250(Arti\002cial)-250(Intellig)10(ence)]TJ -118.872 -8.966 Td [(r)37(esear)37(c)15(h)]TJ/F56 7.9701 Tf 27.177 0 Td [(,)-250(1999.)]TJ -40.954 -9.963 Td [([4])-563(R.)-250(Baxter)40(,)-250(P)111(.)-250(C)1(hristen,)-250(and)-250(T)74(.)-250(Churches.)-250(A)-250(comparison)-250(of)-250(f)10(ast)-250(blocking)]TJ 13.777 -8.966 Td [(methods)-250(for)-250(record)-250(linkage.)-250(In)]TJ/F57 7.9701 Tf 98.717 0 Td [(Pr)45(oceedings)-250(of)-250(the)-250(2003)-250(A)30(CM)-250(SIGKDD)]TJ -98.717 -8.966 Td [(W)92(orkshop)-250(on)-250(Data)-250(Cleaning)10(,)-250(Recor)37(d)-250(Linka)10(g)10(e)10(,)-250(and)-250(Object)]TJ 0 -8.967 Td [(Consolidation)]TJ/F56 7.9701 Tf 45.174 0 Td [(,)-250(2003.)]TJ -58.951 -9.962 Td [([5])-563(M.)-250(Bile)1(nk)10(o.)]TJ/F57 7.9701 Tf 53.993 0 Td [(Learnable)-250(Similarity)-250(Functions)-250(and)-250(Their)-250(Application)-250(to)]TJ -40.216 -8.967 Td [(Recor)37(d)-250(Linka)10(g)10(e)-250(and)-250(Clustering)]TJ/F56 7.9701 Tf 99.832 0 Td [(.)-250(PhD)-250(thesis,)-250(Uni)25(v)15(ersity)-250(of)-250(T)70(e)15(xas)-250(at)]TJ -99.832 -8.966 Td [(Austin,)-250(2006.)]TJ -13.777 -9.963 Td [([6])-563(M.)-250(Bile)1(nk)10(o,)-250(B.)-250(Kamath,)-250(and)-250(R.)-250(J.)-250(Moone)15(y)65(.)-250(Adapti)25(v)15(e)-250(blocking:)]TJ 13.777 -8.966 Td [(Learning)-250(to)-250(scale)-250(up)-250(record)-250(linkage.)-250(In)]TJ/F57 7.9701 Tf 125.273 0 Td [(Pr)45(oceedings)-250(of)-250(the)-250(6th)-250(IEEE)]TJ -125.273 -8.967 Td [(International)-250(Confer)37(ence)-250(on)-250(Data)-250(Mining)-250(\050ICDM-2006\051)]TJ/F56 7.9701 Tf 179.676 0 Td [(,)-250(2006.)]TJ -193.453 -9.962 Td [([7])-563(M.)-250(Bile)1(nk)10(o)-250(and)-250(R.)-250(Moone)15(y)65(.)-250(Riddle:)-310(Repository)-250(of)-250(information)-250(on)]TJ 13.777 -8.967 Td [(duplicate)-250(detection,)-250(record)-250(linkage,)-250(and)-250(identity)-250(uncertainty)65(.)]TJ 0 -8.966 Td [(http://www)65(.cs.ute)15(xas.edu/users/ml/riddle.)]TJ -13.777 -9.963 Td [([8])-563(M.)-250(Bile)1(nk)10(o)-250(and)-250(R.)-250(Moone)15(y)65(.)-250(Adapti)25(v)15(e)-250(duplicate)-250(detection)-250(using)]TJ 13.777 -8.966 Td [(learnable)-250(string)-250(similarity)-250(measures.)-250(In)]TJ/F57 7.9701 Tf 126.173 0 Td [(Pr)45(oceedings)-250(of)-250(A)30(CM)-250(SIGKDD)]TJ/F56 7.9701 Tf 97.466 0 Td [(,)]TJ -223.639 -8.966 Td [(2003.)]TJ -13.777 -9.963 Td [([9])-563(M.)-250(Bile)1(nk)10(o)-250(and)-250(R.)-250(J.)-250(Moone)15(y)65(.)-250(On)-250(e)25(v)25(aluation)-250(and)-250(training-set)]TJ 13.777 -8.966 Td [(construction)-250(for)-250(duplicate)-250(detection.)-250(In)]TJ/F57 7.9701 Tf 125.727 0 Td [(Pr)45(oceedings)-250(of)-250(the)-250(A)30(CM)]TJ -125.727 -8.967 Td [(SIGKDD)-250(workshop)-250(on)-250(data)-250(cleaning)10(,)-250(r)37(ecor)37(d)-250(linka)10(g)10(e)10(,)-250(and)-250(object)]TJ 0 -8.966 Td [(identi\002cation)]TJ/F56 7.9701 Tf 42.065 0 Td [(,)-250(2003.)]TJ -59.827 -9.963 Td [([10])-563(V)129(.)-250(Borkar)40(,)-250(K.)-250(Deshmukh,)-250(and)-250(S)1(.)-250(Sara)15(w)10(agi.)-250(Automatic)-250(se)15(gmentation)-250(of)]TJ 17.762 -8.966 Td [(te)15(xt)-250(into)-250(structured)-250(records.)-250(In)]TJ/F57 7.9701 Tf 98.159 0 Td [(Pr)45(oceedings)-250(of)-250(A)30(CM)-250(SIGMOD)]TJ/F56 7.9701 Tf 98.789 0 Td [(,)-250(2001.)]TJ 42.326 653.549 Td [([11])-563(S.)-250(Borzson)15(yi,)-250(D.)-250(K)35(ossm)1(ann,)-250(and)-250(K.)-250(Stock)10(er)55(.)-250(The)-250(sk)15(yline)-250(operator)55(.)-250(In)]TJ/F57 7.9701 Tf 17.762 -8.966 Td [(Pr)45(oceedings)-250(of)-250(ICDE)]TJ/F56 7.9701 Tf 68.263 0 Td [(,)-250(2001.)]TJ -86.025 -9.963 Td [([12])-563(S.)-250(Chaudhuri,)-250(K.)-250(Ganja)1(m,)-250(V)129(.)-250(Ganti,)-250(and)-250(R.)-250(Motw)10(ani.)-250(Rob)20(ust)-250(and)]TJ 17.762 -8.966 Td [(ef)25(\002cient)-250(fuzzy)-250(match)-250(for)-250(online)-250(data)-250(cleaning.)-250(In)]TJ/F57 7.9701 Tf 157.169 0 Td [(Pr)45(oceedings)-250(of)-250(A)30(CM)]TJ -157.169 -8.967 Td [(SIGMOD)]TJ/F56 7.9701 Tf 30.541 0 Td [(,)-250(2003.)]TJ -48.303 -9.962 Td [([13])-563(S.)-250(Chaudhuri,)-250(V)129(.)-250(Ganti,)-250(and)-250(R)1(.)-250(Kaushik.)-250(A)-250(primiti)25(v)15(e)-250(operator)-250(for)]TJ 17.762 -8.967 Td [(similarity)-250(joins)-250(in)-250(data)-250(cleaning.)-250(In)]TJ/F57 7.9701 Tf 113.126 0 Td [(Pr)45(oceedings)-250(of)-250(ICDE)]TJ/F56 7.9701 Tf 68.264 0 Td [(,)-250(2006.)]TJ -199.152 -9.962 Td [([14])-563(W)92(.)-250(Cohen.)-250(Inte)15(gration)-250(of)-250(het)1(erogeneous)-250(databases)-250(without)-250(common)]TJ 17.762 -8.967 Td [(domains)-250(using)-250(queries)-250(based)-250(on)-250(te)15(xtual)-250(similarity)65(.)-250(In)]TJ/F57 7.9701 Tf 169.602 0 Td [(Pr)45(oceedings)-250(of)]TJ -169.602 -8.966 Td [(A)30(CM)-250(SIGMOD)]TJ/F56 7.9701 Tf 49.119 0 Td [(,)-250(1998.)]TJ -66.881 -9.963 Td [([15])-563(W)92(.)-250(W)92(.)-250(Cohen.)-250(Data)-250(inte)15(grat)1(ion)-250(using)-250(similarity)-250(joins)-250(and)-250(a)-250(w)10(ord-based)]TJ 17.762 -8.966 Td [(information)-250(representation)-250(language.)]TJ/F57 7.9701 Tf 119.526 0 Td [(A)30(CM)-250(T)55(r)15(ansactions)-250(on)]TJ -119.526 -8.966 Td [(information)-250(systems)]TJ/F56 7.9701 Tf 63.983 0 Td [(,)-250(2000.)]TJ -81.745 -9.963 Td [([16])-563(W)92(.)-250(W)92(.)-250(Cohen)-250(and)-250(J.)-250(Richma)1(n.)-250(Learning)-250(to)-250(match)-250(and)-250(cluster)-250(lar)18(ge)]TJ 17.762 -8.966 Td [(high-dimensional)-250(data)-250(sets)-250(for)-250(data)-250(inte)15(gration.)-250(In)]TJ/F57 7.9701 Tf 160.588 0 Td [(Pr)45(oceedings)-250(of)-250(the)]TJ -160.588 -8.967 Td [(8th)-250(A)30(CM)-250(SIGKDD)-250(International)-250(Confer)37(ence)-250(on)-250(Knowledg)10(e)-250(Disco)10(very)]TJ 0 -8.966 Td [(and)-250(Data)-250(Mining)-250(\050KDD-2002\051)]TJ/F56 7.9701 Tf 97.625 0 Td [(,)-250(2002.)]TJ -115.387 -9.963 Td [([17])-563(N.)-250(Cristi)1(anini)-250(and)-250(J.)-250(Sha)15(we-T)80(aylor)55(.)]TJ/F57 7.9701 Tf 131.678 0 Td [(An)-250(Intr)45(oduction)-250(to)-250(Support)-250(V)111(ector)]TJ -113.916 -8.966 Td [(Mac)15(hines)-250(and)-250(other)-250(k)10(ernel-based)-250(learning)-250(methods)]TJ/F56 7.9701 Tf 164.27 0 Td [(.)-250(Cambridge)]TJ -164.27 -8.967 Td [(Uni)25(v)15(ersity)-250(Press,)-250(2000.)]TJ -17.762 -9.962 Td [([18])-563(A.)-250(Doan,)-250(R.)-250(Ramakri)1(shnan,)-250(and)-250(S.)-250(V)111(aith)5(yanathan.)-250(Managing)]TJ 17.762 -8.967 Td [(information)-250(e)15(xtraction.)-250(In)]TJ/F57 7.9701 Tf 83.996 0 Td [(Pr)45(oceedings)-250(of)-250(A)30(CM)-250(SIGMOD)]TJ/F56 7.9701 Tf 98.789 0 Td [(,)-250(2006.)]TJ -200.547 -9.962 Td [([19])-563(T)74(.)-250(Dohzen,)-250(M.)-250(P)15(amuk,)-250(S.-W)92(.)-250(Seong,)-250(J.)-250(H)1(ammer)40(,)-250(and)-250(M.)-250(Stonebrak)10(er)55(.)]TJ 17.762 -8.967 Td [(Data)-250(inte)15(gration)-250(through)-250(transform)-250(reuse)-250(in)-250(the)-250(morpheus)-250(project.)-250(In)]TJ/F57 7.9701 Tf 0 -8.966 Td [(Pr)45(oceedings)-250(of)-250(A)30(CM)-250(SIGMOD)]TJ/F56 7.9701 Tf 98.789 0 Td [(,)-250(2006.)]TJ -116.551 -9.963 Td [([20])-563(I.)-250(P)111(.)-250(Felligi)-249(and)-250(A.)-250(B.)-250(Sunter)55(.)-250(A)-250(theory)-250(for)-250(record)-250(linkage.)]TJ/F57 7.9701 Tf 202.826 0 Td [(J)25(ournal)-250(of)]TJ -185.064 -8.966 Td [(the)-250(American)-250(Statistical)-250(Society)]TJ/F56 7.9701 Tf 101.609 0 Td [(,)-250(1969.)]TJ -119.371 -9.963 Td [([21])-563(H.)-250(Galhardas,)-250(D.)-250(Fl)1(orescu,)-250(D.)-250(Shasha,)-250(E.)-250(Simon,)-250(and)-250(C.)-250(Saita.)]TJ 17.762 -8.966 Td [(Declarati)25(v)15(e)-250(data)-250(cleaning:)-310(Language,)-250(model,)-250(and)-250(algorithms.)-250(In)]TJ/F57 7.9701 Tf 0 -8.966 Td [(Pr)45(oceedings)-250(of)-250(VLDB)]TJ/F56 7.9701 Tf 69.594 0 Td [(,)-250(2001.)]TJ -87.356 -9.963 Td [([22])-563(L.)-250(Gra)20(v)25(ano,)-250(P)111(.)-250(G.)-250(Ipeiroti)1(s,)-250(H.)-250(V)129(.)-250(Jag)5(adish,)-250(N.)-250(K)35(oudas,)]TJ 17.762 -8.966 Td [(S.)-250(Muthukrishnan,)-250(and)-250(D.)-250(Sri)25(v)25(asta)20(v)25(a.)-250(Approximate)-250(string)-250(joins)-250(in)-250(a)]TJ 0 -8.967 Td [(database)-250(\050almost\051)-250(for)-250(free.)-250(In)]TJ/F57 7.9701 Tf 94.277 0 Td [(Pr)45(oceedings)-250(of)-250(VLDB)]TJ/F56 7.9701 Tf 69.595 0 Td [(,)-250(2001.)]TJ -181.634 -9.962 Td [([23])-563(S.)-250(Guha,)-250(N.)-250(K)35(oudas,)-250(A.)-250(Marat)1(he,)-250(and)-250(D.)-250(Sri)25(v)25(asta)20(v)25(a.)-250(Mer)18(ging)-250(the)]TJ 17.762 -8.967 Td [(results)-250(of)-250(approximate)-250(match)-250(operations.)-250(In)]TJ/F57 7.9701 Tf 140.559 0 Td [(Pr)45(oceedings)-250(of)-250(VLDB)]TJ/F56 7.9701 Tf 69.595 0 Td [(,)]TJ -210.154 -8.966 Td [(2004.)]TJ -17.762 -9.963 Td [([24])-563(M.)-250(Hernandez)-250(and)-250(S.)-250(St)1(olfo.)-250(The)-250(mer)18(ge/pur)18(ge)-250(problem)-250(for)-250(lar)18(ge)]TJ 17.762 -8.966 Td [(databases.)-250(In)]TJ/F57 7.9701 Tf 43.157 0 Td [(Pr)45(oceedings)-250(of)-250(A)30(CM)-250(SIGMOD)]TJ/F56 7.9701 Tf 98.789 0 Td [(,)-250(1995.)]TJ -159.708 -9.963 Td [([25])-563(D.)-250(S.)-250(Hochbaum.)]TJ/F57 7.9701 Tf 74.875 0 Td [(Appr)45(oximation)-250(algorithms)-250(for)-250(NP-har)37(d)-250(pr)45(oblems)]TJ/F56 7.9701 Tf 156.181 0 Td [(.)]TJ -213.294 -8.966 Td [(PWS)-250(Publishing)-250(Compan)15(y)65(,)-250(1997.)]TJ -17.762 -9.963 Td [([26])-563(N.)-250(K)35(oudas,)-250(A.)-250(Marat)1(he,)-250(and)-250(D.)-250(Sri)25(v)25(asta)20(v)25(a.)-250(Fle)15(xible)-250(string)-250(matching)]TJ 17.762 -8.966 Td [(ag)5(ainst)-250(lar)18(ge)-250(databases)-250(in)-250(practice.)-250(In)]TJ/F57 7.9701 Tf 120.881 0 Td [(Pr)45(oceedings)-250(of)-250(VLDB)]TJ/F56 7.9701 Tf 69.595 0 Td [(,)-250(2004.)]TJ -208.238 -9.963 Td [([27])-563(N.)-250(K)35(oudas,)-250(S.)-250(Sara)15(w)10(agi,)-250(and)-250(D.)-250(S)1(ri)25(v)25(asta)20(v)25(a.)-250(Record)-250(linkage:)-310(Similarity)]TJ 17.762 -8.966 Td [(measures)-250(and)-250(algorithms.)-250(In)]TJ/F57 7.9701 Tf 91.862 0 Td [(Pr)45(oceedings)-250(of)-250(A)30(CM)-250(SIGMOD)]TJ/F56 7.9701 Tf 98.789 0 Td [(,)-250(2006.)]TJ -208.413 -9.963 Td [([28])-563(A.)-250(K.)-250(McCall)1(um,)-250(K.)-250(Nig)5(am,)-250(and)-250(L.)-250(Ung)5(ar)55(.)-250(Ef)25(\002cient)-250(clustering)-250(of)]TJ 17.762 -8.966 Td [(high-dimensional)-250(data)-250(sets)-250(with)-250(application)-250(to)-250(reference)-250(matching.)-250(In)]TJ/F57 7.9701 Tf 0 -8.967 Td [(Pr)45(oceedings)-250(of)-250(the)-250(6th)-250(International)-250(Confer)37(ence)-250(On)-250(Knowledg)10(e)]TJ 0 -8.966 Td [(Disco)10(very)-250(and)-250(Data)-250(Mining)-250(\050KDD-2000\051)]TJ/F56 7.9701 Tf 131.848 0 Td [(,)-250(2000.)]TJ -149.61 -9.963 Td [([29])-563(M.)-250(Michel)1(son)-250(and)-250(C.)-250(Knoblock.)-250(Learning)-250(blocking)-250(schemes)-250(for)-250(record)]TJ 17.762 -8.966 Td [(linkage.)-250(In)]TJ/F57 7.9701 Tf 36.08 0 Td [(Pr)45(oceedings)-250(of)-250(the)-250(21st)-250(National)-250(Confer)37(ence)-250(on)-250(Arti\002cial)]TJ -36.08 -8.966 Td [(Intellig)10(ence)-250(\050AAAI\051)]TJ/F56 7.9701 Tf 62.11 0 Td [(,)-250(2006.)]TJ -79.872 -9.963 Td [([30])-563(V)129(.)-250(Raman)-250(and)-250(J.)-250(Hel)1(lerstein.)-250(An)-250(interacti)25(v)15(e)-250(frame)25(w)10(ork)-250(for)-250(data)]TJ 17.762 -8.966 Td [(cleaning.)-250(T)70(echnical)-250(report,)-250(Uni)25(v)15(eristy)-250(of)-250(California,)-250(Berk)10(ele)15(y)65(,)-250(2000.)]TJ -17.762 -9.963 Td [([31])-563(S.)-250(Sara)15(w)10(agi)-250(and)-250(A.)-250(Bha)1(midipaty)65(.)-250(Interacti)25(v)15(e)-250(deduplication)-250(using)-250(acti)25(v)15(e)]TJ 17.762 -8.966 Td [(learning.)-250(In)]TJ/F57 7.9701 Tf 38.734 0 Td [(Pr)45(oceedings)-250(of)-250(A)30(CM)-250(SIGKDD)]TJ/F56 7.9701 Tf 97.466 0 Td [(,)-250(2002.)]TJ -153.962 -9.963 Td [([32])-563(S.)-250(Sara)15(w)10(agi)-250(and)-250(A.)-250(Ki)1(rpal.)-250(Scaling)-250(up)-250(the)-250(alias)-250(duplicate)-250(elimination)]TJ 17.762 -8.966 Td [(system:)-310(a)-250(demonstration.)-250(In)]TJ/F57 7.9701 Tf 90.579 0 Td [(Pr)45(oceedings)-250(of)-250(ICDE)]TJ/F56 7.9701 Tf 68.263 0 Td [(,)-250(2003.)]TJ -176.604 -9.963 Td [([33])-563(S.)-250(Sara)15(w)10(agi)-250(and)-250(A.)-250(Ki)1(rpal.)-250(Ef)25(\002cient)-250(set)-250(joins)-250(on)-250(similarity)-250(predicates.)]TJ 17.762 -8.966 Td [(In)]TJ/F57 7.9701 Tf 8.631 0 Td [(Pr)45(oceedings)-250(of)-250(A)30(CM)-250(SIGMOD)]TJ/F56 7.9701 Tf 98.789 0 Td [(,)-250(2004.)]TJ -125.182 -9.963 Td [([34])-563(T)74(.)-250(Softw)10(are.)-250(www)65(.tri)1(lliumsoft.com/trilliumsoft.nsf.)]TJ 0 -9.963 Td [([35])-563(D.)-250(T)80(aft.)-250(Micros)1(oft)-250(brings)-250(.net)-250(to)-250(katrina)-250(relief)-250(ef)25(fort.)]TJ 17.762 -8.966 Td [(http://www)65(.e)25(week.com/article2/0,1895,1855722,00.asp,)-250(2005.)]TJ -17.762 -9.963 Td [([36])-563(S.)-250(T)70(ejada,)-250(C.)-250(Knobl)1(ock,)-250(and)-250(S.)-250(Minton.)-250(Learning)-250(domain-independent)]TJ 17.762 -8.966 Td [(string)-245(transformation)-244(weights)-245(for)-245(high)-244(accurac)15(y)-245(object)-245(identi\002cation.)-245(In)]TJ/F57 7.9701 Tf 0 -8.966 Td [(Pr)45(oceedings)-250(of)-250(A)30(CM)-250(SIGKDD)]TJ/F56 7.9701 Tf 97.465 0 Td [(,)-250(2002.)]TJ -115.227 -9.963 Td [([37])-563(S.)-250(T)70(ejada,)-250(C.)-250(A.)-250(Knobl)1(ock,)-250(and)-250(S.)-250(Minton.)-250(Learning)-250(object)]TJ 17.762 -8.966 Td [(identi\002cation)-250(rules)-250(for)-250(information)-250(inte)15(gration.)]TJ/F57 7.9701 Tf 150.856 0 Td [(Information)-250(Systems)]TJ/F56 7.9701 Tf 65.307 0 Td [(,)]TJ -216.163 -8.967 Td [(2001.)]TJ -17.762 -9.962 Td [([38])-563(A.)-250(Thor)-250(and)-250(E.)-250(Rahm.)-250(M)1(oma)-250(\226)-250(a)-250(mapping)-250(based)-250(object)-250(matching)]TJ 17.762 -8.967 Td [(system.)-250(In)]TJ/F57 7.9701 Tf 34.757 0 Td [(Biennial)-250(Conf)15(.)-250(on)-250(Inno)10(vative)-250(Data)-250(Systems)-250(Resear)37(c)15(h)]TJ/F56 7.9701 Tf 168.288 0 Td [(,)-250(2007.)]TJ ET Q 1 0 0 1 295.992 36 cm 0 Tr /QQAPFce02551e 12 Tf 0 0 0 rg 100 Tz 0 Ts 0 Tw 0 Tc BT 1 0 0 1 0 0 Tm (338)Tj ET 1 0 0 1 0 0 cm 1 0 0 1 -295.992 -36 cm endstream endobj 165 0 obj << /Type /Page /Resources 164 0 R /MediaBox [ 0 0 612 792 ] /Parent 91 0 R /Contents [ 166 0 R ] >> endobj 164 0 obj << /Font << /F55 9 0 R /F56 10 0 R /F34 12 0 R /F31 18 0 R /F57 11 0 R /QQAPFce02551e 232 0 R >> /ProcSet [ /PDF /Text ] >> endobj 167 0 obj [794.1] endobj 168 0 obj [541.7 541.7 680.6 1027.8 402.8 472.2 402.8 680.6 680.6 680.6 680.6] endobj 169 0 obj [1083.3 458.3 1083.3 736.1 1083.3 736.1 1083.3 1083.3 1083.3 1083.3 1083.3 1083.3 1083.3 1361.1 736.1 736.1 1083.3 1083.3 1083.3 1083.3 1083.3 1083.3 1083.3 1083.3 1083.3 1083.3 1083.3 1083.3 1361.1 1361.1 1083.3 1083.3 1361.1 1361.1 736.1 736.1 1361.1 1361.1 1361.1 1083.3 1361.1 1361.1 875 875 1361.1 1361.1 1361.1 1083.3 441 1361.1 944.5 944.5 1222.2 1222.2 0 0 805.6 805.6 944.5 736.1 1013.9 1013.9 1083.3 1083.3 875 1113.5 919.3 782.1 1083.9 770.8 988.2 850.4 1194.5 819.5 958.3 1055 964.7 1567.9 1126.1 1089.2 997.7 1132 1196.1 868.1 822.4 873.8 898.9 1367.7 996.6 929.5 991.4 944.5 944.5 944.5 944.5 944.5 875 875 666.7 666.7 666.7 666.7 736.1 736.1 597.2 597.2 458.3] endobj 170 0 obj [826.4 295.1 826.4 531.3 826.4 531.3 826.4 826.4 826.4 826.4 826.4 826.4 826.4 1062.5 531.3 531.3 826.4 826.4 826.4 826.4 826.4 826.4 826.4 826.4 826.4 826.4 826.4 826.4 1062.5 1062.5 826.4 826.4 1062.5 1062.5 531.3 531.3 1062.5 1062.5 1062.5 826.4 1062.5 1062.5 649.3 649.3 1062.5 1062.5 1062.5 826.4 288.2 1062.5 708.3 708.3 944.5 944.5 0 0 590.3 590.3 708.3 531.3 767.4 767.4 826.4 826.4 649.3 849.5 694.7 562.6 821.7 560.8 758.3 631 904.2 585.5 720.1 807.4 730.7 1264.5 869.1 841.6 743.3 867.7 906.9 643.4 586.3 662.8 656.2 1054.6 756.4 705.8 763.6 708.3 708.3 708.3 708.3 708.3 649.3 649.3 472.2 472.2 472.2 472.2 531.3 531.3 413.2 413.2 295.1] endobj 171 0 obj [596.2 547.3 470.1 429.5 467 533.2 495.7 376.2 612.3 619.8 639.2 522.3 467 610.1 544.1 607.2 471.5 576.4 631.6 659.7 694.5 660.7 490.6 632.1 882.1 544.1 388.9 692.4 1062.5 1062.5 1062.5 1062.5 295.1 295.1 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 295.1 295.1 826.4 531.3 826.4 531.3 559.7 795.8 801.4 757.3 871.7 778.7 672.4 827.9 872.8 460.7 580.4 896 722.6 1020.4 843.3 806.2 673.6 835.7 800.2 646.2 618.6 718.8 618.8 1002.4 873.9 615.8 720 413.2 413.2 413.2 1062.5 1062.5 434 564.4 454.5 460.2 546.7 492.9 510.4 505.6 612.3 361.7 429.7 553.2 317.1 939.8 644.7 513.5 534.8 474.4 479.5 491.3 383.7 615.2 517.4] endobj 172 0 obj [885.4 826.4 736.8 708.3 795.8 767.4 826.4 767.4 826.4 767.4 619.8 590.3 590.3 885.4 885.4 295.1 324.7 531.3 531.3 531.3 531.3 531.3 795.8 472.2 531.3 767.4 826.4 531.3 958.7 1076.8 826.4 295.1 295.1 531.3 885.4 531.3 885.4 826.4 295.1 413.2 413.2 531.3 826.4 295.1 354.2 295.1 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 295.1 295.1 295.1 826.4 501.7 501.7 826.4 795.8 752.1 767.4 811.1 722.6 693.1 833.5 795.8 382.6 545.5 825.4 663.6 972.9 795.8 826.4 722.6 826.4 781.6 590.3 767.4 795.8 795.8 1091 795.8 795.8 649.3 295.1 531.3 295.1] endobj 173 0 obj [753.4] endobj 174 0 obj [963 379.6 963 638.9 963 638.9 963 963 963 963 963 963 963 1222.2 638.9 638.9 963 963 963 963 963 963 963 963 963 963 963 963 1222.2 1222.2 963 963 1222.2 1222.2 638.9 638.9 1222.2 1222.2 1222.2 963 1222.2 1222.2 768.5 768.5 1222.2 1222.2 1222.2 963 365.7 1222.2 833.3 833.3 1092.6 1092.6 0 0 703.7 703.7 833.3 638.9 898.1 898.1 963 963 768.5 989.9 813.3 678.4 961.2 671.3 879.9 746.7 1059.3 709.3 846.3 938.8 854.5 1427.2 1005.7 973 878.4 1008.3 1061.4 762 711.3 774.4 785.2 1222.7 883.7 823.9 884 833.3 833.3 833.3 833.3 833.3 768.5 768.5 574.1 574.1 574.1 574.1 638.9 638.9 509.3 509.3 379.6] endobj 175 0 obj [481.5 481.5 611.1 935.2 351.8 416.7 351.8 611.1 611.1 611.1 611.1 611.1 611.1 611.1 611.1 611.1 611.1 611.1 351.8 351.8 351.8 935.2] endobj 176 0 obj [790.6 746.9 654.2 613.5 666.7 743.8 677.1 549.8 827.6 840.3 849.8 712 666.7 831.1 726 815.2 681.6 791.7 841.7 864.6 930.6 886.4 674.7 855.3 1144.8 726 578.1 918.1 1361.1 1361.1 1361.1 1361.1 458.3 458.3 736.1 736.1 736.1 736.1 736.1 736.1 736.1 736.1 736.1 736.1 736.1 736.1 458.3 458.3 1083.3 736.1 1083.3 736.1 749 1036.1 1037 996 1109.9 1007 867.4 1064 1110.4 626.7 772.9 1138.9 955.6 1284 1075.7 1047.5 875.4 1082.2 1030 856.3 832.3 943.9 827.8 1279.2 1112.9 824.3 943.1 597.2 597.2 597.2 1361.1 1361.1 597.2 774.4 633.3 649.4 739.7 677 684 700.6 827.6 533.6] endobj 177 0 obj [804.5 698 652 566.2 523.3 571.8 644 590.3 466.4 725.7 736.1 750 621.5 571.8 726.7 639 716.5 582.1 689.8 742.1 767.4 819.4 779.9 586.7 750.7 1021.9 639 487.8 811.6 1222.2 1222.2 1222.2 1222.2 379.6 379.6 638.9 638.9 638.9 638.9 638.9 638.9 638.9 638.9 638.9 638.9 638.9 638.9 379.6 379.6 963 638.9 963 638.9 658.7 924.1 926.6 883.7 998.3 899.8 775 952.9 999.5 547.7 681.6 1025.7 846.3 1161.6 967.1 934.1 780 966.5 922.1 756.7 731.1 838.1 729.6 1150.9 1001.4 726.4 837.7 509.3 509.3 509.3 1222.2 1222.2 518.5 674.9 547.7 559.1 642.5 589 600.7 607.7 725.7 445.6 511.6 660.9 401.6 1093.7 769.7 612.5 642.5 570.7 579.9 584.5 476.8 737.3 625 893.2] endobj 178 0 obj [856.5 856.5 856.5 856.5] endobj 179 0 obj [856.5 799.4 713.6 685.2 770.7 742.3 799.4 742.3 799.4 742.3 599.5 571 571 856.5 856.5 285.5 314 513.9 513.9 513.9 513.9 513.9 770.7 456.8 513.9 742.3 799.4 513.9 927.8 1042 799.4 285.5 285.5 513.9 856.5 513.9 856.5 799.4 285.5 399.7 399.7 513.9 799.4 285.5 342.6 285.5 513.9 513.9 513.9 513.9 513.9 513.9 513.9 513.9 513.9 513.9 513.9 285.5 285.5 285.5 799.4 485.3 485.3 799.4 770.7 727.9 742.3 785 699.4 670.8 806.5 770.7 371 528.1 799.2 642.3 942 770.7 799.4 699.4 799.4 756.5 571 742.3 770.7 770.7 1056.2 770.7 770.7 628.1 285.5 513.9 285.5 513.9 285.5 285.5 513.9 571 456.8 571 457.2 314 513.9 571 285.5 314 542.4 285.5 856.5 571 513.9 571 542.4 402 405.4 399.7 571 542.4 742.3 542.4 542.4 456.8 513.9 1027.8] endobj 180 0 obj [658.7 579.2 530.8 455.9 416.4 450.6 513.2 481.1 363.8 592.2 599.5 619.2 506.9 450.6 588.2 529.4 587.7 452.4 556.3 611.7 640.8 670.5 639.4 477.1 609.5 852.5 529.4 374.4 671.1 1027.8 1027.8 1027.8 1027.8 285.5 285.5 513.9 513.9 513.9 513.9 513.9 513.9 513.9 513.9 513.9 513.9 513.9 513.9 285.5 285.5 799.4 513.9 799.4 513.9 543.7 770.7 777.7 733.6 847.5 756.3 656.2 804.8 850.1 449.3 566.3 870.4 699.4 992.9 821.6 782.1 656.2 810.6 777.6 627.8 599.6 699.1 599.4 970.5 849 596.5 699.2 399.7 399.7 399.7 1027.8 1027.8 424.4 544.5 440.4 444.9 532.5 477.8 498.8 490.1 592.2 351.7 420.1 535.1 306.7 905.5 620 497.5 515.9 459.2 463.7 478.8 371.1 591.4 499.2 736.6 582.6 506.2] endobj 182 0 obj [500 500 167 333 556 278 333 333 0 333 675 0 556 389 333 278 0 0 0 0 0 0 0 0 0 0 0 0 333 214 250 333 420 500 500 833 778 333 333 333 500 675 250 333 250 278 500 500 500 500 500 500 500 500 500 500 333 333 675 675 675 500 920 611 611 667 722 611 611 722 722 333 444 667 556 833 667 722 611 722 611 500 556 722 611 833 611 556 556 389 278 389 422 500 333 500 500 444 500 444 278 500 500 278 278 444 278 722 500 500 500 500 389 389 278 500 444 667 444 444 389] endobj 183 0 obj [556 556 167 333 611 278 333 333 0 333 564 0 611 444 333 278 0 0 0 0 0 0 0 0 0 0 0 0 333 180 250 333 408 500 500 833 778 333 333 333 500 564 250 333 250 278 500 500 500 500 500 500 500 500 500 500 278 278 564 564 564 444 921 722 667 667 722 611 556 722 722 333 389 722 611 889 722 722 556 722 667 556 611 722 722 944 722 722 611 333 278 333 469 500 333 444 500 444 500 444 333 500 500 278 278 500 278 778 500 500 500 500 333 389 278 500 500 722 500 500 444 480 200 480 541 0 0 0 333 500 444 1000 500 500 333 1000 556 333 889 0 0 0 0 0 0 444 444 350 500 1000 333 980 389 333 722 0 0 722 0 333 500 500 500 500 200 500 333 760 276 500 564 333] endobj 184 0 obj [556 556 167 333 667 278 333 333 0 333 570 0 667 444 333 278 0 0 0 0 0 0 0 0 0 0 0 0 333 278 250 333 555 500 500 1000 833 333 333 333 500 570 250 333 250 278 500 500 500 500 500 500 500 500 500 500 333 333 570 570 570 500 930 722 667 722 722 667 611 778 778 389 500 778 667 944 722 778 611 778 722 556 667 722 722 1000 722 722 667 333 278 333 581 500 333 500 556 444 556 444 333 500 556 278 333 556 278 833 556 500 556 556 444 389 333 556 500 722 500 500 444 394 220 394 520 0 0 0 333 500 500 1000 500 500 333 1000 556 333 1000 0 0 0 0 0 0 500 500 350 500 1000 333 1000 389 333 722 0 0 722 0 333 500 500 500 500 220 500 333 747 300 500 570 333] endobj 185 0 obj [799.4 285.5 799.4 513.9 799.4 513.9 799.4 799.4 799.4 799.4 799.4 799.4 799.4 1027.8 513.9 513.9 799.4 799.4 799.4 799.4 799.4 799.4 799.4 799.4 799.4 799.4 799.4 799.4 1027.8 1027.8 799.4 799.4 1027.8 1027.8 513.9 513.9 1027.8 1027.8 1027.8 799.4 1027.8 1027.8 628.1 628.1 1027.8 1027.8 1027.8 799.4 279.3 1027.8 685.2 685.2 913.6 913.6 0 0 571 571 685.2 513.9 742.3 742.3 799.4 799.4 628.1 821.1 673.6 542.6 793.8 542.4 736.3 610.9 871 562.7 696.6 782.2 707.9 1229.2 842.1 816.3 716.8 839.3 873.9 622.4 563.2 642.3 632.1 1017.5 732.4 685 742 685.2 685.2 685.2 685.2 685.2 628.1 628.1 456.8 456.8 456.8 456.8 513.9 513.9 399.7 399.7 285.5] endobj 186 0 obj [278 333 278 278 556 556 556 556 556 556 556 556 556 556 278 278 584 584 584 556 1015 667 667 722 722 667 611 778 722 278 500 667 556 833 722 778 667 778 722 667 611 722 667 944 667 667 611 278 278 278 469 556 222 556 556 500 556 556 278 556 556 222 222 500 222 833 556 556 556 556 333 500 278 556 500 722 500 500 500 334 260 334 584 0 0 0 222 556 333 1000 556 556 333 1000 667 333 1000 0 0 0 0 0 0 333 333 350 556 1000 333 1000 500 333 944 0 0 667 0 333 556 556 556 556 260 556 333 737 370 556 584 333] endobj 187 0 obj [611 611 167 333 611 278 333 333 0 333 584 0 611 500 333 278 0 0 0 0 0 0 0 0 0 0 0 0 333 238 278 333 474 556 556 889 722 278 333 333 389 584 278 333 278 278 556 556 556 556 556 556 556 556 556 556 333 333 584 584 584 611 975 722 722 722 722 667 611 778 722 278 556 722 611 833 722 778 667 778 722 667 611 722 667 944 667 667 611 333 278 333 584 556 278 556 611 556 611 556 333 611 611 278 278 556 278 889 611 611 611 611 389 556 333 611 556 778 556 556 500 389 280 389 584 0 0 0 278 556 500 1000 556 556 333 1000 667 333 1000 0 0 0 0 0 0 500 500 350 556 1000 333 1000 556 333 944 0 0 667 0 333 556 556 556 556 280 556 333 737 370 556 584 333] endobj 188 0 obj << /Length1 777 /Length2 1165 /Length3 0 /Length 1715 /Filter /FlateDecode >> stream xڭRkXSWyAe>@@( adژ{\ BDʣ," (P ڂ "2 T+ VB;EPҹ`|Cw:{vrv 0 CqWlݍF#99m< / t?Ç6cr "ဲy<&CAID >O 1>r7( N%Rr#B8 >/) `mJK~IaI*! PUFCr;#Yib14_~?$D,%%D`,AS"`IKZ<1DbަT"H狀'N0 -A8 }kDH7.<cg/Ƅ?DhtHw| BP!`xzD“!"OA 2n(Oa> $xw1&pXo!&pOC977md "zxzooƾa$p],@oaXI0KY5 TM–λWMOmIgVYi k_ۦov5rrpN+X[md˼W. a1F)m{~Dec3.23ٹocﶿ;Hݵץ/h+/Nزsc6/~${3U{$77*nsl|xi T5YY _p vjLLֵTBү< ;u6&".=}7}k0duyP >Vz#q~zQ+}XϪ{/3`1&'*h"z q3+QRƲüQɘ񜩍89ˎR< endstream endobj 189 0 obj << /Type /FontDescriptor /FontName /OMGDYW+CMEX10 /Flags 4 /FontBBox [-24 -2960 1454 772] /Ascent 42 /CapHeight 0 /Descent -600 /ItalicAngle 0 /StemV 47 /XHeight 431 /CharSet (/logicalandtext/uniontext) /FontFile 188 0 R >> endobj 190 0 obj << /Length1 794 /Length2 1854 /Length3 0 /Length 2412 /Filter /FlateDecode >> stream xڭ{;4LL-YL@c l0 L[\ xB?MDd@0)◐*Q!~ 0\2Hq QĻò NQ;4~)\6'?% !>[7(]aly0!̾H'v,VDB:%ŷ́pq6=:xŅCorMEgS(3ʾVߜc  g)dHd2O<X0ޔ d[Y0 @W\zUs wX+" C߂!+2g/0!e[, 2!|(> +Yr!lY z`}5Ge ώ,DJ..)|5z*Dwf.&TOmxK]֭ YV81?+AFFztͤӮ8#PNa'\R+Ꮌ D]|=',Y䏴g|y-rs@.o& >!w>&l]'[ >-YuZ 5}E-`Ain]¼ru&j߫kM$j?Q6.C! ˨0O7CCk iL eMݳsG/#:.M]| Ó!ߦ;mrhem^ /I$Wӵ.)opw'Wz#rzS3ߑLA] 3 APwJĿ9uuK*8Tx7bnڱ#6ȠG{"Gm4v}9Bg(IG(W,->JFj]@_/}G>y.#+*kC$x&hCW:zWu 6?9/qmA?sXYbک)ˬ+P$~{nlm')6cv1~>/vE\ByR`L<3Rg*`9 up\ܦs/>2AvYUEu޵M/sET72󬪝sz~32Rrz%[| n^*:PR46ˠWd>I};iPpV{x*c@0N{z|zk[# endstream endobj 191 0 obj << /Type /FontDescriptor /FontName /XRQSHG+CMMI5 /Flags 4 /FontBBox [37 -250 1349 750] /Ascent 694 /CapHeight 683 /Descent -194 /ItalicAngle -14 /StemV 90 /XHeight 431 /CharSet (/D/beta/delta/i) /FontFile 190 0 R >> endobj 192 0 obj << /Length1 1141 /Length2 6534 /Length3 0 /Length 7251 /Filter /FlateDecode >> stream xڭUX˶@.;wAhh`{܂M kpNϹZ3{7jQZ/m@ P'(@V]]Yrsc02ʺ,a`g% $ C|n!Q>Q^ F+`eK$xr[[B0{<%l /!_+: 7Ȇ `@v`(/KP[gп6.MX qB6 [ 3'Wp@4,JAiK'0 \a W RCпlN= _B '?7`7F ZB@APv?} uuiY0=oÏ0 ߿GfUKjlxTj\Pg| ~0[gWnUP+/CB|?$CpHt!~P?ov@Kx&+쟀h􇄛m@؟xZw@?o Ax-7ˎk@xm?WϿ<'~yy?t (?ޔf[0A /5XCJCh|X)*eZQP{H]k/\Hhc+F].0d57]5R_vO yMFUv*=<ٙ ?GyTf-j ո߇}$WdKi"3ŧ&U',%ݖK]t DXV"qnѼN>~KrH!_2qRcO9rds<Гf8:I<6hUWlMϢ1fLeF6OEx5L-r-Av܅YIߢ:BV}*Y"QœԙOEy->!؆kK[烸ϳ:ZV']A(7cz;D2ڡ1rQ~x(H?ĝn3>}=y{+q,ʔ6շ,b'=a Y{aV{?,=M\.䔺 YI2nAh\pKlz[ \ۢ|ڌsI1^z1YE-Ry5soG%LeǗUx%H%3$c.2f9ߟT@lT*8ٔ5WϸyO`oz{ʱ+Sl|0svvº y:^m44S ґsqZ"ƏvS^yE|bNڹ sHskjɻdn+/ANX6yY*2H'34ay2xJ揱Vh%{dAPW6_[?㪽Jja]͡zdjYu{zY?{"#~c>` ;=4Bw gJdlInJ9|~2+?{djk`Kv#lZ!K~i>WE]:Srx4"#o}fٯ,^fO:CHWr!I#f.R{õ~aKدX{߱եNI#e)fs_5vDqǸm 141UTŸ%  ХNcY#3$p0ING2i\DMHYJT j0q-41jsH i䞒Kgv~r M7+X|50k} ?9jNQ(}uo,dYt(??]WEd3`^Z%î_5*J{|9i&޸;Uvu?oNL]*|=X=&ð ZZ@&v9s~7v5QQA79sjE_8bVF3rALގQijqz./@@ٿ9~l[f_Z=_{Z<(Ĥ6+*){:L?ӟZ񅡗,ګ\^GӑBw+W9}tdWK'6~c#Y)ߙ׋= (0[C4/ow>X`c+杔|zT >(*9t/Mдw_pB Rp$3.& f:Pa,eU|_#J9[m;X1BB̨׭_降|RP"'VЭ~GbP`qIⲸtg"ܛ8'M xf˗&ʹx[x' f]x?y*LMkW@uY"dԟL=>MCC3t]F v7KaDIZGDtap]Fhrp[o|eE]8`1%LvąKBW&Es~I鼳-6{uMSƕ]K9x?U ᎮZΦM+FcےZDtBMfÌ-pW~8!&%.7Ψ={jnHt.!dNn|bOXEFm-H_ȅuX\J2\UARE4KɱNhW ?x`F ;WdOI+[JOaUK. jK b WM $%Bp}/=kWNuKEˌ وǺɽNM82Z+%D+{EFw׭@3g/RSYF)зQ2y,Jy%^T$l{ ᔨ좚N JjMu\0hU N7͘QPfXY`SjgNC#f4PCf"RPk`eYوN  َsTC%F&4#Z)-Vn706]eY`?8q9{/kZϋPͱr=5qgq:$ܒ%=D > d{X'Q[~ā&I>.&u8V(G4l4d(7=Ϟ5xy6 QQt|1o*Ye=%?5M`n4.:wřOE8y[kA Iaf=H)Zlkv LPhyI$-/YVE*pX$g,5HH\E Uk|/OeP^t.Y54\J>|r UYAؾdB km<'Ak;1%nKN+l/kzstBXᄻ2Hd=/*4/=P5Qn>3P;)fYI $l5_+Ҩu;oJ,HU͗(-_!kePoI[  yvZl3dO-fQ*^E>)j(],ME@Am` *&nƷjxm<( _n6},|cɓS?lRR$_ xE;?`QVC*CYYQvmpg5(Q_ Pć%v5C銃R.R Dm.9)dݾIBJ k=4H7˜m1C5ObuTbcuC]b5w!|gYi߳NWJpz4; ·T?,˫ŵ+ɽIZn.]G[GY\L& NY-dnGx: bL(~/Y2 s/:;t ׳vGZ?9ψ"38pR4nS~Ja#\9xb,b7w*? D{KPk:SN/~\*M`m>|jY{(VPa2AU;AC)'RAx!M̋lS_s^םBň)\$FRjVyuV5/ooJ#hmI6Xf?MrI{ 1J nŔo.4+;Avd 4msyܻ nDsxȐ^~ib4˟xZ\^N^VWI 42p Yʆve\j 8sܩ;eqOd}fI2A sוLK2k* S!G56Q<V壊K`oCD04z,ͬ}vx>@T%XS|t{nT* =:O4a $x 9C%}0}?GxgĘ|~`lW"5Qwdkͤ]n9Ue[# ^wjh14)O^s|.BDfb$M"U: Iel$~̸\go*uu5ܳ>!bqKVry{->ڪ*MAyʘ|*]Mf{^qӟF"fiҡEX,CAT~6g?G!|R>Ve?W]KWt,fd@ 7DbxɳڞiyÌ\}YCKI3mZGEo Dw8JfFkeK!0?a^xT"?QQbDhk賗'pH!L-w :R>s%>~,NïX;^I5+\%R=uLr1HoqhOiovlW Y%'CMR6_n fᵧk' 88ҩ=Hk߈dLȑUBEB4"jQql\?;7zu2 |ά@}HrpxDV_T*m1Lsbz¡8%&CbWY{#%0ޝ'l'f=b+`Ik^,Dq'%4S7/xOwj'쪚K]Q/ҐHQOJ2PVBg>?Zw)CT뀗uO^c< k6vp%t*?2JBŌkO&6Yq˰pl%K\~mfaF'Mxt>̫\M a__^d7 Tѵߜ/[K&R24(Fȱ VIز+,Q,Qj2⫈N5L?p>g݉ 'ƭ,PEK5)!26h9u@Ө/N)X / Ii(`a4Fn IUÃUۖN~Gp m 'kp\k%O;4_= _oFyfo8²(r}fiy}B%z*Qܴ$bFopSB$k a[+cc7)M OU¶teUTs+}@lݫi}Ko%ߌ?u0Eˎ"w:2M^|KtъOJ낦8?[N]ڐJ!0x?Y?z -.ViUEɾ0*0>8]EŻG)s;Ic $ 3R L|RoxY<>-,M]F4^jhd~ ^)’@aba2R"Wj֡ q}qvZ%ST5N[ c@Oކ0 ?/;v\+k Ƨնn5ڰ eyp@)glu SX :ޖsgqa]Ҿ - a<i T~%N\܏ܭRʪʊGprG.ן'HOl=!x{WP`>Qm-FcsS)eQ?G\JI":2+lb<E&ΐ੫a6l# endstream endobj 193 0 obj << /Type /FontDescriptor /FontName /WYWESY+CMMI6 /Flags 4 /FontBBox [11 -250 1241 750] /Ascent 694 /CapHeight 683 /Descent -194 /ItalicAngle -14 /StemV 85 /XHeight 431 /CharSet (/C/D/I/K/N/R/S/T/a/alpha/beta/comma/d/delta/e/i/j/k/l/n/o/period/r/s/t/u/w) /FontFile 192 0 R >> endobj 194 0 obj << /Length1 1132 /Length2 5706 /Length3 0 /Length 6420 /Filter /FlateDecode >> stream xڭe\۷ǥ;%{. Ia bA$$PFZ{oyk~p8a($ZHTXTPב0KKA4Ln{1q$-').')A=]/'i@tB> C`r@!pu80ü`>0a"QQaN.H"_t(@o|`^Q_2H8D Pj0YN @jmC.pu@!ܽ0O@D6}7߻:ht!Q av/M?  8B^0ÿ`suC#S/=C m@bߌi`D1?+@BQ.H'@LR xzB@Tb@(t0?`a$ 0 QDnUJ Qe$C2 @7"& a.["0o, $ #"P\C^.p vqSoL( (F1Cb>&3ڨ?$bQ[I$!1I/! @Zޞ0$ f|a0?hr r}*,DC9sNiP{t}WyϞߛX))]]*(u_88J3R 4%{kB ݴ+"G<_d[v-;q0ӎW.*q;l|G[$qJMA^& 6:x*DM[P_N2v~t!͑M,{J:sdz&mЁ! I=җITb9usdٟR==2q]:2|a7h|(ՠ/UyG)(ogXuK2F/oP/(gMZ-(_䔪k|KZ&78 UV)Y z׺1dP1Yl;].ަHKz -#r~V|#3X@pBPpX*G 3/I]iձ:,ont|K`x/tm{YhJ]MT3/KZ첣j q۷ުn4mj)5 Ry4y N6&wӛ-Ѹԧv?lx מcDU *hp" 2 Φ!4"ˠ6VCZ롣nSnɒ`So}`ҡ2,}g9Zڅ}զYLq2/x2T&7l6l;IQ)I}ݜ#@#%]J6cUQ6x-՚7D.JƨS~ܝӈ A)*xiN ~m)qY$Ӗq<ô9YH_vcW[qb%ɋy_g%)"8֔-Bđ{}KZРjI"ꭉYj"XLN4Tr{VUz޶|~.A68}a!X1u^ /~D+_ݖ&\p$?hv4iJb_|w‰[%%MUk3fY7SDDw/(Ϧ"G9F TrLgˠ]yh-Y %9HU;ǶbbD~72b wlszA[]}1w7ӽJJ,nxՖ|_vݚCM- W'D9ZҞ?y}H2 /۱47/3hks_(IK{Dx'P1pr XN9LBp"lWQتIhExGv~2;߆lnb`]ԮMb<:_FCc8SnEO?HK%_LP^[_`"Ҧ52%>=R4>>=ԃw礪-NxEކۙ}foWKרPL7 Wވ%\BhM0/7gn,8Oݱi +s^\Lְ}p_LSꂫtsL"Y!=ذv"uzn#Q-l;ۂSv0wZJD9ypS K/=F"JvZ"J4MhKzaX$ٮ|Fl|]J"sMd-wTm8+Ŕ\3<hIJkM7+?Y<vzBXfBp)j1(ЗmX{`zhi1l?_"a@K_ ;a!8 2?|?qC/gPoRTLSfꂷȥ@)c$,0 5>umk>V;!Nͦm¯Xq7:/%,EGϖĘ$lQw ͆%Iڜ|}c'|IDr}4Q4U7**>ڟ"sR7@-TL~fm;1)ˆ2n%_`3,ڮzzfM=+{RՏىh';@*7&]7T۬!v.;7g6VJC ~yX:kͻg.y.&|ejR8ȚӑUp͌'05I6tS U)Հ4ۇphş7,T5x<\YfУfL!ZL"4+z c JX qL#snP97JTƾDVh;ְ^Q7k<]4]"gOx5]17DBϾ=yhigHmԉD_(È RJcHow]R0j), -6 eĹ6fOћ "ب[U3t(K~jKQ\=[T|_R1. T>KgР>]Akc$HY7$%B~ˑn;zs|RuKkۢ;C4΂^[ѭaxTA48YDD> *uؔF;#}X7!i &;umOqB⮽^KW1ո(,%Qv)f E#34Ɲ-%<܇d>b 'Δjo'_r'9_>jJnB_~e+GqcZ\;-*nww(YG'[r 1goZBB[fAge:h;yh8qj|IRc`QL5<>`JWwAwC7x!P44so9ˢy¿A -RDzS:(˽)+<&ca U&? дVpS X(<%|c}SwZZzPib(A;iQȐQ%3'Y(AGUi=HXcu^ZI؞,t-C"V"Q]LXhuãnΔ?>ck9X1LX@nk͹pe(OshO +] [Of(P;mOݭrTZ kQe cwH4u{2<~h˳Fo؁+QrQ7OFhvKH"n0"C}Tpr+JJ6:yg44~W^"ы,O>)\9 ˙y-Ox{$qc% )8v/bP4 yx.-jH}7NF,kyՎ~gn20ˏ |xJbΑ?>l!YD(`57Щbb5EBaQmīA{p:nf611.Z zV6 ,,}<6U BMy#-խ4 ߝ%A7FKa0ȇ;g9W\ L1qsSƷ?`lrz1?ΐ_*%h*NlݬD1qôf托D% 䫯JWM -Kٶ̡ʼnasωҋ| 9EQ&]AѐSş9%=s"?0[>0d~S糑ɴډ |M3ZzFQ˴rmR -he6_>V@!Վ5<}bf)7\{G\3p wc%1mJ&D>5xk˹Quβy!5;{€ 0[f!.7bpB{0{ڀ"d@qL9d3X "2*cInZJfPox䃠&g!ǦrJQ=ͼ) +T-įoh肫vxjT-s~(vZj(vsy^RQ.+qBrNBbIVu.jM5 .'we4Z J;C챕_5L@䩛SYnddUpNf J^ $u=0v[f䋌ДHT)d3_SO] ƨk`J~$G(H{uKTp'att%'/O/8_h׍y8֏ D{i= VDn57HO<A[=RVMW޼g[P~D8xxHJtSwQ9׾~-_jPkaw*3k+@B"_(LqIBI$n# O(}aI$V)Vvqkarfu;C=ְ^QD*~/|ElUiΔҙ]@??}{~< zsE%;w7т{̰g$)So:۴p+gjk Ma!"ACg!;fW \3vL|DRqG R#3#Z|8LOسqҸ}l0Lԗ%l̷~Ia5Dy.832E>3΃_jIT7ܭK> endobj 196 0 obj << /Length1 1512 /Length2 11275 /Length3 0 /Length 12149 /Filter /FlateDecode >> stream xڭc|ƶWl۶Ɋmm4i؍۶ƶOϻ۳߯緾9Ƽ5Ǽ9*1P΅ *// xdb%'uXۉyW + jdin' l t41Xm?4Ll&@O @3 h 04q-`$mgf܀NTI 0ijog 02*T~xa%\mllQ+ldkim\]Ny{SjMhjjQi#Ka;s @S%K 3_@;vѾ`UVR+ddi0I39Yzt??~_LM-,#''#OX)vv73z|fdwh/ ]`0 3o0!N08Y (>4eЇPQCFQ1 Q}TWCG裞X08Xk'WüK飚pi q;$?tp8]Ia_>0OAOʇ_'VBm|ض:;X_H? ?;iˇt7/N |x8G~}\wc] û_//'XDÛ@q>^kNv&' hK6:@ R?©2Hjg_:B2x7xQ眚&ՀW(!(Vȩf[8>ު!K(_3UMuzls"hWHo7: 9 pN#!J^ǷMIKlƏ>H/ afޢ-X!dpGɃg0Q{m2gY-kr˨@s,܎*fWBNj8xLI*E> "3%ma@fu'{Xtd ZZ|nk7Cɗ4~>$&=x E1Td<òu ӛ˰ :/~ϸOQ{Z.sOuȉ$X?o'R$QDRuIPS,-Y=;}i^%ɏ(>ӻS2u Z<~(a2UXV:RC:FKEl:Ӿ]_@dgUZt%O͠'vY?R-sK#H\Ah]eD[3]wv<{+JqT`]y>47-c%n Hq@JFI͘Ð+-0{/g/HwZ J^{loc;`Ơ2Rn>ā, 4=G.~}y; 3'ӚS$x~{z~#+PMg=%́xNX^l+EOZ5:a@P*CXDH-8̪thdnjI7uuhR4BA "g(e8pZfuƵK4NW="-t] o_9w,L@}(ګ3T]FpN>N]Ȋ,Qr%”Ů]csnvʍsκ5+A3FLR/xxPTz$-5$}3jr.עLi̔ 'f)*h8Dc2g&e`Vi$d,C;юz]}ݧQ waoC!TO*|՟Tun4r/بmԬL1&f"Z dr$E.0%GIt8bu`5ci4)}Uuy}\6ח[ ,B=96\=A]8o(&c}>WCXHeG*Y, uTIrm8hu3z8I䀻ʚ Ի̥X4{U瞷Bn>jF|Hɹ^/|.aXFcS7#X%48Ǚ 9FjYOs\ Ujrk>?+l$(~KaVms1PF>d Ӫgz jN0[n|$7FoRJ69 Gȉ!Ӯ_9)cD(z\exgF6'$M95 R{bۿHd\^  }@CNp]A׎,H+듈 ȷ Y;)!o MurQ]Z"Y4۱?%jH j `ar`st FF1 Մ~ņ2bn}  ϛ'1CP_#o%ќ%14],g<|5m[Ko4OGG]C>ooͭku^_}f"X9j۰גP(:852"RLƊ['ǑXTtDYۈD}qÊDlm ޑ;GG#*zgfQ,Kxn\ףB\6lxr]v)8U=ž~Zv`mXS2;(b^? ?D:B_|X d䇄d@:aId}m'ld)c>;ߓ%0ϊA7{߂5^ ĩqS:}+~~VCUc #kn}|#np2W9 Zn[>Eu\A5Hje_P<|87{F5fH:up}ku֝]HN^%;Y[<](y 9ņMS[8!Rb웡ߥQշS>UqMr>m\a4CZ7E U^n3 .rUL\hѹ|.!$Zjx%  쯒3cdMRzlZ$"lLչdxV3==عj+KU⋥rELL.ib1)E_T# o8_~:(Gw"KH3s0 =I;:C-t:[41>֎RVHX $Ŷ} )+5zgMmm¯E\6 WC2Kda]/k b wIDAfſ=@HxIY0>.5[4dNn4gW4ѾYqRDr9P17#dM_p6& \ CN16hϯ`%)0dSBA$A}Kcӎxyr_L^2_*Ί )mXziiW;S2WOk D9.{8-S! T]y+<`ahw*LwX\sQ* 8sy@ƚB H6sVGмDz7>Ghpص˓ao̎lƢLND~3[s B-U4n%I`Jl3\w:,oT{z "1N1ŨO>i] !#)*B3xs%S{u`jݯNZ15;C 0zMS>q./^Giߨ)C8M^$%wpjލ ]K)iKEX.[*^yy#eG&j͙,!B7εrr8N*2(q)R= _4Mu捗eU<{T4T@]T`x4wJ7]]S*Bܬ+>ʹ_PoH+x.73QW0&,ώѦnp|3%kk(nCwBKzF+mRpp~̿)1gE,K\_'qR׶V]fI:7[:wL$&r記MO2<]h 4Yڜt̋v;+ċ%*mϢ!|tݐrCqטx - X*xߵpWCb cr߯n }#kc"; ڍN|SDua GU}(KAn7us=,F8[.wgj?IW@E5Kn_tY5Gº5W*iӜZRU5! $pt&/1B ޥݙT/|`Bw^0o]tΧ xpٶ'̖;zV ?Mk7\.{@)㋓>XY!sKvX).L6s=L\O"Ąd9(FcPL7(0${p), tLN`x8swX U$?/hrh :b> `kcUZ7C ıY-MP;Rv=`%ݓ~8mxJR>ϘǪbusG"O揿hHm}ޏQӵUyĢAQw93`pL[Cw3("0a* qd{,!$#8gP|)`@X{[2g@dڵA+ =${I%mcN⢍8 xn!Y _qz- 7L.\W#ִp8?=rle߿?X'&MmM5 5,}> $;ɠ\[1Ȓٍo\eUD&yÜ_<~#8"LD`C~H)92zS^AM vcwK5_'jf#P&:Di/VjwkP SNd\֙M|d)\k5|![y*NFgǂcds<$Ƈ젼@H raLūHx p.:9Mbݸp sFKʈ Ve 9.>y6lS!n+ߢVA 6O-Zsψpjf$r)#D FP0-&,PK{mͩ^s?*Ha6p5Ꞝyjwhޝ^/}*-$|ʢ¯]r#@3f5m I83I&x_ LNoylkC:NYUՖS:#(Q,]& ĸcv&޹/ '(G@a&ڜ7 hZ|kSū6$'{%7:,X9J2)COY_Q 0cnMN:诱5T@~#|/-kyI 0+DGIT\PE&F)Jig$q_I%%B*VB!x ޼P C?=y5pPS˓:5 yH%U .A$[IBbZ0Sg߈;Fz"?σXCF~O edq!:尡_K~uJ7Vb.`cP,N3{e5i~.x] \aQC:EZj+y#$Ďbm7;%40piV3a, ,{F^\Y%eo7_.p!0[葹y'nf-d0cz{W ?`aY?8&BV y\mE{y$[7LND:zsDv _Q{|t*ZhŠ(FF/{;mQRךbK4G1:<wҰ6}Qp'kK(p iБ嘲$6\M'i)2E\4 4LM90[~]:1V`ugJ:yNMAO+vW&GeeZI/p%i~2*-4>r ԔʁA^4Ԃ͐ifB Y˳ ͷI`=֓nT XBm5\Lmܻ"w3mntZи0JgT) gY]É[5M#Dj1TR_)Œ0fA5oV HC2+"RHօYD,-N1q0䵲~2Zɵ09ӓKpta_8 XG$67t$o*81IlJ$pA ˚8k j*žz"yH_]۵˲ɢlhAnFۍeJ%!a =kyLiyۍ0C DEyPD7RּڍjYk([qdoNEd]v]#UЏv>_fN8!%"D=@j, Lu# >KǏe ѼO@zusVᣣ&ۥ$oPׁO =$SM%g S7kCin 'gX]\kd۟:)cMp.j^IH`՟$"H `WO$?9yM8lёy0y&w@k;G6asX%aT&x Yb.V̈́nb0_jjIx8o.o# Qyu)Uǎ6b=iہ}yܶW3R\:c,1+b>A4c (?mCf!Q^>jP+RnqY} !NX0r. fS^0M[JM=@u8xMQr 0c S `[X(T9J*[#܍ds%zdn`2'n}g,>3|5ܰ.r΋) !svГ WЗa8EYcLkXY*ՁFT'^$/Dj 9!2~R>x\[kȪuۮxֱ{߆O ~nA">B%X1q*KT&\B-^Ij4ȪQ7;^m1 = ` ?nYU%d1BIt\5@N4_1*:R:DؙhEb˸kʗQVe<&,k1Zk+LF1;MFӄ>?grpЬj>i"ۆ9ޖl0n9"G\ɂf;rG S3D+o=}dHg\6KdQgz0+x3Ao&e@Q UkD(l3S;;SY^;G&-wy_ox'RՏ b¤@p16672zu%A>}`d 7+U;ϗ/M=y"|f+:prOLj!{m!ׇn Ѕ7Sۥ´f\K-EzSZŋ39#84斻M$!\69gxYM.UO6| 07_471b6NA!SN0h~X(ݾDvL\4J}GnXowɺq}z%x|<Ǥ4e67Ə%`Ef 6!dZ3 ԢwK{d,Kw8:^JBoJI9\j`+tS7 L(NմLV0% "äg} \մ˸6rgĽB,?R.r0oܣt7I n$TEZ/6c'SIi@cUrY1HcnVq<4|r'>\S}]千9)3͌j> 3y\X.@T'zH4"37P-~OJ)('|'$֍=l~8} u&0aᴆ7raJYylO5ނws[GsQJHqSR0"XHVhz@yA^77^ f' #x}y'ֻ ]%9ĕ-7?ks3Éo r>&ⲭpBu*2AlZcdU]# ܃f@6W+\Xob!4s5)᧘MYa nHYg"ƣl/ZY/Z-Gl"Q*xhW4tf%$ ~ؐU_$ʥu12\ǚ-*AN7/"zyѢI=f}rP=GV5oWꢭZ˄Odb^ɘRd):t.e`aJETz {PMK^C]x]t/4>И__HPfȜ@&*On4[)(jm&:?.t)5TrinW;JGǢA# dm|6]R ޫ6AMRܙޚMjyDZo+^ȍ,"3fզLѪΐX2l^ 6\bkK./`ҝ5qZU\}Te$ܽvɕ0n(w^]#:_ ywMY˨Kldzgxn*4ۯ endstream endobj 197 0 obj << /Type /FontDescriptor /FontName /KRIPTG+CMMI9 /Flags 4 /FontBBox [-29 -250 1075 750] /Ascent 694 /CapHeight 683 /Descent -194 /ItalicAngle -14 /StemV 74 /XHeight 431 /CharSet (/A/B/C/D/I/J/K/L/N/O/P/Q/R/S/T/U/X/Z/a/alpha/b/beta/c/comma/d/delta/e/epsilon/epsilon1/f/g/greater/i/j/l/less/m/n/o/p/period/r/rho/s/t/theta/u/v/w/x/y) /FontFile 196 0 R >> endobj 198 0 obj << /Length1 818 /Length2 1564 /Length3 0 /Length 2122 /Filter /FlateDecode >> stream xڭR{󾴵}}=_m ]D :gxgڢ8 ˄!{ pƀ#\c[bQڀ&0!\@NoD I@"T S W`Y,4piF(1\ d0!fɑ3D ⃜plS@L`%h q@<˝$.%݇Cx\4}O~Ҙ\ I%B `@pGf$H`r! q}o nƇjey- z ¾.qk?5  apq{4&fáPXDpA0H:A-~&!HF,l,^7Ls#߉‘Q&1ę`M 3|0<wCZә@0uԭ~+O(qKK2*RjIԙ**hre^)R\=(=1kCq Y*U,7@m#xɝ{\h6CsH[C֏6;ތJ<|]Dp]t4'B!=mEO(f_l單Qv&_u'PMJm#-߿j 0vqA&gQbCУ[?TU{kkM.XԮtq?pY+eSƨ ͍{yٲ0n_{]raɥv7zT eCGԠ6Z#wI><,;Vn\!i$XĞX0'a^So;(ƾ{;s; erNg >Ac~d٭VAu?z {Tگ#~ց1'ʻooiVf?dci%G v 3GIѳ^lR'-aHyσkC7SoE_h ^y#L\IhmBQ.𝟚5Y>IkoH܀N<\3UO )]nKU7K|%r-jܪ2 rolIޭͼLh l&gȱ>/UE(/s']h ~sIL;ͽږu+dQ źҲ-ƻ;RlI=QGrPs^#!ZePf#wRCM-Mg'R9-uh>?һT )Xkis s>Oa\m3jIh?I(NPڪ:B6ڡc@JrW)}sy*%R^Gjkӆi]qIs Fe[[2ЯN_Vk%;d-݅MrnŜ{z[RZSf2XWE}uRh=}ӕrQA q\7rbʧGÊ rhS" lRS? ܱYCȵ G-.>z murq(?68]} PVb }+k, endstream endobj 199 0 obj << /Type /FontDescriptor /FontName /YQTKCJ+CMR5 /Flags 4 /FontBBox [-341 -250 1304 965] /Ascent 694 /CapHeight 680 /Descent -194 /ItalicAngle 0 /StemV 89 /XHeight 431 /CharSet (/one/parenleft/parenright/plus/two) /FontFile 198 0 R >> endobj 200 0 obj << /Length1 848 /Length2 1798 /Length3 0 /Length 2377 /Filter /FlateDecode >> stream xڭR{8T{\鸔sՖq*f\سgl GB*[$T"E"r)KGpRJҷ|o]kϻ:Mג> ٲTkFGijZs!2d#(d `OLԌ X9|.@-k$cq28QzP0Ʀ0!X0s nDÁ @eRP0Dg"8g= DZHmHe#0B4fA0_Y2 γYl*EHsLY 3)ɳeAT0AK8Pٶ$ArYRDf";OܥcpAbD}y}7L;C#8.8L PQ, hl.2@c+%[L2B`~C/`؟`Uo q6ʊtDlmX%Ɔ!R\t14&( (>6OJʼn0"-bVDⵆ:ȇIbpG-W_q\r|}*v[1C*} c s5=/ \mN5M\iǍ _nW߭Wc=p0h:gصJ92Yɋs'aǂ专:OJ^,ԯؔl&lnh3&<=L/IOT[vOZm1Y_r;dC)~w,4WHm54 kZ90`0*1wk@Z-ϴZ1;E[OOo 6r$[Vvn(f“… iøaO /]B5VN)8IjxiH_/ }~:Hmx2Nٰs޲p{oPIq@[׷w*)Vz@*c!ڧ=6]ػ1ҙ6BjTto2tqol' K{G{@IR-aB! )=*rX\.IUXQ5oȋ`f:]^/{]gBG31gwytڐ-_ \bak'&;6қI#՚gŦɝq0O)}Ѽ|A%n+L;.d(v9´n o.G@"Tij0:!/L\{Cz7wvfÖQN= ~ y>: 4m484\fyx3uSGC{V|w#V(NG,bKn#=r1zNGFo􎦸C9UVIov.:"jU/IF$}1.(,il_O;Z3T?z+i}jn:qX)M2#ר?9Gx^Q:$XCݡiWq?K4x_lH[ 8wM$`\o0 )ś=+ioql\hd2ӼҶOS7mnzq[4CAA)1|&#oVXE~pW/$M%ruDubBQUUӟ5͗~/H$N|yQtDij|rgF092[.z\p4>(ǝusȺbg%ΔZ:SC+&}b7*Eܾ:ͼOKxb.faFuׯlf`>B1#$Юߜ^u"^=)蚒hNNuOP |Hxl?ޟva01ŞJWj̦9qAZӭAѵY3Ia\C~JJsvxyTy7kmV=_NS픃;^?(~`h> endobj 202 0 obj << /Length1 1041 /Length2 3319 /Length3 0 /Length 3998 /Filter /FlateDecode >> stream xڭy8X2ز}{ %}0fŞ,ɚlٲ$ %["$$K %{dM9}uߟ}\#"hf)u/b1,L5P`] =T`g' TϪ+]_0Eu%~: D`c %k hD`Y@,~  pG! @~1x`?;TÓMd٢;A |Hvah {J=J.}y_}\V|BKk)٣G  !<v0=iZV0~WaGL\3v;UTm/梯Ԉ* Z@biTӃޱ'&ױ-Dwӏ;Uq E{!.I) $'i~|_'= KG\h:6#wX]~lHL_Q>\txl~2_@ %iԦ o2^?4uYY80~6&[̐ L.a.Ry< =^h:l9x;PˡZ;.ۿvͤg7Hp^bVdZdn \Tq/A />,vI&x{m-! 7hڮi ] gW[gWQ-CjV{&oZKKԦ!#K`VڡvU%-%j裂 ԽS/JŇn"Mtnך]Sp<`%-Q oͦW +mIFL9cv0ΏxkA|*T޶rB?5]k]37nޟy׮6Os^k5-ZP.޿n,*֝K:6^XfdY{<ڛgKGD*=:r(dOX7qaӲS \h9$%׈tjg ௔`*gDk; xKR7W.f{q*Lp|͠.˔S 4/}4fO{ďMݝ'9[{QD>'V7܍FR}^3{MWM:4k+SJ!}.L\Stkc#U=cq\!c vX7BK'5\}9Cb;wo{I̛J]%Ga3,)"Gbԅ ތviG'6…5+%>S6/Ӣ Qtޱ윍&wS "̀Gbvn֦|t?0)?<;Xi_e^[6Sz:?%d@6 'qs1HR2FnJbSNcT''19!xngo!j{W5ڵ2wޏ<(!x= ;~wA3gHnr'CŢ3kjcMi;7RATsɜ~2ūGMÇc(/f9լEj]yG6^w| G}d^)$O+ H9>"f#EEm/ L &aGgv؉Y$:ўdUPx*;sӻlPe,a{؟D:Mi@l%M&eTs qlDžs=5xf3HL+m~Sz19_|FuP6#V\NH/|q>i)wt#Vt1IGgӡUqI;(sWGbNwnX *2@%.T/ Ά .\6*z䊤 aYv٣륁YWg3 ɑP=cdQ"DG\eeK(,2ڱ+)-ޅ^C?{:MLYx %큮[o GzK^{I@i3`< F1kEKzћ#Q]v'9=ϗ~@nofٔ^"n6N/;NbzF GB }lȱY{([~u ls-۴%O-zwE`QrZmܫj }ܣ1 endstream endobj 203 0 obj << /Type /FontDescriptor /FontName /XUFFBP+CMR8 /Flags 4 /FontBBox [-36 -250 1070 750] /Ascent 694 /CapHeight 683 /Descent -194 /ItalicAngle 0 /StemV 76 /XHeight 431 /CharSet (/Delta/bracketleft/bracketright/eight/equal/five/four/nine/one/parenleft/parenright/plus/semicolon/seven/six/three/zero) /FontFile 202 0 R >> endobj 204 0 obj << /Length1 1128 /Length2 4226 /Length3 0 /Length 4962 /Filter /FlateDecode >> stream xڭVy<{F 0fkf,פ #3{%Dv![,l)d߉HD5ey=yy뾿}}z>GDLR㈒`)0 24`)i- IqH" P0H`y 2Zxŕ\Uh`Q"(, 0(:P 8c#cǡŸ_), H)%:q3 2“{J?D\EOdXx7E (ߥV?1gD;I0^?1 ^?p"cCamctm2FbpDsI0~4\H~zW+#AN@H/ȑ08g#ID< '0Z&i܉_2 3 wX[ r$ n(47w!ed;MȄh7 Cބ߀ap+d߱4@P(N|Y'J<ܽ~$ Fw"/Nt%K7Y<Oͤ @II4DPG7wJ_1C60 rb;)E<~J#N<؋SaUK2ؘi|o nx&/\_h0_:zپٛ_/j/ѽhi WpSu"hʜY%9˜D=3I_iz }nxfGqv%բǑg*.W\";z^xX[Dyv&נNφDC ID~䒃cͤGguC֍1oց"4$#z9ly;W'cB8$EL]N Ύ˜ƗV&$q>uu~A .fHf8)e{V)9v~zaB@*-Z4g2-E3N,Zd$V2 9 _Vg%c6KHMj^3 jp 3xC{BR}īfYg,?׷tHV߲\  hr2onk"͜u=} 2=//{p "PzŒMNʭΝ *Ö2DV{`ja3QspFpV=ZjT2nmʧ,&-(z<ҘnM|de=dRhv>UߩZ^e,tYz8Ӎ3WHOJx,}ta-)뢒HںT}mWl/tSEG w(4h1a~UUl7d]0L.A{+Y|.g8ċ*UK|=0eDQbN}~Bxꝳ׀0HRoU t{՝;d!&,*Z`[ug ;%Xd!IP#y~ě1z RݩD8Z*%˩JTyƈ'Nk8]W{:t-E$xb_s-hEaސӉveZV#!4M 0IOwǏoD>o[~<٪3ظ͏m)cYnoB|Vm 4}UԂW׍h|vUb$^y6cɏ#1W-?#\+Ү|i}"}C_*W -@e- է' Z^*91F'2a>u fl9%;?7⻱ 74Il˰c(>о4^֩˛tt!#=Y 1_ WûP K~1-PgSRV&#lyPRi~}5z)† )<푗O\3t6AzL~RM#\IMhʥtAq̜=Vy&dWU$unONPtЏy:9#iZ8W wwjs7LVZ,i(nRxq C7Ǜ\.CgڹlrՠWIqp1 :TJh:('Yb"ͨnX-EZ>i}&m6q&*ˤY}xjb~2uoCjX,n84_o[Hǭk;T1k\G['qwMpR FꏲeI"brOp4)+y?cJh\ysW&]coeJ@T8%!nX.˶l/v.>ֵEtx~rQt.=r+HcmxHT;Ӆ>1N~hw35[}U~O]@⪲g2&Jo(!B SIz'Z1 5=(s?Ϋ8*ȲgBVl ۣle2B}n8u2 =[ʊt}?p^䗰IAlT7 %:&C4t(/dSC*ɶ޶ i ԋOͺT,X_$`ڞ'wk9]*_mj]n~Ej+M=p `&O>sf ]5*'-4tr5Frjw\jjZ"Pr^_˽كF'Qx9Eɢn\YAͻN6KPCi,!!f]7Ǯ(Y>[&jMܤ(|p]m&3AU8 e9OA7?]Ov.lnyl}{3va9'fNΖN ?f E,m+KR707^@EVoaЧ$LU8 .# n)ㄴWA ⵡ?Quɉ#)[ f_R'>D(L)\-gyuMMava1]"0Y 3V/t[J 63[%IRLo/#2{bs;=;!kEPUV0阠7avU De8W0v:A?B_t8(S˹W ^4_wvtG "H/[*|焀kssBi:> nfКf`8m79An01 n?++@?HryIC Dpn)j"0OyqNu^w Zyx$m J!m Ɩ?ٗKtug0p#SjUXOXQ^)H:lv+%|cM-WjcO@n\:ḭLa[qGQ *Wa6VhYbx= &+hYOMG(k-eDORԞ!o(聦Lhbuoֆw9g>Pb;mO~?^ A! ʃN;9#uyOQʢ_trU{<mj I'`ecԖh:[W9#5[,QXx~Ș T}r+Za* ^`Y>4Q︑p6՛" 61zi-iziY_Qϗ]8mMݮoӷcYyf`q8z㪝XcV=rȈNqe\0qgR:/\%53WC"o ~ce2k.ZfYQ}y:YRSyrO&h~L֡d endstream endobj 205 0 obj << /Type /FontDescriptor /FontName /JREDYN+CMR9 /Flags 4 /FontBBox [-39 -250 1036 750] /Ascent 694 /CapHeight 683 /Descent -194 /ItalicAngle 0 /StemV 74 /XHeight 431 /CharSet (/Delta/Pi/Sigma/ampersand/bracketleft/bracketright/eight/emdash/equal/five/four/nine/one/parenleft/parenright/percent/plus/seven/six/three/two/zero) /FontFile 204 0 R >> endobj 206 0 obj << /Length1 779 /Length2 744 /Length3 0 /Length 1283 /Filter /FlateDecode >> stream xڭkPWC*T%pS0dCB %{,I,5VEeTV)FQcV5(7:EZ~s޳q`F(d"bUK4D"#QD.G¤dab$ `q (( bQF 5J!cA#HFHgALEjC-NrhRCو [Y6P ,"F`P.س K@e"E1[mT `b b) h8 1ܤݍfPW+H-A0"B# gC,g:A #!Fa&+"G^u$h6@ zc75ge"HF{Z>pR P4jQb '1 `6 ,nl2@C\ǣ"P LGi:,P&㿂dhCyJ%#F@\"H|jMCش^MlvQ5[V/?W1Nc|crm8{k=w:ߏQx5S/:;ۣey%9߲yKѧ2n/5=,]aŵ Uxr}vBlimNS<Ͷ/{;-K~?Ձ)=~>毗DE}^hOҤ5M2 ]=+Q74pfX3花!ߝ2/靇R:3rgV$|c)y9דG>)L/t>5?.O|bS߷{绕v;f7 뿚9aғɡj8+Eʅ-FYƻ|dSYQ_r,y4N.Tpzc/Dn}0fLJusxi_^f/3)U۞zD}e(==Rsw8Ч/M;eMKm3]1[^{gjWO/)ꕥהwȖ[ g+fމkiCC޹w|iOR#5Wm ' l3*}cJ<5ļn?s*-m/i:ȷ`YW3܏U@7Xԍm7%8rg ŋ].HQ}p~Prwk gzL^/_N:yWIZ!գ­i;6nUuM 䏵Y9umc > endobj 208 0 obj << /Length1 828 /Length2 1119 /Length3 0 /Length 1702 /Filter /FlateDecode >> stream xڭRkTSWŲ"bH)y*q+# ByKr&LH QR ,(`KyQع`mW߮|{}wlG0xHĄ<?$=714>$c[`TRݓyr]i+4*M&3ݼdDN2P0LO(A8DTD̤A"$!R 0 _b5JpLE14@HhP 7ߪBa|DrTU*!@.Fl4 y-*bV@2TIe`@L6@[Q5"ގd eJdG0b+Tz FX1B˫.pa#wh`.^k*#UX6͆(!^p1I`546Պ-PL NRGL:m~\TRr75yrn!5(Rn,RϟG?2\ÃRB\pHEF.|=*׵F jDD빏6e*~2#|ǥ}]OTӅJ jom*^M\<z8a՗kΖG520d啬x4.ĩ!+FbA =v:1֯]sѨ \?vy.6|61^[uw_03Xe1uawpСƌܟ_d Yx4=m6 a_#7x>VE{; бUNU=ϻЙ5ImUnӄ\쾺:gE*L4?59};#qx^2l%z?y#qᲇ['&f\En^=[{ʋo#L3׬h CYoo$zÊ:?Vtҏ &8窻 xyڙ_fZum=Yؙx^*^v7!/0ܝSِ]vpΪwʱ R[V1M:A߬2uW'ޅGOT31Wg悔)wz^&e=~"`XYHM K+zl7ݧXțXP4-$txя63 |V7};K vĕI͇U_?:IKƚKs?8/:[)0Ҧ/nu SIgf-nD k32oaݴ) i)[T_qvg˻VU;JV{;M8c}ɇEw%>]a%OTk5{XZӑ=UiXWgç50cņN905Fu}EI ozF񻃾K ɶLw,nE^XAHbh$v7cB熌s>1Wo˺O mwL,S[z]YEب-kCkf\w8S8fp^y\3'{Φ5a endstream endobj 209 0 obj << /Type /FontDescriptor /FontName /NUBZLI+CMSY6 /Flags 4 /FontBBox [-4 -948 1329 786] /Ascent 750 /CapHeight 683 /Descent -194 /ItalicAngle -14 /StemV 93 /XHeight 431 /CharSet (/asteriskmath/bar/greaterequal/minus/prime) /FontFile 208 0 R >> endobj 210 0 obj << /Length1 855 /Length2 1261 /Length3 0 /Length 1840 /Filter /FlateDecode >> stream xڭR{8i!#}Ia>吙y1'rیwLZ^C6Z尨h MPH:ߋ>w=<ߣeh#LdQ `u@IGG"TٳE ؊CD43 ## ;AGCBE@NoIdlpeB0b/"" sC<!A8 @0b$!g+f+0G:B%L"G%pIT7B8Z=A绱Ö/7%pjլGa[,CȄB3D8\6_,YmHog`e˜Dޒp>ksMdF BHOUo`Bq-!шQFt:qHDL "ZL4 pR!)%#`D8FW_Gxep: P e}( ̀N 80!Cp={Q4` C91Gq+?\D"0K[;t20f_n{,UW=1QN="8vEEojL2CɃS?\HMߤt{J&`o:B&>xyOٜѽ~7f7{kkImUr`s[Q⬩\uig/7JNCX^Ll{SyWuk;eϽGo 7jQN eeP.Xj9YY4;90x NuޗXWemb 5V 㴺:m-gtIEff~>tc,B%8UXx6w\*قU<ۿSU LwsAw'n(n]Y?^osVnve[B5JFŜbzny SZ%Q.XMi~N%L4|rGO=#+6zW7=OO+P㽾庫ü{qWǟre1&8NX6_rqLJZG.'?,vȭA4/~Ur}OUsϚ}Q:#/ݹ&WFBCǬhPvBj_Z9n ʧ0,zdFeJpjBIh{mA#,KNۘx&c]1^eďiazJW\40Dm"ilҨƺbaQFg"l.4|}†q_GdFG3ÇOKOiNϫk~Ӽ5W{!kV_+-INxmSWsn ɒ\%:mӃ!B49n./=dv\B{-2]55ibNgՌ+Ӊ#~8{~rMf]B D~MSñ'{u_e'j47ObZZEg񮋞S;50Ȳ>C>trYg3W%S#G66-Seu$(?s[dv#J'|]@޵Ew_F*Oy8mC%?ʾʚ 1 4:7w~/8h+prKm:[^mehve^1섕'7k'[8)&ENBʳcWa/ I [UP7,o_kwSF9|m endstream endobj 211 0 obj << /Type /FontDescriptor /FontName /PRWEFQ+CMSY8 /Flags 4 /FontBBox [-30 -955 1185 779] /Ascent 750 /CapHeight 683 /Descent -194 /ItalicAngle -14 /StemV 89 /XHeight 431 /CharSet (/bar/braceleft/braceright/element/minus/periodcentered) /FontFile 210 0 R >> endobj 212 0 obj << /Length1 1132 /Length2 3047 /Length3 0 /Length 3785 /Filter /FlateDecode >> stream xڭVy0ڻ蘙֨mgFk$Nqяi-U;)YQ(npk@vܒаɼd|scO<FCD?g![9U#S}u9̓ 1>_o_ }oӝv=z:F.{B<^F}<˽TZ qvT1XDᙆ-q{ JQBalyZ6q3h=J1I;L>z❱2=}DKpvizG[ZNȥ~HvԕIƲWƹwE f|Kf;˄gY aa :@ q=CwrÖ1mz9wFus07X'%'W1yb}7 ~ȼ :Gk~WoxVewe{[9#^zmӲriX򀜽PjH@&y?ꐗ$>zhWaeԨ+JVEQ[?]Z"cy^ @ T$k˞hUq]3-_a-d_x+binpມ:brʉ/<,_QT CpU]X%W+3=-}ki`캶ٚwf,Ή_Vpq6FLh%O䚛|9͵1F"q ro$FѤovgKWE6KGAӂm9-gKg\@٦>='"3C2G &'[(&˪ĵvb\1T;EuN9 HlNg)2gΏ[LFȆtVl_Ն_Ê"VKbmEmvxv|Ց~$6J/[/oeQ~)n{5/ t. K0Νv`8jZ> 7Y>}9TBuMhT%ngjQP{9'X~Cw঎b:_4T5e)'QreO'c0{ߩt¦fɱʛ.`$gc ҩW:hrhԻxS9zF>M<*mWL {%Yɸ^fQ9waRPg|$(lswr?9𸴻_߾;o%{y囁Z? fU'frQOjYolR&vеd%.O&VcQB ._Uz9܏U0lMXY>ʒ\{{v{1|vM DI}rO d`Oy)wֺ;P;NܔA`!t\x| ܌[V}-EV/% k*xt bVO{5Q߷OB5 E6 tĮ;$UjGFSk]S/ i2Bm:=^zO:Sc߼ zoҋ&:;*WnAm3ʦovWof5b>4!H}@VYdSg/|n49?Xǘa++!p5X᪢bSFAe)u%mGnxhpV)u3\zi4G?zCPww$Qeϓmbg␥x!k3H ڍw>ko֦ل>Ag"/,u1rk@֭\]|aYX#aULg4'b4>:|=0_a wQO=yOm?nrގocq4W|ֱ>4{?(s)l¢bms%_̸^5g [@6(<(HH9Vݮ9IڥRV. \u*N$Du5ɧ"tt:9[)Svi燏͟SJww Y̮紑G"Tky,m=Tw2<D78fc$k\rgH|IM _S2i"JFW}#c+lFB]C(g[!4ZχCvf߭`mޟM6X4Ν~Isd:5Mzv栂AGaEG֘iDݫz ^K-6Z?]>*VK͗T]<~ _ endstream endobj 213 0 obj << /Type /FontDescriptor /FontName /TVTRRF+CMSY9 /Flags 4 /FontBBox [-30 -958 1146 777] /Ascent 750 /CapHeight 683 /Descent -194 /ItalicAngle -14 /StemV 87 /XHeight 431 /CharSet (/S/angbracketleft/angbracketright/arrowright/asteriskmath/bar/braceleft/braceright/element/greaterequal/lessequal/logicaland/minus/multiply/negationslash/periodcentered/reflexsubset/union) /FontFile 212 0 R >> endobj 214 0 obj << /Length1 741 /Length2 1162 /Length3 0 /Length 1692 /Filter /FlateDecode >> stream xڭyXSWGqbT/ 6HrCbX ,@(4$'M.&7n aFlB!,.F FZq d4<}{96lg&[11 `wȇ$ G8}8p`77bʄ Qaw;A|aFĀ" Ax\1q@dqQ+HER( H$Ib3@b1>D  2 11@@ c5| E0T_&J@0>Jwl,Gd"› sB¼.uvEx"@ų5{mHȡ/)$ 6 WԜy !*}ĕH `Eӡ$B| L&1ܰ2`̝2`7"1y r 0b)GȓI$@ϾCkb9z0Gj|nMZ-%*MUԻ*G #JxjIsdԲ|+MV>2Cqt6j+ټXt:ڍkM.-Ӎ+wgI]!>(xlJҶyX6?Sۑ"6M #DO_$M/pf_0$;6w ]*.^X>:ji: "k{M-seHΦNqkfK%^`5,E7\~7uʶeM}qP*6!̆>]-59/JjqN )oO"&'^<]01{A_drpП:Ʊ{JC^GWd묋?9A%O?<~P)d?+u}M['^drkƱ'%P.ܼƦe%5nqƊ(:\&hќWQW3o4DdO7T6Dž}\ٷ^jFasQclvUea|b5:(ojMi/YrAd?ѥ&W虚,QxZUyWF?30sm#S:(=zK7ezD.z7[MR_'>:^_t=Iӷ6w.˙vMfƫERct`2ؚ>Ϫ4ݙV^d0uڶx|}+oHݺcuoj^py][t a&[s^]\m편@otwa5YYMAﲷp^Aі=_s#|4Jw̫rGO K9U[:-8ݯElyF rG^vjM_p tT4NE? 4pT~N ﶖnlM-ٝɦԕ'_ޜn&}qv;ٶCu[[5Ÿnlh7ՃBD endstream endobj 215 0 obj << /Type /FontDescriptor /FontName /ZORBSI+CMTI9 /Flags 4 /FontBBox [-35 -250 1148 750] /Ascent 694 /CapHeight 683 /Descent -194 /ItalicAngle -14 /StemV 70 /XHeight 431 /CharSet (/G) /FontFile 214 0 R >> endobj 216 0 obj << /Length1 786 /Length2 1066 /Length3 0 /Length 1602 /Filter /FlateDecode >> stream xڭR{8Y(iDIT(3fXŘ"EaoYC]\=OEWPZE'TڭPmwplǎ l0 !!{F@ ^!<[CCEGjN_Zs!w̶1=eEH|S}{ˡ<8se[Q[˄xT{ DmS~d?}y^fiok!'v@n+*k㯽f6/?’-7svP붦}ruJԒ 9nutQQ4kukt`oէJd=ob,eLVsz6?>Mu,5a:&uY9f2o{yU .` is[zLmX`F8q]jΎ7bOT{˕^{fy~JEHyAbz3߼Qħ=SZHZ{EGJF%"ay̼qkPxg N9pҗ1?iNw S"oqRf% h5o;]S.Z$k2nNʼnC֘VI 3n¸c Ǭh񣋿KިucMޙԻ)wyJ]3 2eWkLBOfejؙ͙;_zl/e 9,|hr%=0Qz/ endstream endobj 217 0 obj << /Type /FontDescriptor /FontName /SCAZVY+LASY9 /Flags 4 /FontBBox [-20 -196 971 683] /Ascent 0 /CapHeight 0 /Descent 0 /ItalicAngle -14 /StemV 42 /XHeight 431 /CharSet (/a50) /FontFile 216 0 R >> endobj 218 0 obj << /Length1 1608 /Length2 7638 /Length3 0 /Length 8458 /Filter /FlateDecode >> stream xڭTeXK:DbfFKnAZCBn9wu^{kYLtz\6Pk<;[ \rP'QIB+H`(~~@#lX{p~ANPg - 6V} `U~nPA@0+'A8 ` :P wip,Y8 w@@o's0` zov[B.0CL G0 U[A/{+p}~EX!p]r?h1@vV0';?rqqs'8ɖ!' =([(/?| ؟V6PdxH `? D?qxwh%7'Vׂ W1\^t}r#6;skAwu_lWY\[p6vup{TV1_Go~#n>?4OqoOv(Rmdځ+GEj<ICib=N620+F;}sG%>+ǎQ&}Xf)rX3hٯo# ae+7־q) Yn<&%oQ5FvA?hiχ6rIIC Ov~z: ;_jXiי6k .M {IL. 4I1O}$XgPHG',r>kf}4Bq|j&\?QN?O0,>WɪQ~w 503-yE|[gAD lX0r[]F|(vȗntFW)@5ǭow;l!Iʲ&;(,D_-Ѽq|X}/ UňG SPɺy$?wg5ބtLjYt}FR1lPe0l;|\EЍlάQH%iFS)vzSN qǤG E0ú1&KӏM[*6׿žm0sx3".Fk0Nj5n.tP." /劰-³46IW8/<:My8UkJYޕ˜ڡRuIc 4b-Nn (]-Ʋ}SCDwEX?hPcy<pz"C-C'pu @WHnq;a]`Dsd&UqrcogDC7}1|f602dNg* D^sA%,$z!My)Wd16Ko5xzqo]63*_K2¹X IS L1C_CyrnBM \̜:%+9,qos@F|a%\4EE;o]ho4+|ݡo ѭ][>]4Msg,,77Uyȭ6ӤrUI}=:<ɴHv|YT(aFʨ뻆'.m_ F'^ʡ3}$K!bia av5n-R_x:&lNaxbI^:@^bå(i1@~UrҞn}~OوBYl9EvL ~,pX۬^1l& VIq0RL_O(gDMQMľt5WYzO%y= ߙ F'.8;5RٟqȊ$ӫ~]e O6cq,zwck>X!G&eIuqemoo0q9,?hUHöGZZTʷe& GZvuuEpțsY'nU0˂u-:+*6XNN_=6à.Lu+9󚜺NGz_O948Ls /Oc%X$r@.}ӨbF?!GvInGkfҮM68w1Eخ=z⣼ CVܳp8K/FݬXbam0WM‹"MH,g})mHmaqW'JKm(Ű.K#1r$mpZL%GUܽA̔txRYԤA4풑HѰi4c.3aˣf¡GA$A,(Cd_tSbt}|Қ$cXeb^>^}6g)ru - OH]4x]X/N>7׸]SiC ?HwK8 鴆ʼn<$LԃCnx'KS| k p7'D>GcgBW&F4m>/|5q>ZpMo\:y@e^%N x,'MEɐ_dvbt%Rxi5`GʂtAdC0 zW/U~IϷm kҶ/r[}?vc!aӧu3bσOMi!Li}$|w$D kj5ZSD?Eˆoo)a@Wk o(;Ѝ%c^iLGVElb3*;&g}yyQgk(9r,Oe~Y:ʮ4~`~/Ro1:9ɐvG/G>2QcO%v5e'od^`{ t:n8p!ӳ5kOo!z܃f]}ό=>r4Fm >ͩNb{V+7zk KauKGZX'G,@FJaV/|ouRCu,໛oȐx@_~b4FPa뷁O8/CuQ Obs>LU3S*j?h#dCء?~Zٙ `ԍWp}6[ONivjjTDIdsu +TMK]]9(2 UjYQ %Z˼S4}#Q8nX2~NM.&i9uxNoiUiNhE[+p2aj];uXM_O''p穸)g~AQ?"i[/(™Ƌ\~sn sne~gxĻbeK/-TBC%Gf+U޽W7>dfhrHjpR/}EFs MfxrҎQОҮ>8_I5>k3X$KDWё拚-j\1?)[,:ȾC6vXp#ȭ1ZZZY&,}q`͊ uw{9 z1X8S?~m`yK"[ǭh\^T\= o\>Ni=B^8w)12TAmty!γg@kvEVKݳf }w"V]i/K˹K,YPzJ԰B]? ?:Q𯉼ULrFVكdѣ_p 3n΃ݜh>Uhw<aH¤Ni@{]OrZ_+)+EʟOF'`;0Nz+ջ|2/Ȼ8*0IclK_-vFq4$T>S_B"y!崎,h5.'(Ufef.fs sX T9!$S2˕F H'b;$-s s= ן!O]4@8I.Pxh,`%G Td)DϰθȿʆKOȕ|Jx7{7Zu1[xIcPeFmï)fes: 9A{NGCT @VF+Z-2d@XQi%~H`:I8b]/HoҏZ\m:b ̐axC7% t]?X4"K݈H$]oE9>VzT-CHSPXbT(`Ӏ QQLz־ⳍ;~98ƴz{zaU o %7 w$i!2M0%OSjE ;4z܇ rg&c~I|bg|[-@*z8&`.Sk:=9W~[}#gLf~ћ Q\VLpp5,': uRg6yٹִBN$ۖMͥb3۹tTtr D;w>EsX*[IaMhֽ}PcU oc~Ѕ|P@a?ĨVMp_ 'uj&7e<u\Σ/*XL+3Z3?F9ƇrS NJ&ɇ=z"Y.QNtGoSAwaatK3w:6)6wjSGs O7UX&fXd}" UT@\NVpuWVj-hi^K^]g 'z3>KQ4as@:DWHȄXW)S!2¯IX93m,:7v G#w eEQCNf E)˧B:![Y.X7IN5!x5bd O|\WW<(|5C]jj@Bz2M}}2BugېF`+gQ8kDql{)QSטτLުr4&46ziuԜtjlg8>sg}C?nREa@knƕuHrI(r琷׈&Ϳ 5*U]қ\ڶ+K>&W6) LUR, #j blS)=d|4Vah'GhW寭0|b/Ϭ|&ΆEnLOgH4vsFtk+\ޯ3"k0OgkufqIBOXMG)=UC.p1L ՜CίMfC$8T ]"ִ|m(zC&JPw B5]~c4Ҹǟ}~Զ(]ێݒ%\X>%}%)!ɀϭ܎up^C;MU-t2XۛeM1~7NEXd.+ RohFuǰWe%{Q6jAvoOeSֿJކ>@5Pl!._̂Ɍ LGLxp~d32Q/68ȉ܌CB5 =2XSrk-lq_ތ9 3GҡçI O!-$/U'.]&.%9>U\ 9ŻZNt %`_?To ehf~Tl*(-C3av`N-31 $Bpd׃.-GZ:[8'+X)ԅz[5O`COF wW(!'$;i[s0/c7 1R=xGWdԬD̀<9V)&u⦲1)0=6}%s>L$ԉ瞃7}30s_Tq-B]&s?A[UF'0فwzpd>+Dqpj45ZRsz xjJ}]>ER_5[ˌiP ;gYG!ճ-: Y\+{93[cٝ-/:LRpc9QWT1}\czȰ+ S)s.*S w MbIUR@H(5w+zOl+ubIV L%]';miZd3jO9T30?#F" Pd'K67d{O&眽IcZ-,vP]" 7nܲQtߵ̲gPdRǎeVUs8{GK5.'n>˙ژ ՊXf42b%#/EEWTt4Fxe@ptMEܺ ǎC={\<GV4Cc/"8EN;il)[hL4ÊE˰uuNZ!XΚDyxV}94 NF ~> gƁ=*|AJ7 ,t!y~ͩ|~_;+7uBA:TU*Fs5De`_Pƻ- ZHw1P;nXgXl Ar40iΎݓܪ!Xz_h0FtZ_Hk2s4mJޟyvW *^+Sb[)๩?7"e}+9;yb$E= aPə{ɈsO ( Sk6}uSsFʘMh*+9otE 6h*#'~ZJeGcP&$P1NKtC*>tY+8p endstream endobj 219 0 obj << /Type /FontDescriptor /FontName /PPOJOV+NimbusSanL-Bold /Flags 4 /FontBBox [-173 -307 1003 949] /Ascent 722 /CapHeight 722 /Descent -217 /ItalicAngle 0 /StemV 141 /XHeight 532 /CharSet (/C/D/E/M/O/P/Q/R/a/c/d/e/f/fi/g/h/hyphen/i/l/m/n/o/p/r/s/t/u/v/x/z) /FontFile 218 0 R >> endobj 220 0 obj << /Length1 1166 /Length2 5894 /Length3 0 /Length 6660 /Filter /FlateDecode >> stream xuVuX۾&aaf.V@i% PQw}>>Z~w=άk h>A~$@f2kC<;! }K("!vh(d =ZvH Kޮ"]$ Ѕ!H~K)!n88CPO$8vUw_$ 27}7"(!!(APP'8v!WM CM;uSv rF% ?ʑA p6 wPDN" +O\oP#9x u Ɯ hP(@<?H߰!p PGe@K@Pc;- qseFB}@~ Pkeu{8pm;7@dh!nS = :6?3KtյoS?ǹ񯑼 Hԭ7\ؘh(:@kn_RWc' *\Vfp;7(|@ȟ`P /(A;iTvBt( g !(YAA( #p'֕vHi'y+t_{GmL8KԆW+0x x2="a~֦u-exw"9Z'T0wwbRT /Jԕ:-q 6LSp'=UGMgF?L|Џ6.wH\B+7t n"8RBf!uLRG*^oV㲼Z#č-L }U);#./ؐ_"6{d0-ИQv `[eh+?2^Fȥ g|Ş|.q5tITne0, 97 +#)0OEE'Ϻ1,HXqeۻ'˪R^@eN:M8}MWE @?l 7H~ e7 ^ꩲg`K=,??3N#B'|̈́91M.ڪ-:FPi+4ٚ|_W'Lmݡ>~yO :KP핢bW 欸/ArAI-XzE'ʑzR_61Y]4axx>9Y w}r?$i[ISX4Xh;yxWﴙh2l<2˨( T[nsHtȐJh%ЫAp#^!qqof2'Io(uDA~W]5bZ:R~cX ZA2{ zՊi׵s*Arg!N :!0jr`JTj'Jbɕ":}$rKO9zinS07%:@ӈD%"L cV^ou&h}wg;M }vi]W|aWaCȦGÖ gb ?#f &J;ssmi<}X_|˥;xjLpX F h2`(NFD;Y2Z;WZpaVAp]ߊnJyy<\*7A=͉m=\n 7o'ٱ/_0gϸ^fE ܡ|4VǃC=oJ~ WJD&Μ& 1.&/|ݫBW1ǟFتc&木\w;WP⯯,, *+uF>5g^Up0r |:YvůHQR{*q <=uB/wFG`hLdTZ-X0 |(Ϥܼ@+怣ZC<5dxv@btz03țwwv*'wolg~ߵmh'G7\o1F[a<}cҠ/I.Y$$Gs\$a= L ?<2 ~F|P*fδ @uط% LDLZA\Z*C6RzCرDht62׶k"~ *OSb:P? 6hQ֊jt*'#jgメ*w$/yzpã7x9Ta{?-@XU>pZYjom3'WI̮TgI;jSJR~=u|?1ԩ9#3^0]Ggn2f\+#> ^mhkOp&*w(~!5My@k?FPLĐ*q2߬+.Mv݀]gLNb3(Az^O7N6_dZf}*FI̵ 0rfIZojϬT)dv "}`kDKFh!kl2wwɴy m*0y~׾-;F*S4ª0 ĶM)wƈ=hlL0wۼķ_ Єˏi1ҸA:`I '' )s0Sh(Eoz ޗ|~1l$*.lHU[¦zc%jܓa^mklN/ uNwͰLcӢ8}}f"#eɶ5Gfg`1-ids}Żとtl:v%>AKiޜJ *F:j\pwr5:C0[ :421]>0Rӝ=G8ɪ\ཥ.:Ma;&o̱ 47[H)DOcWċ֭2*2WyZΓơ pK[iQ6zB.ѐ̇g_EKs~R 7}KZ_(Trù&Q 8/ThcFK+\P`hi77n߅U ZsR*>sݾkZcG 6s,6ܣUK ZSuTC%^NhTl"7y\a)oU ;83z W%1.|ni=#U):>>< 2]C@S:K;KgzDv6̇f /7NǝagXhg\Xp]3,[OK./lL; \B'+Qېyz`YiNxJL'H}*7;S#G#x֥悪CxJ!Čmc {*1~oIs!5xƏ iA"]]HkZF|CQXڌS +۠V%D.68-:V[7zZS<+MϹڏwX23WH/W?&mJ!XvxJ%{2j{ ym#O)Q:12$X#{IV7lJHqQ,vf\kT\Ue}0M0HH͉jpbAOY8l {w%',_#l=^Z& BB7:9] 9;c8x?A/En)`yG8CMAuTM'o4gtu*P?9+r1S6؞~^h!j bKл8mO۟-iR=SDkqgx)ՍĮܦ=S'>aG #yTȪv/Q,%xWE:>ʞ}׶_,F-`D.sNfECwY'K;'XE0 ' EiLN82)Qܵg3m.g l_bXILƓYTk*nn~zTJ^=lk;-|hw`O&)cGw7F'`fڗIٗ\uаӜ'>,bp&fk1VxHht7dwlbaoYI$)3˰Zŷ,*輦X,5P^!ӽ+!Ζga!$yG,7'BI3^g_}8n)7"{U=0 mF#yn ݷꉅl^>aʵy fETjW{3|R,+d)k2=Yf9it|R& oLi 9Wb;Fsz!`VI}1ͦR)Z?|zXq~($Rm0$ipJ6 RεYmj oxS#1]Ɏxw%?D90WlL+/hzw$! &2 A5D ~;QSHّE|3&"x1qL-lμ/}(6v41ٳ٣x/w L߸;i}VH/␁v o$I 9?{&T];"\YY4EUL6]d7G Ԋ}EJm(iLGu|R"yi˹f-`m2p.ƗZ>@sMHe9d!DxS +[g(7퇇LVVO endstream endobj 221 0 obj << /Type /FontDescriptor /FontName /VVBTXO+NimbusSanL-Regu /Flags 4 /FontBBox [-174 -285 1001 953] /Ascent 712 /CapHeight 712 /Descent -213 /ItalicAngle 0 /StemV 85 /XHeight 523 /CharSet (/B/C/G/K/M/R/S/U/V/W/a/at/b/c/comma/d/e/f/g/h/hyphen/i/j/k/m/n/o/period/r/s/t/u/v/w) /FontFile 220 0 R >> endobj 222 0 obj << /Length1 1626 /Length2 16458 /Length3 0 /Length 17307 /Filter /FlateDecode >> stream xڬeT]&w'H;'4qw ! Ι3|9?z{^UW)H kFfJ- 46|9)(D kQ @h XY,ZUI?% ]Cionj pZl!@`bn ((jJK%U@k%@ knL@vF kcJg`]66@;+s{o= ?>&}ZX}>)mYEjdOI}:[.2m, \?s3 G{skD@[?|;Y'_ޠY/ @KFxϜFMͭ)krcG9 f1` 4g9|P߱G-F[}-- >w 1|3Y?ZVdi_uR-nmI 3#.@cEs#3g%W6Y[?yWK ,EbfndaV+OIJTVILpPsT\m>R@Oaa {9=)?rv.ϺYUI翄636Ɵ> V<4_^JJMvb)Uuz'. d:b'M?ԅmIՙ&$A[lFǤ[|~9' Ym{쇒n‰V6;G2Ld/ĚH6:0ܓSأktpNPH>_G#c9bx58}łnM08:r8È{PDtǽ,F:ThO >$+W=ƈBr \#d,8$p|tR!|\ R'CS4,69*}ؾ3tه9ODc)R&drZXa Vgr|TzQH蕩$AFp~ B="_ҥXh`aZj?2C d4(h]3::bcvY47aVC:N!Ȫ՟GiUi\z *`#%Ѹ EYqsw+t;N:wZ$1^A/]:f|?'U !=Jut,!ɂ$=[\եbE2HOӄ0+(pjZHUgIFN"֨Lեq++S<5q"PEMt[S<:j! .~ AEUo%9->.DN3-TFoA =w\vCh=RrƌB)|X \Ђ{IGui:̪ۺH/{hj¶FMhC^0%3$=ζ$7:a%J Őaqgt \w_sݶ ]8҇Pt,à yp7g Agvk>߅Y3KD*%(z4Q}=`Ӛsqd+x\/Q96` OUM %nwC]pmD,8UD4p@KuWHsoĜ&,mKjCgCl93{œ-[g=֚9"r8&^WrQڕc{/{!\̢3]G ָBŽTBm>S =X?MMR7 ,gӑ!tS<&˜` lOS ZfώZYBp.:s<; &ʔuQo,S߶ [W@a8< v& qLw'~n{Ez7 2&z>zT:2ļ6{Q{lD:H D`[.M߆~{yOGfq lh>ֳm Vku *9W m! K"SDhKyhG^?[ljW&#Wa3Sz- f")C%bT@qr',i ș`0(:)Rc+Z# 1;q¤yLҔ6t;!ؕ줘htwp&g%\4~GdC]EN-_W4BtYf* r"ĢQqZWL"3c൓ku)0"^] iUuJ뙷 kU"/ ݰu:S~m Tm[j}hjx~~_/n^oyXbʵ'6(T.ۃȜHԅ{nk:DFGO)"|Quz H^J\ϚC:ncLD)+=Fv('5DkиrOZnee7j'm5x 1ˣASZt[6U5|b05F7şP,=r(lv['N7V<"X]¥Vf`6у(h5`Ըm-a~@szVS]]?OeKC]uدڑ4h-(i$g__H}_Ϣ _*IQdPRz!]|8*NSc*;[9=2D{SSO m{\/,_1kmsA7 GO_疥/l^kk4D)s9P3dmm:}QOPӪBʝ~Q4t#V@U)BtTy=ࡹ*WneY,ЙDx("η15ٴĨ CVKֳe_.®"Bey *Y'iJo.Wi?ALU2ǘ;!gLesJr*~cФٵ^jRm=sIgg)i!Hxj񡮩4etYXAvJK+"pot8|w&?{)G\-R[ cHJ+sVY-^}zyy#av5> FG9 TSc V֚5QN;eۑ0(ZamX(m9fYL=`bZ4 {uHHQ1 塞$V K9 n3A/J)>:)Lx+Ęq\ˇ aFH}JտNbݤ88R]6~Р/ tV+x~sp]]i!)(}YM 3/? !Lɴ-,~% O]S& [gim9mT+FI=W`-!T(ݟ} 뮣9P}CYø̎a Kzp񰂗 Ȍa|XNDBBa뚝M٣2^yCV|eIKv͊i/BfFk~9n`y:w|wKh+WNW($ǢAm6-N1 yͼBɝSy(|^wZ=q3شQ V˧r=Bʳ5ɺ=p̬?'޲,ٗ^f8?}}:/j_СFV-lգ%w9 Q}?-M,oܟaIy$>G+cx)v"J] > 5::2,]2ZW#Owco>³ZowRyAi'42{ٺ{^D v2&Yz~U?j59v]4e d POk*O Hw5W=sy~Q!,H#;-2Dp^)mv9Nd\l 0 t3>;AFq/V gS(|{;֝8aQ x.\p\ \ѶQvL 2t#S`iGty+h|M[S&nOYz-ʔ ~s0"ޏG.7+D[K%m3BF8hh M9\=R5%s3$-[r^K0y/=^Bqt`wBE jgھG65N]-JrW _8<$,:#8iFnծ7@C1p|QinoM 147^m(mmk ޭߓrÖ j z X11mpz|KB'[D #Ӌ[g9%q|%6dWox0$ҙ^u %岘RS{ G%N}3pʒBwPr l*"S_GαV.$(Fp qg#|r\t ˚S_0ٕf%wV Si( h#p8+|C\N |}E l\:;|3 ǒCim.fPw]#y:ԛ~9 Wl si|{+R{]M_@@ԉ2(#e; ѱ&/ahS17 :6\b$_?XA\:RCȶM<ރK>;nH7>l-؀M~ǻxw-sۇNbe[!q7;ZLQl#I8͋rxsy-A%='*ӑz՟ӣp\n5b,>GZbjSB7r0qڍbGb^gEj,Љa&Tpܭs)֬p( E3έ2 S֕LHh[7{wXڷ VczŔv\n\N~ :?A,|)~>juok"ؐCm}:TC?V~!Xkru5D" n5% v:0SG S@grxe_rBLq#>aҕ~vϭA7] >}frG*>S? T|~vw y$[&scy/\ι1~4 ƒbf~Za$GVđԅ3"-~l|f-N5 g.n?qswPo~-tJoΒ ?$ozF N<+YEeڗT^gZi9 sB+}٫:g.##4!Ƿ)KmӖw ;Z8T \;HxGCUH()~)L9%uO\sMLs C0!;ɠ)~qv1QG{c_"uw#tyO+*eC`T(A`5/JJm/u(ؤF/p-OD:׉K+.X%JkT-k8핿cR._ÆT^2Q&H[Py=SG$&JJܯ,&6>x/FJA-E[ڸI r2|5Ewf\ԥC٘lw" +~!09 #l+#Z$ Iq?V-_fiA*'ӸUf1rV|H~է7cʡ׾jY?7,4+Rk` 3b1a,oQ{+⚀Wu60?׶`/8c!B}@}laIK]R#3[07װ7"ɮ:̊(X٨G*\^}ۂF6_Tҳ4'b8 ^w&;<:pVG C KKe[mLbωqdɅ9@WѻԼިN,bau )YxScVuX# =j^:hzh~Ire+=;O<ĥ݋2m[sr+fqsE qSQ1RG{>~]!Pnr[ kgcPUw!5,jz7֝g89K'zѻ#k[UF:կ[#pfH!hZ8Xz.WvӗaPGү_y ˤn+`h_G^M+]󄘜&Rܭ㯋^c }6`ߕz{qu#Ԥӳ˙BGȆrqm#g!w;5[]},{E `)i_V*JwNig~z.xG,90,3yOXMa%kE#*cG"J)6H*#pG^BN9@U FE䱙s5 0$LB;jF`4@I5嚫Mc%yNΪHeUYd,C>: b/=y_NCE)8O \^f|1\SkY\ɐJ~ȽYplY'ITHo Oe@ D#s@BV4/iydn ;,emX%\ ~ 4߲e'Z yq٥hgxa.Ow[p+L+oCdp&2'xn{ \F )Xe1 @׋`0OppI?Ɇ(+?]if4Dzzi&&NݑDSDEu`|%dL9btVw_DU\8#YP zۊ67vY(Ћf~[܋˴|UɂYIWnXZaZ?:<6l:A$0M>m;B׷ ͻ@Vsz4.waR %1- ETkS$>O(e-N Νy\ds;RbUp-~NП?2EN 8a|k<ntItoPIqI>eB 7ڰ!lY^;r/2|ﰺv{8Wc$ >Lb?6< ޷ob#||S|D% ,",wyC)g@W{mi?nDR(Llist+Q?LLT#0$tˁ9*W/E+$GPu!LOg5i;-ON(gKJ:?4g Տ&N7۲.w?{!gMg }h&$;qM].QdH]cpzW Q'uyP!֚Cg߈ b, ?T_*"۰/EG 7I藜7gH;?.Yy}$83+#駕[sqʭwygjov.]GpG aS滎{C3,+o``|;zY[* /{FC̉ʒ?UGW^ީ]GӘ67 #OXS)@yEKel(Wc[3VJILY![ #'85P23'ID+p,K~3O5|j.>Ic^熥vIs&c!7K9#f >[#*zjUct'S]42*StB|ٕ˱[+ (aA.ydsxV!cNmWovg718z?:D(Ɗ[9FJ-sM _{};񍐢@ 4[~0ꈶ&dD0D_eRTKeD>,/mKq9Kca齲_$I\eh{ίȌN Owj,le74;Uef'`0zmX,E[B(XJnE=>29'YazߖvմwX;6 .y"~^n"|F{` ds⾦2Ǡ/5O."2Tr]4s 9p0u1{"Qz# 3 ?DilbX{l8U+n8aa61,DŅ6b_˯N ..Sk7T:&/'4jȈ O?1GE]!zHڈ0a0Jѱn֮)4%VA$ʩm+aEĝ+JcKH*6]ק3[zi^q00Xķ6$sR0u2(*@wt&ތR^Dg,p?OMu}͈HzeN_o1mu,;uXDP~'8Yts5mh4d+Gb`5Q$Jzp?%-R'0ACXptA2Hx;2/mGT?"yqAq˗H* 2\En^1[y =1^YR͇&:ܑp.N^YI9Tt.zfR02e09H%2giH^7;/tDbZKĻ-.0/oϏ5@ i7M}ێV+T\Tɠ0jٴR.Lŷ0m.W r0Y'N'|}gȗwQ/t ]ߓ+9RA6\!-6S?^zp?3|6gnn1IYq]Bq^  _AeRF}R?'8d~9*XAr?"3Lv0N=N7+uMv$T.zWjq{VrQZ?s&!D[ݹrHL073SHuQ.  ªX|u:r-MI`h5o %Ȼ WΊ .׆CaZSN??,AD[VJl]h>떄Ѕzs{ƙ6Cg*<Tc.6iB]Jn~ 2SՕ|LGG]KK/yZ~-O'Pd_btZ6B3ٟGTo6BOsR)r~/Xj)(TNNƆϜڼypfMt |ϰz7k5PD/p`bٷI'ɔ#$%!U I]>yvM7-Rѿxa0Ӎ_iqAQ CRw+N$<H6sFHh%g#7l.406r9ceoդlHmQIgig">O D9wk{{4=e ;_%3CIs3ͮQl-$ocAڙI*u;e3ˢp_ Τ{(vreo)ZTqX%K:ܟXC^lgf5=w}gCKJ6>88jś;̜Xc_5r}oV`gIHgؒ!%E$t7?3_0bvZ/6ޣqEdTCDtƫJe w*)2XW0B5)tM6',Pio֮99xebiYBRSy(x5\jn*& ԹO P,D|V:we 6BN|Np!{mnh4+*)pSVN3 .y(3_\-`u">쳶5-Ma#Q۳c/Z? 's@Gm* -,𯜉,$[^l(Z=/}-,-WgW&H@HOI2U"}D4EMBP r!4~_%Y7 %ϊ}bRL @a Wm)Fx(pڱ; r|yDz/)bM.=觜{<qr?~̹:ra]7@gh Kn$:Ö\DRX„IeW`늋q҇=sF_#΋ ;y 9'r}ޢ:U>x* *&1Z)yhr Cl_bFgY>"4 <_i{{fNrԼ 1FŻ&xU=Rd_P0aBB}SXC׺";{/&8̸X 0KJh -"2wr7ڥO. R|TI@p]9# o 6X#_AD"A_!(}z;ۀՔWAX1V~h_$vP,E Q?΍O a-u|]gx__4,=6 4:y1>XY{iyWiDoY5,19@~]=ݥuIgQ 5˼I[Qi+fZ]ń VL.o׊ڕKWPhFz/cOxlO%/zG& J[}ZƖ_rP7u߫_fq ѸVK76|>98Y&H3ᨊ*#Xy'0v,n+P%[ҟV>& ]q]zI ߺÕi#X%9j[݂%%y~|W/wnԬ/9 'Xk<#i1y QvEC=VeSs&Ք2 xJ<1`<\E B(gWLy3l} hB͆kLCgDd@b1t6RX.]n-g(BOE)):g_̘{#SyV^ z8p W=Q(.,qu%l.Qejh_ɑvL/b6\VE֦a[xh64=(dSስ~Q3RM0$sT+WԭzFri *\~ʑޟVӥ4h+-ח88\x3f#>c/&t! l U(Po~łTIg׾!ؘrb-Z ~eѲa-)զ~܍P ,amMby ?}hߧ*p{vv˩Ԣ$jR*Q^Cr$!VZ*Pzjep /67ہQG'S}pO$n9.kchg3]3y/oΫPĴKNvFP Gɤbb#yP=~KLێHm#r ښ5շU"e8p*1e*cWB$y|NZY'9Ŕ+_ EK2؜EC{׊[uhtMI{a(L4sfwnX'D= Oca VI&t?5xuVyM Qm`GY\T>$4&8:.Ub2svcЖ&KYZG Ox%ψG &QQ38ѦLGG\w Ds#t'J=t :7PR 7q7Y.(_xӁ٘(HACvCrW!-/8k+#I>?qY?*'W+!b !TlYue:vwLAva=d'))n1M A+d oFր85~9YkUt(w(%(;\{q]>^NQ_fyx|$ endstream endobj 223 0 obj << /Type /FontDescriptor /FontName /IDLREL+NimbusRomNo9L-Medi /Flags 4 /FontBBox [-168 -341 1000 960] /Ascent 690 /CapHeight 690 /Descent -209 /ItalicAngle 0 /StemV 140 /XHeight 461 /CharSet (/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/a/ampersand/b/c/colon/comma/d/e/eight/f/fi/five/four/g/h/hyphen/i/j/k/l/m/n/nine/numbersign/o/one/p/parenleft/parenright/period/q/r/s/seven/six/t/three/two/u/v/w/x/y/z/zero) /FontFile 222 0 R >> endobj 224 0 obj << /Length1 1630 /Length2 18241 /Length3 0 /Length 19091 /Filter /FlateDecode >> stream xڬctf]&Tl[wl۶mmbNŶmŮz޷O}~1&؛XI^(`JP3qsQqSpWZaEƮVbƮ@& 4a^V*uMjZZc0_O+ {w/*p̭lQE%miI:@ht6(ZL.@j3?0v\V݀@TtGw o\Vnf$WnZSrpqu1urt$&<]-]bW p0ki`OIu5w=]eY8{_iX[gtg-/_um/ ֜oLS׿-ai{s3ӿfns:AT $mf@sXF׿!Tw,3@ -_9_.}n v;wEck1?yWkM?Im_j-r)YZ̍m_ru{3=/j+,Lm!*/]ʟQALZNS`ew\ռ?w0`DD<>\z.oB,l~bϳ'@oLm,i3#UuT;luWOȷvEs *Z~R[l% K7|Ex^$x2=_Y_PK4xozfr"DvA$k QWUIDEbCsQy*[:/cm\Z+!xZ毩j^ %t^ղs}rGJ.g>'M-ES\ҧ8@Ol2AgVYjT$jarn 9eLJa+·TR0^JV4ZYù/ ^z(*6nO{vAW1 sG*z3  N,n;QuUh&,0'"H0)&9P\/䎣WLf@ @e&< f%@Įi fp08h*ö7)Sv6A&^ڊ .V\fdۺG$^UO"R@G}zzUZ=l0\U*~D8>}9Z'@2`bQ, VD;K| += eJ@ ]&ʭn;.y', î>5r AHʑ%tՒBA# (_$Y7&@8"%CٗTG%ZhN !c9UyQ9֙ k.gY#XUBCM|FfL; DjW\#=Lo;n#+?:MU 1eιeGs(0xʩyUߕ>ٹLaQ/y>S'o7XvFKn动}n=rn>ḿlj+ʻv'A1@4bbԿzR?{ "Ho"Qf7?=q3h ;^vki&A' v!ja4CP9-y݃gFF,͘ >kf4 $gwPZ/߂ 2~WvZ"u lԸYz]=r*!rO^Xs3~imfm4Eׂ ~ZW|0w)&UHM`uPF `{A(j.sj&-%wM: "NOSEJ4i3V:J!HidM0IrywdX|_ M- Im3 h 0w~_HFY\u1AuoRc"v@7&+J8=Y_&*نJhҲ/iX+PQ>stM;feU\_~5+%F^lhځjI"vOs'?9i>}*:+rKl~cc:IMl3cYI(y-Y1l6Һ6 `Ƞ #Li.H5>\ĸ.pSmBcrQS>qiH5_%i%rb:Kȥso7fZজ1Rםv2#0XjHZ/! Nfu~dॾN%Dԁ+S)1=nFk;d<2J+_/YO3O~j6/%W>sh1?rpn.F'3[jfYw?L.":I8ČmrO-3U;ϧmpJhlh9;*4Vg1Eza$n0+@Rj[:_ȿƵŵO+F]3,u lV-7܅N. ϰ, NKսw< )7rj6wui%WSU~sItdqݖ P8T2,Q9%C&YfzTsFWS,HJ(1u>7Q-[ffgBE]D|{\z(t Hc\ N 1xɎy #G-=؉#Lۜ%51/# S9Q[8Av>+ᩬg?,l2lhWLM8VE}{P8/q984EM]b|֛p~>M‼;})2!rjo#;0~I{䁗&#e6/EB"1 :Ah g@\I;>'B#)|ԏ4qf |M?g+LHVIBzZN#<;Ϯ٧RȵU+ a]0h3Qx,Duv2pɛ:qJ4%F 9PL2OA`RLv ͉pccbk2+4}W>cGݣ ٬ZԪ2UK?VO}q4Fڵ>t)Y0PPrĵcEɱ^L@/o#G_9qsVSK{:PƔ_HwM.\JEh6IF_m~ԝ8JeO|j7\rd]!E[/ UY Q`3ulpzw bu{+o0X2?Uz_}:DIG1a2.~Q.WiCpYp8l BŽ kTFZ$mɅ(K|?`ʜlUa!E}Yƌ@(57I[ԁz xW4S:O1a2tĞNzD:84txDތC8y?!Y )Ia7~uD&1(X>|H .I{=g%` 4=z{k!Tn;+1x*78+ o3$UWbOo< jъͿo歓ѠNmђE x_DbX/&!5gO|3a N t" j!>8`+wK_ xi_C4e=ta>J]dro\ʯ3v8ʰWxnfTߢ@|]F(h4:ص+639Jw=F"H 't_8>J>mZrAwDy*;r6X| }h @v17QQJ(!`wG[#B幍E:ͥOpʱ×x3!u:6J6q^v>`Q?=C $>U@knnW7XY0MypB媌V8ݘR֜,D}9EwY= %sAf%wz[ "\ᄔ_&,3l@{YQl'c>f/Fv`A\y#'05ig.X.La+BUgK֨I% 5FgOk {7x50C^~{m㶗6X$ZˆDUyJkɿGoNa:~Y% X.xss8hD+Z} q1aKW(z jWV4,o#ڿ- E%eD{d?E^^ ONzH 24ږ")$#;Ƶ,BAK!|.~1S+zNrʅڑf1c@EI |D&3AžͲ[I 8|jqrn{-/-f )+V#91&6%vTJ#ذӮ4;Bh>na'^#͕w^hbj]՟~L(Lul!bx8 7>b}dv ͛s(rnQKw]ӚOIze٬GW%oF{^ ̇f} VqTVr=m3-)M9Io0.5}l:ϔski$ ᇰܓ k(^Ȳ,AG>HX4z nwNOmȟ ^c) d1 tS7e&`4GMDÕI;A3gC}g 8dSZ&s5`n`gk"u]A$$A]W Բ"<σR=z#'# 9qK:DH2r7|a#Ow!+ Qvt$VVUj,3N&gms|`ɱ뮞EuopLbhwaqLDҠ|y2  :\i{撮]IP@eO4^'䞀gw^DdPQ7)+i^cEG]S__,Mfh u f14~ /jYGo7vq#5huzт/hQ l1nܷxR=3*%ﰢO0Qs^8 s\9tt%[澆te;;ƟM? z^d?EƊnDŽlgCoJ2F|֍17|Mpߝ89.t aNNAMW)kl7/Lnh(TR靜9Yʔ5:Q˗dn gKΩ3N,綏hc]db˃^\2_%gr#-N^2 ;ӆ?ш}xf\g&~XXd#)AU$S@+:ɔ-jX\ BL,;ׯB/j̭lhr<[,w1rEםs loϟZ7[WIJ?X;nfaicV hu2^uQ=~oM?U#}+sL5c|䊼91 z!enx6JL*3(uAg Q`>ٔ@+G(&^V$JWs)+ IB[ 0_Qu ۹!WH] þGRo%5Ç-#{?S@٧ HZpii#¸unQ+ dz#Kay)rhI uy86^p3)Gc?] >2I> 2lJ L[r͕X {a\UO(JO_U6[ *>Jy!:g0?~ C"H z>3!aeO*wU"1ڐjLr}hM2!b \}Xy+* "# 9(xQ~ȯPRB >\A ]G,%=ћuC}XD%=8wMQH$P\Hub1905A9F<_;T@f>uNStm.7ͮ1x!|zT~kдUю?->Kפ^6/=HP!א AGRl|^9~"ai@51M)""ZZ` 6 (tҾP|{ S֎Pȇؙ9R)[A튏QNQ;ٱBe4<ޡ.]#s㾭Rn$L35bj lw6'o`` _bO~)(0:"Ϥ"rhC0U#ژ؝qԘy9?lA5^n 2?U5Qৈ\ӯz;*J?gX&Fk`#[@'虂"_L$_DSTn<~\HG3k;}t>NS,DJpwmd( 4 y{hBxxX" J*~K'p򖇅 [䫉Xj/73r 60٥TLP.$ߛ TK($ q]BO=MM9 imITZŚ4;ΈlDU֢|5Ŏ0/nofW\jƹNJ?iJdڛ2WvkO*9κؐ~\N+j<훐o<4-@a Q/?dP)vn"oCHʼ}r` N1I:ޑ - ҁ]!p|M?}EU ])Xx _ ?9 GP4".T:>pN^9oI,{Xfvewh*p!$GbcU7z FE ?*%.g|^^Pҋܵn >5粽TyAQ?b8D9; ro|&z-vnب.=/2'_/FL5[^N N D_jȭ=g׍(fn!2grm6TqctK5|XFԈg[t"P0f'AYqM+U ŲǴLP4^Wc,~YʛafnxZ֟aDe TNKTUC#oʲu<#"qװY{.xnK` Ƌ? Smrza4gA*FP$̅&(~9eHT NLB)y>wu L|`.˔;gSDF0֠_tkB8>&.xi4Ie8qaVi1n@brnՆalk@~X{ex,z$)Y_zU.||@=іR[?kjqlp;QJTELJζ =R10yȶk`a{KREݼ,}nS*)V;-VJ<4Ti5bx&I76 wo8ߗ6o@14zY~" Kު_O|tu!=?h9ˀNb Qw; dmZX`dTo]bfǥ#O3HvM͉UU>ZV $]6TW%|J&f-TQ9\tAښY ,[d|IN/WfV ~sP޴.qUde7]g*Zi-uvP0HBb\{.Lci 5q ߨSr8G[.XdR^ 4ցݚWbqI LVx=fCƜ~ޞFW \IAu!ՏFhBЍVWZsϖYؾ˅|!iaPd,'K˃uv]BN_ [od6Eتvl ֺ/MBeDf2@sڈw+K>]t1N*M^51xwY2O?^ʁ3o-h7v(W K:LJip ߰!*b?{1]$;w 5/, Ԟt??q#М8яP x{_:a{>|ͨ|y{_T kgu(syafC,hMq7|,c:~_S5M=avrN5:/!HP }ٟ?ǫX H`"v$f"<@qNDRɠ5!/UW^_I۝- hw4鼖Jq*tʇg{-OG5Oץ.’Mu\*@FY?){3RZh*FCHn191巒 "Bp1qY (U=/LbRh8]po~7&C<lQtJkM̟Uw mӤMۃaH2k, Q+ipP(@/n{J1rvW4l:TLQHU湄ر{MNχ;vy,lT ! r=G {3Y* kr8]^kѤ:}]nxw(8׸-Ww >;B Xc֓m+zwHSx!0 Mv~\6tǀLYUvbe"VMN%TeɏޠO=y%/z#gIN^ ںG$Ў&qb.9;Tyvʹc)<Wsr^_#hPg|ĨqL\$ﶱ;o= CR$jܧhx:d1N !>J7EtJ2y$p`z|zg*7S^p703?X1$ ,DP.]dC%VNii)S_xODRgNB -BU9 zd|˼1Ε?EawJ{ɵnnwG:%C_bl@KKTEDZ*T&z:Ts*6;bٱT&4Rh,B_r%qdhC9]9frYψ_̐{={>wML΁!VxVD8? 5qt3/,{Z]#X- >59 EZԍh-$ϩ8yiK6u )?ld#\s Kwy S*<IF&=܄lNe(R]EnS ?COKR O<ϰ3Z19XͼW0Gݕ]F&:8ba 3 cxḟ%$վ7G~ߤVj6s⾫Pf3jV08!"}q뢉!\K&2X-ȟF>rS޶d.ͻGȟ;j`",ղ-嬸_f>ƂY#@X+O$Av>A\Ģ8$=ƋcL$/A=c=*ɟm_ ]کy$+yx``TcLO,"@qb`I3;]5+ #Q_*۶ t<vbw:^k%KQu0>[ wjN\l Ͻu$k I%] NOʏ~D}Hy=pJz5xXw_D `r ǼKoJ 4xk#T|Lr-Kq#ʄ upVA*vz7?A؂gdaVTث߰75ΒHKOLJ}?ӖnxZ-ت4= qG֯pX*8ZZ"“ X8%l Tե?=x>܉-۔gkSde+ ܟm~O)@YB9J#V;Fx*ݽud\835~H&ϑybCIKaoKQ/)'x2^V]y̑`d1Vlc-)&wfg}ljo+$2vlpAv15sWUf*EJ|F~)Xw>Ϲs ++m;m]O& YbF7]|A ' (c_M; P_HH`Ӡ 3ӆ1B)4T!M6d]n$&r&-MGٸ ߸`EpTt5a.xNLpzSG?ߴՍp̋`!&:gv) 1z&4ˠtO2Gع|[_4U\rw$ /\{iG{ ۡ>YqPAi1K J7SM.v9Œlt\<˯KPRG-N'Ln0Ug6}cB9ÀEtѽ?-bZǫjNJV=Xdnxk<7[ћ. V8&xF3!+qs7qd< Vb%meƆe$d Pt_ұ1c"QO~4SdL@{1]0baC]xZ7B\yd'C| Ũ"OO_+w`kVd7x? ۪<ι[ Q*F[g>/osr:> ,Va"pR6q-`'A~/2kngb8­ "9[l{`[_Ju )㓺_fk3Rpjwnͬ9iX`I齤xiK9T*g[#}[ D5%&PDCRݦ$n1Ċ V,Y< Y?bzlo?O'pS/kYCmx1"Z 8WHJ|'YfK/wgb52>nGr߯p%pbQbka*A& xy[} &t$!"mTFTAGە0&\ۤJ7ְ-؏ "#bJSt#0zY`OQpzOH# T06Gj[S Upn`$Gϑ5 0Sd;uNQ˓'--JJc y1 V0pYy9RR-DoM?Q|>ۼs+)J1k{P+4pK;MgM"K]FQ Va6 TN,$k5 rkM%w}x`I`T [Sw"\LOGRl~7pݒ8`By71k KBddCVVSlD*F+TVzS\e%*4W=bꖇ6H9^1LJW@1hZ"&Fr|mrd //zXf#ק)T+j>:`| Ϫ,xj)^T)ܮ>rӥmV!wLᖧG0;!%FX9߆avضhYYDgCF{(`,HV #/1t؈MYJ2-ڿ ;BNHH;L]$> endobj 226 0 obj << /Length1 1647 /Length2 15433 /Length3 0 /Length 16293 /Filter /FlateDecode >> stream xڭce]%mUڶmvmYiҶJy߾}{?9c+fD+dĊ*tBf:&zFn"y+;cWge{;y{.Y:e3 W)#[ =@ŌH̔H̄ H҅RMY?-l!2䯧/oƶV&DV&fg3*"s{'"/LVLKșȈꯛ?-g"+g" '#3p'غ_rp/LoTEQbiOlg0ߝ&//_ LbO,c3"S+g[#Ͽ98Y+ Wg+f@Kdfadjk/?uo98z_WV.f0Lcmaa_DL:fg&adj$253awNe>$oE7qF%ZVo{4FHackD2Yzn g?9+B 1ѳl,nafhbbIdndeW9Z_0UK+?j2 $EEi_v!goP {y1s1s0#3O1ZʃHs_h&o/?_5 V]333e{` z̼IQ>&Б&€Z^]*ÏivϥsCi꣱> [T<T[4GA e7;`G{Jӝ,NP7T? HLлP/ȓN(GG{qirxɣsqժcQd[2Gց2X^ۯ(3wwVϋ:ydd@x/aAɅC5\7W{=]'<.L wSGh6 VQ&ܓB]2`ZruD tj^3c^7Wą?ElR[*Cap6V`.;7Gj1,trX^"q\Z; Es '>BFþ@ JΌnpO;EœD*Il:ճaz.cԺ2l!;*W^_M+n ֡<@ĜSD?]S~Xum逵$6)c3b4JM5vs)u yz kHےYsr7A`cK#:6ۀ'B`xQXmolC?ޒzg1x 8{k)|KsGrkV4cp; G[banw"z@iA(g8X!_%Yx1:^ ~&9+e8,D[ɯ%77߀:S|xy=Qpu7?*5<d)1J{I^ib^J*@szu<{ߢN&)D3R,j!T2 q85J;,QА\ϐ3@T>_m3]c8;[ѼѪ}\7,1V +D8֜Fz^lLp&5oּIu~Obg{|W<1{j4Dkƒ5˨S`-Dc>R^vCr74߄tC}bz2XڊFF$ h^2/²E r8NeO"SOUx\G6Ϸ֖ZN;?_,7goyz󣵚p>WDLd]`|:! ΰ*ܧ{8qPwb> S2`++=:R֙Q ; re_TA '2l&:uģlt\q@|Nceeڇd| C;9bҔ9+#-b 8î|Ž蓅QȜsGe EjHk/\U%B#W"܌wyv/R_ }< xZ$οky % xrxv\K_@CƕIΪ-6ρh8/g1Œ$V횁s.!RԐ<,(E ^nJ, ˑN]g5ټY*䞶Íhs eT3üܽx#I*sijr~Z'jC\baӷ5*txY_s$(KʛVxݶ2hȆvY&]Qj2?d$ !Q%N:>a>dnMCA }:zDz<:,lN`7 zߑ֩T7p`e-ƄC":0|0k;ME4jAlѲqWkJ M=-V,ULߢ\6>VO@&b܁d>.NmQ{Jcj_e難3<{Fu**Tŭe˺|Ȓk݇5?()>g ANg~¥6sJvد1 }c`FHH)C`mE[^:zJX TLL}PTޒt2sV9k6^;$-IUbf&{_Р Ķ4qu*$8X&_~FmūS 5/KlI8g)ڒ y} vc_P((Vs>3Fͻpq,&Az؂v`50M@tɪ >{-ZyZ %/Gl2:w"Ouy&|UJO2[B7__ůUr1F\-Nj\rC 9:+GaovRq@Td*[_1>3];0CǾ]z!?7*6@W*+ T ]4 p!x/WǼ,v6b'`zzgY!n~{7Gf͕@/QH93<ϴ Z:/_gdO`d=;aM&P O*SʀFVq.e%: мVYgO-e5AP)Q{(Ȳ5e'9th p)IIA`b0֔)2wˆFO!w'~nlNXA]vd!㍞ 8 .ijpf3=i5$J]:t薈&/Չ'Pӛ_-%]vB^&F9F' Xd{yU? xYPz}<%@c(XDBut%]&i:[t3:-zjkj4L\M˛׭ /veyq:ԽҋL1~L 6D[" ~yALvƉ@g5m=z,T?6S߽t1;% 4IV"0{_~3k8|zoixQ(9_<?{һI`.z H~ԍo)ݴF{c#=84!Ƿؘз]@1(y2v0pӰp!R:W Up<XqQn1!sh(f2յ"2H0 $NsQdO)rh<Bqd qȒnFOD*?uaJƊKżEJپ5:@tl=z#`oWmͤ YU(f3oӷ> mlLxKP~%~ NO׻0gxa ~jIg,qCJM՞-Rpy;>kUDLw=g5E%.y)8,DӝE.TnLl}llL!#WrPQ#mIm˰N.2CO/˱ѿA[P]gÆkyf)[-`+d1ӅTg4&;'( }.\;}捡n(BaAxRIx+2N뉋,cN#dnSHdREYm(VT:T4FVd4,i߂:x5Ә,Y,?\\|rO`͏_\R8:O7FaUo$ޡf_Q%VQđFF~0$N)pSR\PG~ѨP5Ї"Cie"! OX%fDu9ox耦yy>gEͿ="_f'k\ECF$S:pDDpC+ص۝\S*vϞfv= $:xu9 $b w6]?Fƺ&h hF:?pWd g8)gl﷏ >⾻,~&*k7gHd@UI}!jhz2\?tTgqXE`˲PS&kۂ a<7w6_jN]^|]bGs`i"hKC˛BفyLw涚s+ye૧kT1fppz¨Ev(CEQ&R~c)T+ZkJ`ꢰ|]-{wLAAVZZ MJvT/5]D2O|"7Ixo,jm/&Cxd;w6,þwRgZwBqAs ?W ,4$Nd9؇*e+zp FAu-UNr^jO[ٙ:-qb7 ԣCAUoO 0-eeV=ˤq"Y\z,<l t=brRƨ:I'}!,l ̣n,_׋N$tɪ^r4;J<1Ra5CTV[n/eё~p`:Źx t1C%`ï"d#|[3Cն{PL%Eq3_r K~^-%e,pEbۧ{DosvaƸ:uŰy>H_Q"A '0Ȯ*݊axz1h|>.d~0$^0`cER!{V2:V'p &rVEKqftK ext)ͨih"(12iqMhn`Tv e5$Ǧuq/!DCSçʦ$Ee.Rloo^koȮ&&e@QHgf)>?Ի~(7:j4{2dž"١M59I#E R\[9$,6i6 8Q>VZ?@,B`^#R9M (H-mx"9 2]KÖ{sYT[N$M%^9P9R6\="3yY8 =ޘR0i25ȂPA[},Y,INV)hq3a,jsvw%vs5J ANԤ)i3@}™sTg|y†u[PjӴdSƋv]^L$\=ʞJo^!a\$FN_`;O**?.ԉm +[ )ɊMys*wH-#'O.|VE,AR~-1rX$1nZe 3yjfX^n4r:EӅ#=5ה0 HDNIPb~ ~D M{?sG;zymՍ"Lhls^#NNsX e<͆UA֙Jml= $Oqb_莎 67ԟ-s,Xe0gw[ZW]ahV; ĦQpb+nWͤh/`INU)"a'Q?ʏsRیpmy':HQ9ulR Zup(x7UbT2X%rng(`?n߃[u x_w9.hSmeԾ;7!N [~Oq۠+DfiitꃵX=}!*(c3:C9)=n-jչ,u%j\θunLI%|f*AD4>wAyAFN*޹P+QTTCN|)!wS]|R8L,*2zhå;)xt Xr4O2W1S i  Cb~xAoV۵4$k7 rY;8v >O薒Ҫ0>:`TsviʰX >L8{fuLJbbDhk0֡ zz ?3zDh8gZOF̈́SK )&I*z@^l3V"7VJAt(yJ魤+GF /sx՟*sDT^EU``IRDarh&ڷ~|A:[Ǡ;L\/F/?w܋XRo !æޚ oXCg>`*t5 ^hƶJI&Iv6&|6N-.'{1bf:rx)5o/2&ϿxKo=TALpe%OxGt9PpnFɨO qO}5]U6uG +"b` (Owo95s]aطr!8#L8s[wD9PqјўJdk yzY:PiӞLQ0i%#"I*uYeKRicW6h(Õmt"5ށ,"I|ZA8:uz6Og3DḪcּhVD&ՖO-sڕOel/}y=vLb!T-rtEE7Ny$ >'Bp+V5"KhʹYPk(T` c^Ӊ#iIC$ZՀ/qYv&%;e\wB+1EreoA@[t*lI11>I]atd|sg1D_HπviK|TiE]{=GKh^p8~"Y2HR0gI+CWjuu!4`<I,םvՒ3` F޹j6ЅlTz:—_akZҗ]q&iJ"gao)˔t{Y *nCe)476،rn4+Qr[K !&LHA 2ԯ靣Lzhi<3>sW)ݞޏY"}I''bwGj+ F>h.dHu,sY*vSg&.pv\ZaA)WisKd55Rk (+DMPh^F"0-H 2m1Bg_I(C8H*H3_&Hg -x}bj \1R%fWŤ+3Zƾ4pk="c"e|zf)pOnDgP},`uؙO#5*ἣ|ɿ9[4^Xk.˚((!\qLe32<%>mQd.'20jrbڢJzxG!v1ݘ.jۙ-?TmN<QmKxukI'TW f b$3o_aI%1%MiubeaIo%OZm臭 ʓ5~L4E|u4{OU0t$X*[摱.G]wrQbT8HېװhPVXR+~Sg"5КSsEFr,mtMK wQ?zUMeNb ÊM `4vw|:Gf=.O|y<2k+ntApi4;^ o$Ӆ' =k",fg+l~A7ۙZqT'AWa_NXaR; Yz{]'GH a5JY |S:%G *8?l!糁L9IY_Ub ^DED d,)Z=g[Ox*`F)enHv.||6@VAp#·E#FGitU,[dT-Χ,i[G)ϼ= K!܌° l6#3HuTAضQXNVW8ؾiuPOd6Vyz73}1Pa&KENkn-~ؓpх۷ZkhDLd0>>6(? JwfM)˭Q?c7pA8Jhi1ͣ#yA%nJCOQ8 ^ӺZuȔ;¿뫜 y yMC S5 ph;r&[Sa rUYQ7>id۷+:am S(M2x.-]8v"s ؚႥzVq˄d2ݵ zR"()m}wL I4hM"4c@G{<_u"a˰#/GȰd@RD?4𔸽qNgצ݋:&67>D ō.ZsҨTPvZd(Vj13C$>1Q=}#3?s/DF%&P| GX݀l&iЁ_޵"ڪRL@aЁ ؐXAT %w\nYtJ=Up S=S{*IwG/Vg=BpžEn.HZ_8yODŽ'o.,ϲDhww[Xv. ]u?sPUbuDóԸ?btQó: p6 P+D/ NPrQ"=cJ.BKE΍kL^<.q`Jb!>UgL+< uBgeg{`s$~Da٣Lb{9om]O*s~ T[Vel$[C y,:0a 6\,/ B1Ul)>Zճ˹GCuXXah/"~PWH_6Jm ˀ" oA'Tހ endstream endobj 227 0 obj << /Type /FontDescriptor /FontName /GJDUND+NimbusRomNo9L-ReguItal /Flags 4 /FontBBox [-169 -270 1010 924] /Ascent 668 /CapHeight 668 /Descent -193 /ItalicAngle -15 /StemV 78 /XHeight 441 /CharSet (/A/B/C/D/E/F/G/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/a/b/c/comma/d/e/eight/f/fi/five/four/g/h/hyphen/i/j/k/l/m/n/nine/o/one/p/parenleft/parenright/period/q/quoteleft/r/s/seven/six/t/three/two/u/v/w/x/y/z/zero) /FontFile 226 0 R >> endobj 181 0 obj << /Type /Encoding /Differences [2/fi/fl 35/numbersign 38/ampersand/quoteright/parenleft/parenright/asterisk 44/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon 61/equal 63/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y 91/bracketleft 93/bracketright 96/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z 147/quotedblleft/quotedblright 150/endash 173/hyphen] >> endobj 48 0 obj << /Type /Font /Subtype /Type1 /BaseFont /OMGDYW+CMEX10 /FontDescriptor 189 0 R /FirstChar 83 /LastChar 86 /Widths 178 0 R >> endobj 50 0 obj << /Type /Font /Subtype /Type1 /BaseFont /XRQSHG+CMMI5 /FontDescriptor 191 0 R /FirstChar 12 /LastChar 105 /Widths 176 0 R >> endobj 49 0 obj << /Type /Font /Subtype /Type1 /BaseFont /WYWESY+CMMI6 /FontDescriptor 193 0 R /FirstChar 11 /LastChar 119 /Widths 177 0 R >> endobj 83 0 obj << /Type /Font /Subtype /Type1 /BaseFont /WDAPQT+CMMI8 /FontDescriptor 195 0 R /FirstChar 12 /LastChar 118 /Widths 171 0 R >> endobj 12 0 obj << /Type /Font /Subtype /Type1 /BaseFont /KRIPTG+CMMI9 /FontDescriptor 197 0 R /FirstChar 11 /LastChar 121 /Widths 180 0 R >> endobj 120 0 obj << /Type /Font /Subtype /Type1 /BaseFont /YQTKCJ+CMR5 /FontDescriptor 199 0 R /FirstChar 40 /LastChar 50 /Widths 168 0 R >> endobj 51 0 obj << /Type /Font /Subtype /Type1 /BaseFont /KKYNBK+CMR6 /FontDescriptor 201 0 R /FirstChar 40 /LastChar 61 /Widths 175 0 R >> endobj 82 0 obj << /Type /Font /Subtype /Type1 /BaseFont /XUFFBP+CMR8 /FontDescriptor 203 0 R /FirstChar 1 /LastChar 93 /Widths 172 0 R >> endobj 18 0 obj << /Type /Font /Subtype /Type1 /BaseFont /JREDYN+CMR9 /FontDescriptor 205 0 R /FirstChar 1 /LastChar 124 /Widths 179 0 R >> endobj 85 0 obj << /Type /Font /Subtype /Type1 /BaseFont /XSOADY+CMSY5 /FontDescriptor 207 0 R /FirstChar 0 /LastChar 106 /Widths 169 0 R >> endobj 55 0 obj << /Type /Font /Subtype /Type1 /BaseFont /NUBZLI+CMSY6 /FontDescriptor 209 0 R /FirstChar 0 /LastChar 106 /Widths 174 0 R >> endobj 84 0 obj << /Type /Font /Subtype /Type1 /BaseFont /PRWEFQ+CMSY8 /FontDescriptor 211 0 R /FirstChar 0 /LastChar 106 /Widths 170 0 R >> endobj 8 0 obj << /Type /Font /Subtype /Type1 /BaseFont /TVTRRF+CMSY9 /FontDescriptor 213 0 R /FirstChar 0 /LastChar 106 /Widths 185 0 R >> endobj 124 0 obj << /Type /Font /Subtype /Type1 /BaseFont /ZORBSI+CMTI9 /FontDescriptor 215 0 R /FirstChar 71 /LastChar 71 /Widths 167 0 R >> endobj 61 0 obj << /Type /Font /Subtype /Type1 /BaseFont /SCAZVY+LASY9 /FontDescriptor 217 0 R /FirstChar 50 /LastChar 50 /Widths 173 0 R >> endobj 6 0 obj << /Type /Font /Subtype /Type1 /BaseFont /PPOJOV+NimbusSanL-Bold /FontDescriptor 219 0 R /FirstChar 2 /LastChar 173 /Widths 187 0 R /Encoding 181 0 R >> endobj 7 0 obj << /Type /Font /Subtype /Type1 /BaseFont /VVBTXO+NimbusSanL-Regu /FontDescriptor 221 0 R /FirstChar 44 /LastChar 173 /Widths 186 0 R /Encoding 181 0 R >> endobj 9 0 obj << /Type /Font /Subtype /Type1 /BaseFont /IDLREL+NimbusRomNo9L-Medi /FontDescriptor 223 0 R /FirstChar 2 /LastChar 173 /Widths 184 0 R /Encoding 181 0 R >> endobj 10 0 obj << /Type /Font /Subtype /Type1 /BaseFont /NDILWE+NimbusRomNo9L-Regu /FontDescriptor 225 0 R /FirstChar 2 /LastChar 173 /Widths 183 0 R /Encoding 181 0 R >> endobj 11 0 obj << /Type /Font /Subtype /Type1 /BaseFont /GJDUND+NimbusRomNo9L-ReguItal /FontDescriptor 227 0 R /FirstChar 2 /LastChar 122 /Widths 182 0 R /Encoding 181 0 R >> endobj 13 0 obj << /Type /Pages /Count 6 /Parent 228 0 R /Kids [ 4 0 R 16 0 R 46 0 R 53 0 R 59 0 R 80 0 R ] >> endobj 91 0 obj << /Type /Pages /Count 6 /Parent 228 0 R /Kids [ 89 0 R 103 0 R 118 0 R 122 0 R 162 0 R 165 0 R ] >> endobj 228 0 obj << /Type /Pages /Count 12 /Kids [ 13 0 R 91 0 R ] >> endobj 229 0 obj << /Type /Catalog /Pages 228 0 R >> endobj 230 0 obj << /Producer (MiKTeX pdfTeX-1.40.3) /Creator (TeX) /CreationDate (D:20070710235942-07'00') /ModDate (D:20070722031705+02'00') /Trapped /False /PTEX.Fullbanner (This is MiKTeX-pdfTeX 2.6.2693 \(1.40.3\)) >> endobj 231 0 obj << /Length 0 /LC /QQAP >> stream endstream endobj 232 0 obj << /Type /Font /Subtype /Type1 /BaseFont /Helvetica /Encoding /WinAnsiEncoding >> endobj 233 0 obj << /Length 0 /LC /QQAP >> stream endstream endobj 234 0 obj << /Length 0 /LC /QQAP >> stream endstream endobj 235 0 obj << /Length 0 /LC /QQAP >> stream endstream endobj 236 0 obj << /Length 0 /LC /QQAP >> stream endstream endobj 237 0 obj << /Length 0 /LC /QQAP >> stream endstream endobj 238 0 obj << /Length 0 /LC /QQAP >> stream endstream endobj 239 0 obj << /Length 0 /LC /QQAP >> stream endstream endobj 240 0 obj << /Length 0 /LC /QQAP >> stream endstream endobj 241 0 obj << /Length 0 /LC /QQAP >> stream endstream endobj 242 0 obj << /Length 0 /LC /QQAP >> stream endstream endobj 243 0 obj << /Length 0 /LC /QQAP >> stream endstream endobj xref 0 244 0000000000 65535 f 0000028815 00000 n 0000034042 00000 n 0000015233 00000 n 0000015122 00000 n 0000000015 00000 n 0000494338 00000 n 0000494506 00000 n 0000493915 00000 n 0000494675 00000 n 0000494846 00000 n 0000495018 00000 n 0000492790 00000 n 0000495194 00000 n 0000041528 00000 n 0000043541 00000 n 0000028701 00000 n 0000015393 00000 n 0000493352 00000 n 0000033415 00000 n 0000033603 00000 n 0000033649 00000 n 0000033721 00000 n 0000033795 00000 n 0000033864 00000 n 0000033954 00000 n 0000033975 00000 n 0000039902 00000 n 0000040102 00000 n 0000040148 00000 n 0000040222 00000 n 0000040294 00000 n 0000040473 00000 n 0000040542 00000 n 0000040610 00000 n 0000040683 00000 n 0000040704 00000 n 0000040936 00000 n 0000042965 00000 n 0000043178 00000 n 0000043224 00000 n 0000043296 00000 n 0000043365 00000 n 0000043455 00000 n 0000043476 00000 n 0000066602 00000 n 0000066488 00000 n 0000043730 00000 n 0000492222 00000 n 0000492506 00000 n 0000492364 00000 n 0000493073 00000 n 0000096157 00000 n 0000096043 00000 n 0000066800 00000 n 0000493633 00000 n 0000124372 00000 n 0000127982 00000 n 0000138681 00000 n 0000124258 00000 n 0000096356 00000 n 0000494197 00000 n 0000127507 00000 n 0000127701 00000 n 0000127747 00000 n 0000127819 00000 n 0000127888 00000 n 0000127961 00000 n 0000131553 00000 n 0000131767 00000 n 0000131813 00000 n 0000131998 00000 n 0000132067 00000 n 0000132157 00000 n 0000132178 00000 n 0000132394 00000 n 0000132621 00000 n 0000132716 00000 n 0000132785 00000 n 0000172249 00000 n 0000172135 00000 n 0000138942 00000 n 0000493213 00000 n 0000492648 00000 n 0000493774 00000 n 0000493492 00000 n 0000196492 00000 n 0000227355 00000 n 0000206859 00000 n 0000196378 00000 n 0000172496 00000 n 0000495305 00000 n 0000199815 00000 n 0000200027 00000 n 0000200073 00000 n 0000200259 00000 n 0000200328 00000 n 0000200401 00000 n 0000200422 00000 n 0000200639 00000 n 0000200866 00000 n 0000200962 00000 n 0000230830 00000 n 0000227238 00000 n 0000207096 00000 n 0000230317 00000 n 0000230529 00000 n 0000230576 00000 n 0000230646 00000 n 0000230738 00000 n 0000230760 00000 n 0000273631 00000 n 0000278582 00000 n 0000284195 00000 n 0000289790 00000 n 0000292544 00000 n 0000294899 00000 n 0000258519 00000 n 0000258402 00000 n 0000231081 00000 n 0000492932 00000 n 0000297302 00000 n 0000273514 00000 n 0000258742 00000 n 0000494055 00000 n 0000278094 00000 n 0000278294 00000 n 0000278341 00000 n 0000278413 00000 n 0000278483 00000 n 0000278560 00000 n 0000283707 00000 n 0000283907 00000 n 0000283954 00000 n 0000284026 00000 n 0000284103 00000 n 0000284173 00000 n 0000289302 00000 n 0000289502 00000 n 0000289549 00000 n 0000289626 00000 n 0000289696 00000 n 0000289768 00000 n 0000292073 00000 n 0000292256 00000 n 0000292303 00000 n 0000292380 00000 n 0000292452 00000 n 0000292522 00000 n 0000294428 00000 n 0000294611 00000 n 0000294658 00000 n 0000294730 00000 n 0000294800 00000 n 0000294877 00000 n 0000296831 00000 n 0000297014 00000 n 0000297061 00000 n 0000297138 00000 n 0000297210 00000 n 0000297280 00000 n 0000328096 00000 n 0000327979 00000 n 0000297564 00000 n 0000349992 00000 n 0000349875 00000 n 0000328261 00000 n 0000350133 00000 n 0000350158 00000 n 0000350244 00000 n 0000350937 00000 n 0000351604 00000 n 0000352263 00000 n 0000352840 00000 n 0000352865 00000 n 0000353478 00000 n 0000353629 00000 n 0000354211 00000 n 0000354872 00000 n 0000354915 00000 n 0000355647 00000 n 0000491774 00000 n 0000356334 00000 n 0000356809 00000 n 0000357467 00000 n 0000358129 00000 n 0000358788 00000 n 0000359309 00000 n 0000359969 00000 n 0000361803 00000 n 0000362044 00000 n 0000364575 00000 n 0000364808 00000 n 0000372179 00000 n 0000372471 00000 n 0000379011 00000 n 0000379306 00000 n 0000391576 00000 n 0000391945 00000 n 0000394186 00000 n 0000394437 00000 n 0000396933 00000 n 0000397194 00000 n 0000401312 00000 n 0000401647 00000 n 0000406729 00000 n 0000407092 00000 n 0000408493 00000 n 0000408728 00000 n 0000410549 00000 n 0000410809 00000 n 0000412768 00000 n 0000413041 00000 n 0000416946 00000 n 0000417352 00000 n 0000419163 00000 n 0000419384 00000 n 0000421105 00000 n 0000421320 00000 n 0000429898 00000 n 0000430193 00000 n 0000436973 00000 n 0000437284 00000 n 0000454712 00000 n 0000455165 00000 n 0000474377 00000 n 0000474923 00000 n 0000491337 00000 n 0000495422 00000 n 0000495492 00000 n 0000495545 00000 n 0000495768 00000 n 0000495829 00000 n 0000495928 00000 n 0000495989 00000 n 0000496050 00000 n 0000496111 00000 n 0000496172 00000 n 0000496233 00000 n 0000496294 00000 n 0000496355 00000 n 0000496416 00000 n 0000496477 00000 n 0000496538 00000 n trailer << /Size 244 /Root 229 0 R /Info 230 0 R /ID [ <6BCC795BE49244E0C838E6A163CC22D9> <6BCC795BE49244E0C838E6A163CC22D9> ] >> startxref 496599 %%EOF