We consider mining dense substructures (maximal cliques) from an uncertain graph, which is a probability distribution on a set of deterministic graphs. For parameter 0 < \u03b1 < 1, we consider the notion of an \u03b1-maximal clique in an uncertain graph. We present matching upper and lower bounds on the number of \u03b1-maximal cliques possible within a (uncertain) graph. We present an algorithm to enumerate \u03b1-maximal cliques whose worst-case runtime is near-optimal, and an experimental evaluation showing the practical utility of the algorithm.<\/p>\n","protected":false},"excerpt":{"rendered":"
We consider mining dense substructures (maximal cliques) from an uncertain graph, which is a probability distribution on a set of deterministic graphs. For parameter 0 < \u03b1 < 1, we consider the notion of an \u03b1-maximal clique in an uncertain graph. We present matching upper and lower bounds on the number of \u03b1-maximal cliques possible […]\n<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"footnotes":""},"msr-content-type":[3],"msr-research-highlight":[246574],"research-area":[13561],"msr-publication-type":[193716],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-field-of-study":[249475,250741,265347,267609,267606,260257,250747,246691,249139,267603,250813,267600,252823,250738,250870,267597,267594,267591,252826],"msr-conference":[266118],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-925062","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-highlight-award","msr-research-area-algorithms","msr-locale-en_us","msr-field-of-study-algorithm-design","msr-field-of-study-block-graph","msr-field-of-study-clique","msr-field-of-study-clique-graph-theory","msr-field-of-study-clique-graph","msr-field-of-study-clique-width","msr-field-of-study-combinatorics","msr-field-of-study-computer-science","msr-field-of-study-discrete-mathematics","msr-field-of-study-factor-critical-graph","msr-field-of-study-graph","msr-field-of-study-intersection-number-graph-theory","msr-field-of-study-null-graph","msr-field-of-study-pathwidth","msr-field-of-study-power-graph-analysis","msr-field-of-study-simplex-graph","msr-field-of-study-split-graph","msr-field-of-study-trivially-perfect-graph","msr-field-of-study-voltage-graph"],"msr_publishername":"IEEE","msr_edition":"","msr_affiliation":"","msr_published_date":"2015-4-12","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"","msr_chapter":"","msr_isbn":"","msr_journal":"","msr_volume":"","msr_number":"","msr_editors":"","msr_series":"","msr_issue":"","msr_organization":"","msr_how_published":"","msr_notes":"","msr_highlight_text":"Invited to a special issue of the journal IEEE TKDE for the best five papers from ICDE 2015.","msr_release_tracker_id":"","msr_original_fields_of_study":"","msr_download_urls":"","msr_external_url":"","msr_secondary_video_url":"","msr_longbiography":"","msr_microsoftintellectualproperty":0,"msr_main_download":"","msr_publicationurl":"","msr_doi":"","msr_publication_uploader":[{"type":"doi","viewUrl":"false","id":"false","title":"10.1109\/ICDE.2015.7113288","label_id":"243106","label":0},{"type":"url","viewUrl":"false","id":"false","title":"https:\/\/lib.dr.iastate.edu\/cgi\/viewcontent.cgi?article=1047&context=ece_conf","label_id":"243132","label":0},{"type":"url","viewUrl":"false","id":"false","title":"https:\/\/arxiv.org\/abs\/1310.6780","label_id":"243109","label":0},{"type":"url","viewUrl":"false","id":"false","title":"https:\/\/dblp.uni-trier.de\/db\/conf\/icde\/icde2015.html#MukherjeeXT15","label_id":"243109","label":0},{"type":"url","viewUrl":"false","id":"false","title":"https:\/\/ieeexplore.ieee.org\/document\/7113288\/","label_id":"243109","label":0},{"type":"url","viewUrl":"false","id":"false","title":"https:\/\/lib.dr.iastate.edu\/ece_conf\/43\/","label_id":"243109","label":0}],"msr_related_uploader":"","msr_attachments":[],"msr-author-ordering":[{"type":"user_nicename","value":"Arko Mukherjee","user_id":42639,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=Arko Mukherjee"},{"type":"guest","value":"pan-xu","user_id":925065,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=pan-xu"},{"type":"guest","value":"srikanta-tirthapura","user_id":925044,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=srikanta-tirthapura"}],"msr_impact_theme":[],"msr_research_lab":[],"msr_event":[],"msr_group":[],"msr_project":[],"publication":[],"video":[],"download":[],"msr_publication_type":"inproceedings","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/925062"}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-research-item"}],"version-history":[{"count":1,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/925062\/revisions"}],"predecessor-version":[{"id":925068,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/925062\/revisions\/925068"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=925062"}],"wp:term":[{"taxonomy":"msr-content-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-content-type?post=925062"},{"taxonomy":"msr-research-highlight","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-highlight?post=925062"},{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=925062"},{"taxonomy":"msr-publication-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-publication-type?post=925062"},{"taxonomy":"msr-product-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-product-type?post=925062"},{"taxonomy":"msr-focus-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-focus-area?post=925062"},{"taxonomy":"msr-platform","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-platform?post=925062"},{"taxonomy":"msr-download-source","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-download-source?post=925062"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=925062"},{"taxonomy":"msr-field-of-study","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-field-of-study?post=925062"},{"taxonomy":"msr-conference","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-conference?post=925062"},{"taxonomy":"msr-journal","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-journal?post=925062"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=925062"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=925062"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}