{"id":168322,"date":"2015-01-01T00:00:00","date_gmt":"2015-01-01T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/on-1-eps-restricted-assignment-makespan-minimization\/"},"modified":"2018-10-16T20:15:09","modified_gmt":"2018-10-17T03:15:09","slug":"on-1-eps-restricted-assignment-makespan-minimization","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/on-1-eps-restricted-assignment-makespan-minimization\/","title":{"rendered":"On (1, eps)-Restricted Assignment Makespan Minimization"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Makespan minimization on unrelated machines is a classic problem in approximation algorithms. No polynomial time (2 &#8212; <i>\u03b4<\/i>)-approximation algorithm is known for the problem for constant <i>\u03b4<\/i> > 0. This is true even for certain special cases, most notably the <i>restricted assignment<\/i> problem where each job has the same load on any machine but can be assigned to one from a specified subset. Recently in a breakthrough result, Svensson [16] proved that the integrality gap of a certain configuration LP relaxation is upper bounded by 1.95 for the restricted assignment problem; however, the rounding algorithm is <i>not known<\/i> to run in polynomial time.<\/p>\n<p>In this paper we consider the (1, \u03b5)-restricted assignment problem where each job is either heavy (<i>p<\/i><sub><i>j<\/i><\/sub> = 1) or light (<i>p<\/i><sub><i>j<\/i><\/sub> = \u03b5), for some parameter \u03b5 > 0. Our main result is a (2 &#8212; <i>\u03b4<\/i>)-approximate <i>polynomial time<\/i> algorithm for the (1, \u03b5)-restricted assignment problem for a fixed constant <i>\u03b4<\/i> > 0. Even for this special case, the best polynomial-time approximation factor known so far is 2. We obtain this result by rounding the configuration LP relaxation for this problem. A simple reduction from vertex cover shows that this special case remains NP-hard to approximate to within a factor better than 7\/6.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Makespan minimization on unrelated machines is a classic problem in approximation algorithms. No polynomial time (2 &#8212; \u03b4)-approximation algorithm is known for the problem for constant \u03b4 > 0. This is true even for certain special cases, most notably the restricted assignment problem where each job has the same load on any machine but can [&hellip;]<\/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":[],"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":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-168322","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-algorithms","msr-locale-en_us"],"msr_publishername":"Society for Industrial and Applied Mathematics Philadelphia, PA, USA","msr_edition":"SODA '15 Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, San Diego, California","msr_affiliation":"","msr_published_date":"2015-01-04","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"Proceedings of SODA","msr_pages_string":"1087-1101","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":"","msr_release_tracker_id":"","msr_original_fields_of_study":"","msr_download_urls":"","msr_external_url":"","msr_secondary_video_url":"","msr_longbiography":"","msr_microsoftintellectualproperty":1,"msr_main_download":"324197","msr_publicationurl":"","msr_doi":"","msr_publication_uploader":[{"type":"file","title":"On (1, \u03b5)-Restricted Assignment Makespan Minimization","viewUrl":"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2015\/01\/On-1-E-Restricted-Assignment-Makespan-Minimization.pdf","id":324197,"label_id":0}],"msr_related_uploader":"","msr_attachments":[],"msr-author-ordering":[{"type":"user_nicename","value":"dechakr","user_id":31593,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=dechakr"},{"type":"text","value":"Sanjeev Khanna","user_id":0,"rest_url":false},{"type":"text","value":"Shi Li","user_id":0,"rest_url":false}],"msr_impact_theme":[],"msr_research_lab":[199562],"msr_event":[],"msr_group":[144938,144924],"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\/168322"}],"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":2,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/168322\/revisions"}],"predecessor-version":[{"id":524838,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/168322\/revisions\/524838"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=168322"}],"wp:term":[{"taxonomy":"msr-content-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-content-type?post=168322"},{"taxonomy":"msr-research-highlight","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-highlight?post=168322"},{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=168322"},{"taxonomy":"msr-publication-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-publication-type?post=168322"},{"taxonomy":"msr-product-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-product-type?post=168322"},{"taxonomy":"msr-focus-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-focus-area?post=168322"},{"taxonomy":"msr-platform","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-platform?post=168322"},{"taxonomy":"msr-download-source","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-download-source?post=168322"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=168322"},{"taxonomy":"msr-field-of-study","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-field-of-study?post=168322"},{"taxonomy":"msr-conference","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-conference?post=168322"},{"taxonomy":"msr-journal","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-journal?post=168322"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=168322"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=168322"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}