{"id":479862,"date":"2018-04-16T06:38:47","date_gmt":"2018-04-16T13:38:47","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&#038;p=479862"},"modified":"2021-11-29T18:07:26","modified_gmt":"2021-11-30T02:07:26","slug":"online-dynamic-algorithms-set-cover","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/online-dynamic-algorithms-set-cover\/","title":{"rendered":"Online and dynamic algorithms for set cover"},"content":{"rendered":"<p>In this paper, we give new results for the set cover problem in the fully dynamic model. In this model, the set of active\u0080\u009d elements to be covered changes over time. The goal is to maintain a near-optimal solution for the currently active elements, while making few changes in each timestep. This model is popular in both dynamic and online algorithms: in the former, the goal is to minimize the update time of the solution, while in the latter, the recourse (number of changes) is bounded. We present generic techniques for the dynamic set cover problem inspired by the classic greedy and primal-dual offline algorithms for set cover. The former leads to a competitive ratio of <i>O<\/i>(log<i>n<\/i><sub><i>t<\/i><\/sub>), where <i>n<\/i><sub><i>t<\/i><\/sub> is the number of currently active elements at timestep <i>t<\/i>, while the latter yields competitive ratios dependent on <i>f<\/i><sub><i>t<\/i><\/sub>, the maximum number of sets that a currently active element belongs to. We demonstrate that these techniques are useful for obtaining tight results in both settings: update time bounds and limited recourse, exhibiting algorithmic techniques common to these two parallel threads of research.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In this paper, we give new results for the set cover problem in the fully dynamic model. In this model, the set of active\u0080\u009d elements to be covered changes over time. The goal is to maintain a near-optimal solution for the currently active elements, while making few changes in each timestep. This model is popular [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","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-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-479862","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-algorithms","msr-locale-en_us"],"msr_publishername":"ACM","msr_edition":"","msr_affiliation":"","msr_published_date":"2017-6-19","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":"","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":"","msr_publicationurl":"https:\/\/dl.acm.org\/citation.cfm?doid=3055399.3055493","msr_doi":"","msr_publication_uploader":[{"type":"url","viewUrl":"false","id":"false","title":"https:\/\/dl.acm.org\/citation.cfm?doid=3055399.3055493","label_id":"243109","label":0}],"msr_related_uploader":"","msr_attachments":[{"id":0,"url":"https:\/\/dl.acm.org\/citation.cfm?doid=3055399.3055493"}],"msr-author-ordering":[{"type":"user_nicename","value":"Ravishankar Krishnaswamy","user_id":33330,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=Ravishankar Krishnaswamy"},{"type":"text","value":"Anupam Gupta","user_id":0,"rest_url":false},{"type":"text","value":"Amit Kumar","user_id":0,"rest_url":false},{"type":"text","value":"Debmalya Panigrahi","user_id":0,"rest_url":false}],"msr_impact_theme":[],"msr_research_lab":[199562],"msr_event":[],"msr_group":[144924,144938],"msr_project":[800338],"publication":[],"video":[],"download":[],"msr_publication_type":"inproceedings","related_content":{"projects":[{"ID":800338,"post_title":"Optimization with Uncertainty","post_name":"optimization-with-uncertainty","post_type":"msr-project","post_date":"2021-11-29 18:01:50","post_modified":"2021-11-29 18:02:20","post_status":"publish","permalink":"https:\/\/www.microsoft.com\/en-us\/research\/project\/optimization-with-uncertainty\/","post_excerpt":"Classical algorithms (exact\/ approximation) work with an input which is entirely specified up front. While this offline model is useful for static optimization problems, there are several domains which need algorithms to make decisions with partial\/uncertain information which evolves over time. We seek to design algorithms in such uncertain environments and also design frameworks to evaluate their quality using different metrics. Models such as online algorithms, stochastic optimization, and algorithms with recourse fall into this&hellip;","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-project\/800338"}]}}]},"_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/479862"}],"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\/479862\/revisions"}],"predecessor-version":[{"id":479865,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/479862\/revisions\/479865"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=479862"}],"wp:term":[{"taxonomy":"msr-content-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-content-type?post=479862"},{"taxonomy":"msr-research-highlight","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-highlight?post=479862"},{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=479862"},{"taxonomy":"msr-publication-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-publication-type?post=479862"},{"taxonomy":"msr-product-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-product-type?post=479862"},{"taxonomy":"msr-focus-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-focus-area?post=479862"},{"taxonomy":"msr-platform","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-platform?post=479862"},{"taxonomy":"msr-download-source","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-download-source?post=479862"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=479862"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=479862"},{"taxonomy":"msr-field-of-study","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-field-of-study?post=479862"},{"taxonomy":"msr-conference","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-conference?post=479862"},{"taxonomy":"msr-journal","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-journal?post=479862"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=479862"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=479862"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}