{"id":964224,"date":"2023-08-27T12:28:52","date_gmt":"2023-08-27T19:28:52","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&p=964224"},"modified":"2023-10-04T15:29:46","modified_gmt":"2023-10-04T22:29:46","slug":"improved-diversity-maximization-algorithms-for-matching-and-pseudoforest","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/improved-diversity-maximization-algorithms-for-matching-and-pseudoforest\/","title":{"rendered":"Improved Diversity Maximization Algorithms for Matching and Pseudoforest"},"content":{"rendered":"

In this work we consider the diversity maximization problem, where given a data set X<\/span><\/span><\/span><\/span> of n<\/span><\/span><\/span><\/span> elements, and a parameter k<\/span><\/span><\/span><\/span>, the goal is to pick a subset of X<\/span><\/span><\/span><\/span> of size k<\/span><\/span><\/span><\/span> maximizing a certain diversity measure. [CH01] defined a variety of diversity measures based on pairwise distances between the points. A constant factor approximation algorithm was known for all those diversity measures except “remote-matching”, where only an O<\/span>(<\/span>log <\/span><\/span>k<\/span>)<\/span><\/span><\/span><\/span> approximation was known. In this work we present an O<\/span>(<\/span>1<\/span>)<\/span><\/span><\/span><\/span> approximation for this remaining notion. Further, we consider these notions from the perspective of composable coresets. [IMMM14] provided composable coresets with a constant factor approximation for all but “remote-pseudoforest” and “remote-matching”, which again they only obtained a O<\/span>(<\/span>log <\/span><\/span>k<\/span>)<\/span><\/span><\/span><\/span> approximation. Here we also close the gap up to constants and present a constant factor composable coreset algorithm for these two notions. For remote-matching, our coreset has size only O<\/span>(<\/span>k<\/span>)<\/span><\/span><\/span><\/span>, and for remote-pseudoforest, our coreset has size O<\/span>(<\/span>k^{<\/span>1<\/span>+<\/span>\u03b5}<\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span> for any \u03b5<\/span>><\/span>0<\/span><\/span><\/span><\/span>, for an O<\/span>(<\/span>1<\/span>\/<\/span><\/span><\/span>\u03b5<\/span>)<\/span><\/span><\/span><\/span>-approximate coreset.<\/p>\n","protected":false},"excerpt":{"rendered":"

In this work we consider the diversity maximization problem, where given a data set X of n elements, and a parameter k, the goal is to pick a subset of X of size k maximizing a certain diversity measure. [CH01] defined a variety of diversity measures based on pairwise distances between the points. A constant 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Mahabadi","user_id":40780,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=Sepideh Mahabadi"},{"type":"text","value":"Shyam Narayanan","user_id":0,"rest_url":false}],"msr_impact_theme":[],"msr_research_lab":[199565],"msr_event":[],"msr_group":[437022],"msr_project":[],"publication":[],"video":[],"download":[],"msr_publication_type":"inproceedings","related_content":[],"_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/964224"}],"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\/964224\/revisions"}],"predecessor-version":[{"id":964230,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/964224\/revisions\/964230"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=964224"}],"wp:term":[{"taxonomy":"msr-content-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-content-type?post=964224"},{"taxonomy":"msr-research-highlight","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-highlight?post=964224"},{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=964224"},{"taxonomy":"msr-publication-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-publication-type?post=964224"},{"taxonomy":"msr-product-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-product-type?post=964224"},{"taxonomy":"msr-focus-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-focus-area?post=964224"},{"taxonomy":"msr-platform","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-platform?post=964224"},{"taxonomy":"msr-download-source","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-download-source?post=964224"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=964224"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=964224"},{"taxonomy":"msr-field-of-study","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-field-of-study?post=964224"},{"taxonomy":"msr-conference","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-conference?post=964224"},{"taxonomy":"msr-journal","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-journal?post=964224"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=964224"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=964224"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}