{"id":955893,"date":"2023-07-18T13:32:04","date_gmt":"2023-07-18T20:32:04","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&p=955893"},"modified":"2023-07-18T13:32:04","modified_gmt":"2023-07-18T20:32:04","slug":"approximation-algorithms-for-fair-range-clustering","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/approximation-algorithms-for-fair-range-clustering\/","title":{"rendered":"Approximation Algorithms for Fair Range Clustering"},"content":{"rendered":"

This paper studies the fair range clustering problem in which the data points are from different demographic groups and the goal is to pick k<\/span><\/span><\/span><\/span> centers with the minimum clustering cost such that each group is at least minimally represented in the centers set and no group dominates the centers set. More precisely, given a set of n<\/span><\/span><\/span><\/span> points in a metric space (<\/span>P<\/span>,<\/span>d<\/span>)<\/span><\/span><\/span><\/span> where each point belongs to one of the \u2113<\/span><\/span><\/span><\/span> different demographics (i.e., P<\/span>=<\/span>P_<\/span>1<\/span><\/span>\u228e<\/span>P_<\/span>2<\/span><\/span>\u228e<\/span>\u22ef<\/span>\u228e<\/span>P_<\/span>\u2113<\/span><\/span><\/span><\/span><\/span>) and a set of \u2113<\/span><\/span><\/span><\/span> intervals [<\/span>\u03b1_<\/span>1<\/span><\/span>,<\/span>\u03b2_<\/span>1<\/span><\/span>]<\/span>,<\/span>\u22ef<\/span>,<\/span>[<\/span>\u03b1_<\/span>\u2113<\/span><\/span>,<\/span>\u03b2_<\/span>\u2113<\/span><\/span>]<\/span><\/span><\/span><\/span> on desired number of centers from each group, the goal is to pick a set of k<\/span><\/span><\/span><\/span> centers C<\/span><\/span><\/span><\/span> with minimum \u2113_<\/span>p<\/span><\/span><\/span><\/span><\/span>-clustering cost (i.e., (<\/span>\u2211_{<\/span>v<\/span>\u2208<\/span>P}<\/span><\/span><\/span><\/span>d<\/span>(<\/span>v<\/span>,<\/span>C<\/span>)^<\/span>p<\/span><\/span>)^{<\/span>1<\/span>\/<\/span><\/span><\/span>p}<\/span><\/span><\/span><\/span><\/span><\/span><\/span>) such that for each group i<\/span>\u2208<\/span>\u2113<\/span><\/span><\/span><\/span>, |<\/span><\/span><\/span>C<\/span>\u2229<\/span>P_<\/span>i<\/span><\/span>|<\/span><\/span><\/span>\u2208<\/span>[<\/span>\u03b1_<\/span>i<\/span><\/span>,<\/span>\u03b2_<\/span>i<\/span><\/span>]<\/span><\/span><\/span><\/span>. In particular, the fair range \u2113_<\/span>p<\/span><\/span><\/span><\/span><\/span>-clustering captures fair range k<\/span><\/span><\/span><\/span>-center, k<\/span><\/span><\/span><\/span>-median and k<\/span><\/span><\/span><\/span>-means as its special cases. In this work, we provide efficient constant factor approximation algorithms for fair range \u2113_<\/span>p<\/span><\/span><\/span><\/span><\/span>-clustering for all values of p<\/span>\u2208<\/span>[<\/span>1<\/span>,<\/span>\u221e<\/span>).$<\/span><\/span><\/span><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

This paper studies the fair range clustering problem in which the data points are from different demographic groups and the goal is to pick k centers with the minimum clustering cost such that each group is at least minimally represented in the centers set and no group dominates the centers set. More precisely, given a […]<\/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":"","msr-author-ordering":null,"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"ICML","msr_doi":"","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"","msr_other_contributors":"","msr_speaker":"","msr_award":"","msr_affiliation":"","msr_institution":"","msr_host":"","msr_version":"","msr_duration":"","msr_original_fields_of_study":"","msr_release_tracker_id":"","msr_s2_match_type":"","msr_citation_count_updated":"","msr_published_date":"2023-7-1","msr_highlight_text":"","msr_notes":"","msr_longbiography":"","msr_publicationurl":"","msr_external_url":"","msr_secondary_video_url":"","msr_conference_url":"","msr_journal_url":"","msr_s2_pdf_url":"","msr_year":0,"msr_citation_count":0,"msr_influential_citations":0,"msr_reference_count":0,"msr_s2_match_confidence":0,"msr_microsoftintellectualproperty":true,"msr_s2_open_access":false,"msr_s2_author_ids":[],"msr_pub_ids":[],"msr_hide_image_in_river":0,"footnotes":""},"msr-research-highlight":[],"research-area":[13561],"msr-publication-type":[193716],"msr-publisher":[],"msr-focus-area":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[246691],"msr-conference":[260284],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-955893","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-algorithms","msr-locale-en_us","msr-field-of-study-computer-science"],"msr_publishername":"","msr_edition":"","msr_affiliation":"","msr_published_date":"2023-7-1","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":"","msr_doi":"","msr_publication_uploader":[{"type":"url","viewUrl":"false","id":"false","title":"https:\/\/arxiv.org\/abs\/2306.06778","label_id":"243109","label":0}],"msr_related_uploader":"","msr_citation_count":0,"msr_citation_count_updated":"","msr_s2_paper_id":"","msr_influential_citations":0,"msr_reference_count":0,"msr_arxiv_id":"","msr_s2_author_ids":[],"msr_s2_open_access":false,"msr_s2_pdf_url":null,"msr_attachments":[],"msr-author-ordering":[{"type":"text","value":"S\u00e8djro S. Hotegni","user_id":0,"rest_url":false},{"type":"user_nicename","value":"Sepideh 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":"Ali Vakilian","user_id":0,"rest_url":false}],"msr_impact_theme":[],"msr_research_lab":[199565],"msr_event":[],"msr_group":[437022],"msr_project":[],"publication":[],"video":[],"msr-tool":[],"msr_publication_type":"inproceedings","related_content":[],"_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/955893","targetHints":{"allow":["GET"]}}],"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":3,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/955893\/revisions"}],"predecessor-version":[{"id":955932,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/955893\/revisions\/955932"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=955893"}],"wp:term":[{"taxonomy":"msr-research-highlight","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-highlight?post=955893"},{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=955893"},{"taxonomy":"msr-publication-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-publication-type?post=955893"},{"taxonomy":"msr-publisher","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-publisher?post=955893"},{"taxonomy":"msr-focus-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-focus-area?post=955893"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=955893"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=955893"},{"taxonomy":"msr-field-of-study","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-field-of-study?post=955893"},{"taxonomy":"msr-conference","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-conference?post=955893"},{"taxonomy":"msr-journal","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-journal?post=955893"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=955893"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=955893"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}