{"id":"https://openalex.org/W7162780230","doi":"https://doi.org/10.48550/arxiv.2605.29165","title":"An Improved Greedy Approximation for (Metric) $k$-Means","display_name":"An Improved Greedy Approximation for (Metric) $k$-Means","publication_year":2026,"publication_date":"2026-05-27","ids":{"openalex":"https://openalex.org/W7162780230","doi":"https://doi.org/10.48550/arxiv.2605.29165"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.29165","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.29165","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.29165","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137397135","display_name":"Moses Charikar","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Charikar, Moses","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137317794","display_name":"Vincent Cohen-Addad","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cohen-Addad, Vincent","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083209855","display_name":"Ruiquan Gao","orcid":"https://orcid.org/0009-0006-9837-8598"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gao, Ruiquan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034276567","display_name":"Fabrizio Grandoni","orcid":"https://orcid.org/0000-0002-9676-4931"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Grandoni, Fabrizio","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137318273","display_name":"Euiwoong Lee","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lee, Euiwoong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5003496696","display_name":"Ernest van Wijland","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"van Wijland, Ernest","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11502","display_name":"Facility Location and Emergency Management","score":0.8891000151634216,"subfield":{"id":"https://openalex.org/subfields/1407","display_name":"Organizational Behavior and Human Resource Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11502","display_name":"Facility Location and Emergency Management","score":0.8891000151634216,"subfield":{"id":"https://openalex.org/subfields/1407","display_name":"Organizational Behavior and Human Resource Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.03400000184774399,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.022099999710917473,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/leverage","display_name":"Leverage (statistics)","score":0.5598999857902527},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.5490999817848206},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.5385000109672546},{"id":"https://openalex.org/keywords/facility-location-problem","display_name":"Facility location problem","score":0.5045999884605408},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.47589999437332153},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.45249998569488525},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.4433000087738037},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.4417000114917755}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5974000096321106},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5895000100135803},{"id":"https://openalex.org/C153083717","wikidata":"https://www.wikidata.org/wiki/Q6535263","display_name":"Leverage (statistics)","level":2,"score":0.5598999857902527},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.5490999817848206},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.5385000109672546},{"id":"https://openalex.org/C108005400","wikidata":"https://www.wikidata.org/wiki/Q1305598","display_name":"Facility location problem","level":2,"score":0.5045999884605408},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.47589999437332153},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.45249998569488525},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.4433000087738037},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.4417000114917755},{"id":"https://openalex.org/C182964748","wikidata":"https://www.wikidata.org/wiki/Q208216","display_name":"Triangle inequality","level":2,"score":0.41929998993873596},{"id":"https://openalex.org/C51823790","wikidata":"https://www.wikidata.org/wiki/Q504353","display_name":"Greedy algorithm","level":2,"score":0.4081999957561493},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.40790000557899475},{"id":"https://openalex.org/C206729178","wikidata":"https://www.wikidata.org/wiki/Q2271896","display_name":"Scheduling (production processes)","level":2,"score":0.3596999943256378},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32839998602867126},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.3237999975681305},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3172000050544739},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.2892000079154968},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2831999957561493},{"id":"https://openalex.org/C21080849","wikidata":"https://www.wikidata.org/wiki/Q13611879","display_name":"Data point","level":2,"score":0.26339998841285706},{"id":"https://openalex.org/C164866538","wikidata":"https://www.wikidata.org/wiki/Q367351","display_name":"Cluster (spacecraft)","level":2,"score":0.2590000033378601},{"id":"https://openalex.org/C99140742","wikidata":"https://www.wikidata.org/wiki/Q843550","display_name":"Polynomial-time approximation scheme","level":3,"score":0.251800000667572}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.29165","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.29165","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.29165","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.29165","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Clustering":[0],"is":[1,26,43,123,224,238],"a":[2,33,38,75,164],"basic":[3],"task":[4],"in":[5,37,81,91,106,157,179,246],"data":[6],"analysis":[7,204],"and":[8,11,99,202],"machine":[9],"learning,":[10],"the":[12,23,28,41,59,88,104,114,132,170,176,191,206,242,255],"optimization":[13,19],"of":[14,35,61,64,146,199,208],"clustering":[15],"objectives":[16],"are":[17],"well-studied":[18],"problems;":[20],"amongst":[21],"these,":[22],"$k$-Means":[24,80,122,141],"objective":[25],"arguably":[27],"most":[29],"well":[30],"known.":[31],"Given":[32],"collection":[34],"points":[36,65],"metric":[39,154,210],"space,":[40],"goal":[42],"to":[44,57,66,124,189,205],"partition":[45],"them":[46],"into":[47],"$k$":[48],"clusters,":[49],"each":[50],"with":[51,153,241],"an":[52,144,147,231],"associated":[53],"center,":[54],"so":[55],"as":[56],"minimize":[58],"sum":[60],"squared":[62,209,216],"distances":[63,217],"their":[67],"cluster":[68],"centers.":[69],"In":[70],"this":[71,200,226],"paper,":[72],"we":[73],"present":[74],"polynomial-time":[76],"$3+2\\sqrt{2}+\u03b5&lt;5.83$-approximation":[77],"algorithm":[78,194,201,237],"for":[79,113,121,131,140,150,175,254],"general":[82],"metrics.":[83],"This":[84,233],"substantially":[85],"improves":[86,102],"on":[87,103,163,169],"current-best":[89],"$(9+\u03b5)$-approximation":[90],"[Ahmadian,":[92],"Norouzi-Fard,":[93],"Svensson,":[94],"Ward":[95],"-":[96,111,160,185,252],"FOCS'17,":[97],"SICOMP'20],":[98],"even":[100],"slightly":[101],"$5.92$-approximation":[105],"[Cohen-Addad,":[107,247],"Esfandiari,":[108],"Mirrokni,":[109],"Narayanan":[110],"STOC'22]":[112],"Euclidean":[115],"special":[116],"case.":[117],"A":[118],"natural":[119],"approach":[120],"leverage":[125],"Lagrangian":[126],"Multiplier":[127],"Preserving":[128],"(LMP)":[129],"approximations":[130],"facility":[133,151],"location":[134,152],"problem.":[135,259],"The":[136,187],"previous":[137],"best":[138],"results":[139],"build":[142],"upon":[143],"adaptation":[145,198],"LMP":[148,172,193,235],"$3$-approximation":[149],"connection":[155,211],"costs":[156,212],"[Jain,":[158,180],"Vazirani":[159,184],"J.ACM'01]":[161],"based":[162],"primal-dual":[165],"method,":[166],"rather":[167],"than":[168],"improved":[171,192],"greedy":[173],"$2$-approximation":[174],"same":[177],"problem":[178],"Mahdian,":[181],"Markakis,":[182],"Saberi,":[183],"J.ACM'03].":[186],"barrier":[188,227],"using":[190],"was":[195,213],"that":[196],"no":[197],"its":[203],"case":[207],"known":[214],"(since":[215],"violate":[218],"triangle":[219],"inequality).":[220],"Our":[221],"main":[222],"contribution":[223],"overcoming":[225],"by":[228],"providing":[229],"such":[230],"adaptation.":[232],"new":[234],"approximation":[236],"then":[239],"combined":[240],"framework":[243],"recently":[244],"introduced":[245],"Grandoni,":[248],"Lee,":[249],"Schwiegelshohn,":[250],"Svensson":[251],"STOC'25]":[253],"related":[256],"(metric)":[257],"$k$-Median":[258]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-30T00:00:00"}
