{"id":"https://openalex.org/W6891571451","doi":"https://doi.org/10.4230/lipics.icalp.2025.62","title":"Deterministic k-Median Clustering in Near-Optimal Time","display_name":"Deterministic k-Median Clustering in Near-Optimal Time","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W6891571451","doi":"https://doi.org/10.4230/lipics.icalp.2025.62"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2504.15115","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2504.15115","pdf_url":"https://arxiv.org/pdf/2504.15115","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"type":"article","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2504.15115","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Costa, Mart\u00edn","orcid":"https://orcid.org/0000-0002-0726-9083"},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Costa, Mart\u00edn","raw_affiliation_strings":["University of Warwick, Coventry, UK"],"raw_orcid":"https://orcid.org/0000-0002-0726-9083","affiliations":[{"raw_affiliation_string":"University of Warwick, Coventry, UK","institution_ids":["https://openalex.org/I39555362"]}]},{"author_position":"last","author":{"id":null,"display_name":"Farokhnejad, Ermiya","orcid":"https://orcid.org/0009-0008-6529-8625"},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Farokhnejad, Ermiya","raw_affiliation_strings":["University of Warwick, Coventry, UK"],"raw_orcid":"https://orcid.org/0009-0008-6529-8625","affiliations":[{"raw_affiliation_string":"University of Warwick, Coventry, UK","institution_ids":["https://openalex.org/I39555362"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.44276206,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":{"id":"https://openalex.org/T11502","display_name":"Facility Location and Emergency Management","score":0.9394000172615051,"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":0.9394000172615051,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.016300000250339508,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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":0.013500000350177288,"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/deterministic-algorithm","display_name":"Deterministic algorithm","score":0.8094000220298767},{"id":"https://openalex.org/keywords/randomized-algorithm","display_name":"Randomized algorithm","score":0.7468000054359436},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.6717000007629395},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5450999736785889},{"id":"https://openalex.org/keywords/running-time","display_name":"Running time","score":0.517300009727478},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.5077999830245972},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5049999952316284},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5026999711990356},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.4790000021457672}],"concepts":[{"id":"https://openalex.org/C13533509","wikidata":"https://www.wikidata.org/wiki/Q1064349","display_name":"Deterministic algorithm","level":2,"score":0.8094000220298767},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.7468000054359436},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6965000033378601},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.6717000007629395},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5450999736785889},{"id":"https://openalex.org/C3017489831","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Running time","level":2,"score":0.517300009727478},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5085999965667725},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.5077999830245972},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5049999952316284},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5026999711990356},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.4790000021457672},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4465999901294708},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4332999885082245},{"id":"https://openalex.org/C38506071","wikidata":"https://www.wikidata.org/wiki/Q6522941","display_name":"Freivalds' algorithm","level":5,"score":0.42899999022483826},{"id":"https://openalex.org/C99140742","wikidata":"https://www.wikidata.org/wiki/Q843550","display_name":"Polynomial-time approximation scheme","level":3,"score":0.4237000048160553},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3939000070095062},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.3921999931335449},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.37439998984336853},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.373199999332428},{"id":"https://openalex.org/C196921405","wikidata":"https://www.wikidata.org/wiki/Q786431","display_name":"Online algorithm","level":2,"score":0.367000013589859},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.35839998722076416},{"id":"https://openalex.org/C102408133","wikidata":"https://www.wikidata.org/wiki/Q5156350","display_name":"Competitive analysis","level":3,"score":0.3091000020503998},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.29820001125335693},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.29030001163482666},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.27889999747276306},{"id":"https://openalex.org/C123842658","wikidata":"https://www.wikidata.org/wiki/Q2918980","display_name":"Property testing","level":2,"score":0.27570000290870667},{"id":"https://openalex.org/C138600008","wikidata":"https://www.wikidata.org/wiki/Q498144","display_name":"Christofides algorithm","level":4,"score":0.2754000127315521},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.2583000063896179},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.2581000030040741},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.2508000135421753}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2504.15115","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2504.15115","pdf_url":"https://arxiv.org/pdf/2504.15115","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:drops-oai.dagstuhl.de:23439","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.62","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol334-icalp2025/LIPIcs.ICALP.2025.62/LIPIcs.ICALP.2025.62.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"publishedVersion"},{"id":"doi:10.4230/lipics.icalp.2025.62","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.icalp.2025.62","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":""}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2504.15115","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2504.15115","pdf_url":"https://arxiv.org/pdf/2504.15115","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W6891571451.pdf","grobid_xml":"https://content.openalex.org/works/W6891571451.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"metric":[1,15],"k-median":[2,66,151,173],"problem":[3,82],"is":[4,28,102,135,166],"a":[5,14,31,62,69,84,90,120,171,188,193,201,227],"textbook":[6],"clustering":[7],"problem.":[8],"As":[9],"input,":[10],"we":[11],"are":[12],"given":[13],"space":[16],"V":[17,35,50],"of":[18,36,93,99,129,140,148,170,218],"size":[19],"n":[20],"and":[21,25,58,232],"an":[22,116,215],"integer":[23],"k,":[24],"our":[26,141],"task":[27],"to":[29,51,105,160],"find":[30],"subset":[32],"S":[33],"\u2286":[34],"at":[37],"most":[38],"k":[39,221],"\"centers\"":[40],"that":[41,67,77,118,191,205],"minimizes":[42],"the":[43,96,127,130,133,138,145,161,167,230],"total":[44],"distance":[45],"from":[46],"each":[47],"point":[48],"in":[49,55,71,123,132,182,195],"its":[52],"nearest":[53],"center":[54],"S.":[56],"Mettu":[57],"Plaxton":[59],"[UAI'02]":[60],"gave":[61,115],"randomized":[63,231],"algorithm":[64,79,101,117,152,174,190,208],"for":[65,80,235],"computes":[68,119,192],"O(1)-approximation":[70],"\u00d5(nk)":[72,124,196],"time.":[73,156,197],"They":[74],"also":[75,199],"showed":[76],"any":[78,149,206],"this":[81,143,154,184,210],"with":[83,153,175,209],"bounded":[85],"approximation":[86,134,147,169,216],"ratio":[87,217],"must":[88,213],"have":[89,214],"running":[91,97,155,177,211],"time":[92,98,212],"\u03a9(nk).":[94],"Thus,":[95],"their":[100],"optimal":[103],"up":[104],"polylogarithmic":[106],"factors.":[107],"For":[108],"deterministic":[109,150,172,189,207,233],"k-median,":[110],"Guha":[111],"et":[112],"al.":[113],"[FOCS'00]":[114],"poly(log":[121],"(n/k))-approximation":[122],"time,":[125],"where":[126],"degree":[128],"polynomial":[131],"unspecified.":[136],"To":[137],"best":[139,168],"knowledge,":[142],"remains":[144],"state-of-the-art":[146],"This":[157],"leads":[158],"us":[159],"following":[162],"natural":[163],"question:":[164],"What":[165],"near-optimal":[176],"time?":[178],"We":[179,198],"make":[180],"progress":[181],"answering":[183],"question":[185],"by":[186],"giving":[187],"O(log(n/k))-approximation":[194],"provide":[200],"lower":[202],"bound":[203],"showing":[204],"\u03a9(log":[219],"n/(log":[220],"+":[222],"log":[223,224],"n)),":[225],"establishing":[226],"gap":[228],"between":[229],"settings":[234],"k-median.":[236]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
