{"id":"https://openalex.org/W7162523399","doi":"https://doi.org/10.4230/lipics.socg.2026.33","title":"Near-Optimal Bounds for Parameterized Euclidean k-Means","display_name":"Near-Optimal Bounds for Parameterized Euclidean k-Means","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7162523399","doi":"https://doi.org/10.4230/lipics.socg.2026.33"},"language":"en","primary_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:25839","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.33","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.33/LIPIcs.SoCG.2026.33.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"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.33/LIPIcs.SoCG.2026.33.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074251728","display_name":"Vincent Cohen-Addad","orcid":"https://orcid.org/0000-0002-0779-8962"},"institutions":[{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Cohen-Addad, Vincent","raw_affiliation_strings":["Google Research, New York, NY, USA"],"raw_orcid":"https://orcid.org/0000-0002-0779-8962","affiliations":[{"raw_affiliation_string":"Google Research, New York, NY, USA","institution_ids":["https://openalex.org/I1291425158"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137185539","display_name":"Karthik C. S.","orcid":"https://orcid.org/0000-0001-9105-364X"},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"C. S., Karthik","raw_affiliation_strings":["Rutgers University, Piscataway, NJ, USA"],"raw_orcid":"https://orcid.org/0000-0001-9105-364X","affiliations":[{"raw_affiliation_string":"Rutgers University, Piscataway, NJ, USA","institution_ids":["https://openalex.org/I102322142"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137157485","display_name":"David Saulpic","orcid":"https://orcid.org/0000-0003-4208-8541"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Saulpic, David","raw_affiliation_strings":["Universit\u00e9 Paris Cit\u00e9, CNRS, IRIF, F-75013, Paris, France"],"raw_orcid":"https://orcid.org/0000-0003-4208-8541","affiliations":[{"raw_affiliation_string":"Universit\u00e9 Paris Cit\u00e9, CNRS, IRIF, F-75013, Paris, France","institution_ids":["https://openalex.org/I204730241","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5137124748","display_name":"Chris Schwiegelshohn","orcid":"https://orcid.org/0009-0008-9114-0661"},"institutions":[{"id":"https://openalex.org/I204337017","display_name":"Aarhus University","ror":"https://ror.org/01aj84f44","country_code":"DK","type":"education","lineage":["https://openalex.org/I204337017"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Schwiegelshohn, Chris","raw_affiliation_strings":["Aarhus University, Denmark"],"raw_orcid":"https://orcid.org/0009-0008-9114-0661","affiliations":[{"raw_affiliation_string":"Aarhus University, Denmark","institution_ids":["https://openalex.org/I204337017"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5074251728"],"corresponding_institution_ids":["https://openalex.org/I1291425158"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.95632429,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"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":0.8385999798774719,"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":0.8385999798774719,"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":0.039000000804662704,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.02500000037252903,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.6207000017166138},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.616599977016449},{"id":"https://openalex.org/keywords/vertex-cover","display_name":"Vertex cover","score":0.6144000291824341},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5799999833106995},{"id":"https://openalex.org/keywords/exponential-time-hypothesis","display_name":"Exponential time hypothesis","score":0.5616999864578247},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.49380001425743103},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.460999995470047},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.43209999799728394},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.4189999997615814}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.769599974155426},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6467999815940857},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.6207000017166138},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.616599977016449},{"id":"https://openalex.org/C40687702","wikidata":"https://www.wikidata.org/wiki/Q11515519","display_name":"Vertex cover","level":3,"score":0.6144000291824341},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5799999833106995},{"id":"https://openalex.org/C71017364","wikidata":"https://www.wikidata.org/wiki/Q5421532","display_name":"Exponential time hypothesis","level":3,"score":0.5616999864578247},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.49380001425743103},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.460999995470047},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.43209999799728394},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.4189999997615814},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.41749998927116394},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41659998893737793},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3831999897956848},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.37950000166893005},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.3725000023841858},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.34549999237060547},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.34040001034736633},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.336899995803833},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.31520000100135803},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.313400000333786},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.29600000381469727},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28450000286102295},{"id":"https://openalex.org/C55974624","wikidata":"https://www.wikidata.org/wiki/Q1188504","display_name":"Exponential family","level":2,"score":0.2808000147342682},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.27810001373291016},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.26170000433921814},{"id":"https://openalex.org/C182124507","wikidata":"https://www.wikidata.org/wiki/Q166154","display_name":"Line segment","level":2,"score":0.2612999975681305},{"id":"https://openalex.org/C100808899","wikidata":"https://www.wikidata.org/wiki/Q1192100","display_name":"Set cover problem","level":3,"score":0.25940001010894775},{"id":"https://openalex.org/C170836113","wikidata":"https://www.wikidata.org/wiki/Q5406126","display_name":"Euclidean shortest path","level":5,"score":0.25589999556541443}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:drops-oai.dagstuhl.de:25839","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.33","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.33/LIPIcs.SoCG.2026.33.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.socg.2026.33","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.socg.2026.33","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:drops-oai.dagstuhl.de:25839","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.33","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.33/LIPIcs.SoCG.2026.33.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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7162523399.pdf","grobid_xml":"https://content.openalex.org/works/W7162523399.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"k-means":[1,56,93,150,166,212],"problem":[2,131],"is":[3,25,155,173,189,213],"a":[4,11,15,20,88,104,163],"classic":[5],"objective":[6],"for":[7,90,111,127,165,211,215],"modeling":[8],"clustering":[9],"in":[10,19,57,94,167],"metric":[12,21],"space.":[13,169],"Given":[14],"set":[16],"of":[17,37,55,64,145,205,218],"points":[18,30],"space,":[22],"the":[23,35,38,53,62,128,141,178,199],"goal":[24],"to":[26,33,44,86],"find":[27],"k":[28],"representative":[29],"so":[31],"as":[32,175],"minimize":[34],"sum":[36],"squared":[39],"distances":[40],"from":[41],"each":[42],"point":[43],"its":[45],"closest":[46],"representative.":[47],"In":[48,67,99],"this":[49,100],"work,":[50,101],"we":[51,102,139,196],"study":[52],"approximability":[54],"Euclidean":[58,92,149,168],"spaces":[59],"parameterized":[60],"by":[61,151,181],"number":[63],"clusters,":[65],"k.":[66,219],"seminal":[68,200],"works,":[69],"de":[70],"la":[71],"Vega,":[72],"Karpinski,":[73],"Kenyon,":[74],"and":[75,78,81,184,208],"Rabani":[76],"[STOC'03]":[77],"Kumar,":[79],"Sabharwal,":[80],"Sen":[82],"[JACM'10]":[83],"showed":[84],"how":[85],"obtain":[87],"(1+\u03b5)-approximation":[89,164],"high-dimensional":[91],"time":[95,124,160],"2^{(k/\u03b5)^O(1)}":[96],"\u22c5":[97,158],"dn^O(1).":[98],"introduce":[103],"new":[105],"fine-grained":[106],"hypothesis":[107],"called":[108],"Exponential":[109],"Time":[110],"Expanders":[112],"Hypothesis":[113],"(XXH)":[114],"which":[115],"roughly":[116],"asserts":[117],"that":[118,153,198],"there":[119,154],"are":[120],"no":[121,156],"non-trivial":[122],"exponential":[123],"approximation":[125],"algorithms":[126],"vertex":[129,135],"cover":[130],"on":[132,147],"near":[133],"perfect":[134],"expanders.":[136],"Assuming":[137],"XXH,":[138,195],"close":[140],"above":[142],"long":[143],"line":[144],"work":[146],"approximating":[148],"showing":[152],"2^{(k/\u03b5)^{1-o(1)}}":[157],"n^O(1)":[159],"algorithm":[161,179,204],"achieving":[162],"This":[170],"lower":[171],"bound":[172],"tight":[174],"it":[176],"matches":[177],"given":[180],"Feldman,":[182],"Monemizadeh,":[183],"Sohler":[185],"[SoCG'07]":[186],"whose":[187],"runtime":[188,202],"2^O(k/\u03b5)":[190],"+":[191],"O(ndk).":[192],"Furthermore,":[193],"assuming":[194],"show":[197],"O(n^{kd+1})":[201],"exact":[203],"Inaba,":[206],"Katoh,":[207],"Imai":[209],"[SoCG'94]":[210],"optimal":[214],"small":[216],"values":[217]},"counts_by_year":[],"updated_date":"2026-05-30T09:04:40.226872","created_date":"2026-05-28T00:00:00"}
