{"id":"https://openalex.org/W4416399837","doi":"https://doi.org/10.4230/lipics.fsttcs.2025.19","title":"Clustering in Varying Metrics","display_name":"Clustering in Varying Metrics","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4416399837","doi":"https://doi.org/10.4230/lipics.fsttcs.2025.19"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2510.07860","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.07860","pdf_url":"https://arxiv.org/pdf/2510.07860","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":"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/2510.07860","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069364300","display_name":"Deeparnab Chakrabarty","orcid":"https://orcid.org/0000-0001-7596-6035"},"institutions":[{"id":"https://openalex.org/I107672454","display_name":"Dartmouth College","ror":"https://ror.org/049s0rh22","country_code":"US","type":"education","lineage":["https://openalex.org/I107672454"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Chakrabarty, Deeparnab","raw_affiliation_strings":["Department of Computer Science, Dartmouth College, Hanover, NH, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Dartmouth College, Hanover, NH, USA","institution_ids":["https://openalex.org/I107672454"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067955248","display_name":"Jonathan Conroy","orcid":null},"institutions":[{"id":"https://openalex.org/I107672454","display_name":"Dartmouth College","ror":"https://ror.org/049s0rh22","country_code":"US","type":"education","lineage":["https://openalex.org/I107672454"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Conroy, Jonathan","raw_affiliation_strings":["Department of Computer Science, Dartmouth College, Hanover, NH, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Dartmouth College, Hanover, NH, USA","institution_ids":["https://openalex.org/I107672454"]}]},{"author_position":"last","author":{"id":null,"display_name":"Sarkar, Ankita","orcid":"https://orcid.org/0000-0001-6787-7286"},"institutions":[{"id":"https://openalex.org/I107672454","display_name":"Dartmouth College","ror":"https://ror.org/049s0rh22","country_code":"US","type":"education","lineage":["https://openalex.org/I107672454"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sarkar, Ankita","raw_affiliation_strings":["Department of Computer Science, Dartmouth College, Hanover, NH, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Dartmouth College, Hanover, NH, USA","institution_ids":["https://openalex.org/I107672454"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5069364300"],"corresponding_institution_ids":["https://openalex.org/I107672454"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.40685551,"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":false,"primary_topic":{"id":"https://openalex.org/T11502","display_name":"Facility Location and Emergency Management","score":0.4438000023365021,"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":0.4438000023365021,"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":0.2053000032901764,"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":0.1492999941110611,"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/treewidth","display_name":"Treewidth","score":0.8458999991416931},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.7626000046730042},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.7591999769210815},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6743000149726868},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.4528999924659729},{"id":"https://openalex.org/keywords/correlation-clustering","display_name":"Correlation clustering","score":0.4036000072956085},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.40049999952316284},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.3977999985218048}],"concepts":[{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.8458999991416931},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.7626000046730042},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.7591999769210815},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6743000149726868},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.59170001745224},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.4528999924659729},{"id":"https://openalex.org/C94641424","wikidata":"https://www.wikidata.org/wiki/Q5172845","display_name":"Correlation clustering","level":3,"score":0.4036000072956085},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.40049999952316284},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3977999985218048},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.38510000705718994},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.351500004529953},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34779998660087585},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3427000045776367},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.3416999876499176},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.33709999918937683},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32199999690055847},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.31940001249313354},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3109999895095825},{"id":"https://openalex.org/C27964816","wikidata":"https://www.wikidata.org/wiki/Q5164359","display_name":"Constrained clustering","level":5,"score":0.30820000171661377},{"id":"https://openalex.org/C164866538","wikidata":"https://www.wikidata.org/wiki/Q367351","display_name":"Cluster (spacecraft)","level":2,"score":0.2854999899864197},{"id":"https://openalex.org/C4679612","wikidata":"https://www.wikidata.org/wiki/Q866298","display_name":"Aggregate (composite)","level":2,"score":0.2840999960899353},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.27869999408721924},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.27630001306533813},{"id":"https://openalex.org/C2781039887","wikidata":"https://www.wikidata.org/wiki/Q1391724","display_name":"Factor (programming language)","level":2,"score":0.26179999113082886},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.25220000743865967}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2510.07860","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.07860","pdf_url":"https://arxiv.org/pdf/2510.07860","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2510.07860","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2510.07860","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"},{"id":"doi:10.4230/lipics.fsttcs.2025.19","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.fsttcs.2025.19","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:2510.07860","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.07860","pdf_url":"https://arxiv.org/pdf/2510.07860","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4416399837.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,68,94],"introduce":[1],"the":[2,18,38,43,49,64,75,114,141,160,189],"aggregated":[3],"clustering":[4,15,39],"problem,":[5],"where":[6,48],"one":[7],"is":[8,28,51,77,159,174,180,191],"given":[9],"$T$":[10,65,127],"instances":[11],"of":[12,37,153],"a":[13,60,135,149],"center-based":[14],"task":[16],"over":[17,63],"same":[19],"$n$":[20],"points,":[21],"but":[22,102],"under":[23],"different":[24],"metrics.":[25],"The":[26],"goal":[27],"to":[29,33,79],"open":[30],"$k$":[31,110],"centers":[32],"minimize":[34,59],"an":[35,165],"aggregate":[36],"costs":[40],"--":[41,47],"e.g.,":[42],"average":[44],"or":[45],"maximum":[46],"cost":[50,66],"measured":[52],"via":[53],"$k$-center/median/means":[54],"objectives.":[55],"More":[56],"generally,":[57],"we":[58,90,118,133,163],"norm":[61],"$\u03a8$":[62,158],"values.":[67],"show":[69,96],"that":[70],"for":[71],"$T":[72,87],"\\geq":[73],"3$,":[74],"problem":[76],"inapproximable":[78],"any":[80,176],"finite":[81,177],"factor":[82,178],"in":[83,137,167],"polynomial":[84],"time.":[85,139,169],"For":[86],"=":[88,193],"2$,":[89],"give":[91],"constant-factor":[92],"approximations.":[93],"also":[95],"W[2]-hardness":[97],"when":[98,106,188],"parameterized":[99,107,121],"by":[100,108,145,184],"$k$,":[101],"obtain":[103,119],"$f(k,T)\\mathrm{poly}(n)$-time":[104],"3-approximations":[105],"both":[109],"and":[111,157],"$T$.":[112],"When":[113],"metrics":[115,128,142],"have":[116,129],"structure,":[117],"efficient":[120],"approximation":[122,179],"schemes":[123],"(EPAS).":[124],"If":[125,140],"all":[126],"bounded":[130,154],"$\\varepsilon$-scatter":[131],"dimension,":[132],"achieve":[134],"$(1+\\varepsilon)$-approximation":[136],"$f(k,T,\\varepsilon)\\mathrm{poly}(n)$":[138],"are":[143],"induced":[144],"edge":[146],"weights":[147],"on":[148],"common":[150],"graph":[151],"$G$":[152],"treewidth":[155,190],"$\\mathsf{tw}$,":[156],"sum":[161],"function,":[162],"get":[164],"EPAS":[166],"$f(T,\\varepsilon,\\mathsf{tw})\\mathrm{poly}(n,k)$":[168],"Conversely,":[170],"unless":[171],"(randomized)":[172],"ETH":[173],"false,":[175],"impossible":[181],"if":[182],"parametrized":[183],"only":[185],"$T$,":[186],"even":[187],"$\\mathsf{tw}":[192],"\u03a9(\\mathrm{poly}\\log":[194],"n)$.":[195]},"counts_by_year":[],"updated_date":"2025-11-28T00:00:00","created_date":"2025-10-11T00:00:00"}