{"id":"https://openalex.org/W2963287397","doi":"https://doi.org/10.1145/3301446","title":"Approximation Schemes for Clustering with Outliers","display_name":"Approximation Schemes for Clustering with Outliers","publication_year":2019,"publication_date":"2019-02-18","ids":{"openalex":"https://openalex.org/W2963287397","doi":"https://doi.org/10.1145/3301446","mag":"2963287397"},"language":"en","primary_location":{"id":"doi:10.1145/3301446","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3301446","pdf_url":null,"source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020188279","display_name":"Zachary Friggstad","orcid":"https://orcid.org/0000-0003-4039-3235"},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Zachary Friggstad","raw_affiliation_strings":["Department of Computing Science, University of Alberta, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Computing Science, University of Alberta, Canada","institution_ids":["https://openalex.org/I154425047"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023279386","display_name":"Kamyar Khodamoradi","orcid":"https://orcid.org/0000-0003-1289-6839"},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Kamyar Khodamoradi","raw_affiliation_strings":["Department of Computing Science, University of Alberta, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Computing Science, University of Alberta, Canada","institution_ids":["https://openalex.org/I154425047"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062142425","display_name":"Mohsen Rezapour","orcid":"https://orcid.org/0000-0001-9648-8394"},"institutions":[{"id":"https://openalex.org/I80543232","display_name":"K.N.Toosi University of Technology","ror":"https://ror.org/0433abe34","country_code":"IR","type":"education","lineage":["https://openalex.org/I80543232"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Mohsen Rezapour","raw_affiliation_strings":["Department of Mathematics, K.N. Toosi University of Technology, Tehran, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, K.N. Toosi University of Technology, Tehran, Iran","institution_ids":["https://openalex.org/I80543232"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010339836","display_name":"Mohammad R. Salavatipour","orcid":"https://orcid.org/0000-0002-7650-2045"},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Mohammad R. Salavatipour","raw_affiliation_strings":["Department of Computing Science, University of Alberta, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Computing Science, University of Alberta, Canada","institution_ids":["https://openalex.org/I154425047"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5020188279"],"corresponding_institution_ids":["https://openalex.org/I154425047"],"apc_list":null,"apc_paid":null,"fwci":7.4585,"has_fulltext":false,"cited_by_count":43,"citation_normalized_percentile":{"value":0.97065964,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"15","issue":"2","first_page":"1","last_page":"26"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11502","display_name":"Facility Location and Emergency Management","score":0.9994999766349792,"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":0.9994999766349792,"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/T11106","display_name":"Data Management and Algorithms","score":0.9836000204086304,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9789999723434448,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.748700737953186},{"id":"https://openalex.org/keywords/outlier","display_name":"Outlier","score":0.6441603899002075},{"id":"https://openalex.org/keywords/facility-location-problem","display_name":"Facility location problem","score":0.622519850730896},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5540534257888794},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.5417419672012329},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5342261791229248},{"id":"https://openalex.org/keywords/overhead","display_name":"Overhead (engineering)","score":0.48372748494148254},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.48331403732299805},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46247637271881104},{"id":"https://openalex.org/keywords/data-point","display_name":"Data point","score":0.43903037905693054},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.41373783349990845},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.41101136803627014},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35996881127357483},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3399290442466736},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3100779354572296},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.25609439611434937},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1466619372367859}],"concepts":[{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.748700737953186},{"id":"https://openalex.org/C79337645","wikidata":"https://www.wikidata.org/wiki/Q779824","display_name":"Outlier","level":2,"score":0.6441603899002075},{"id":"https://openalex.org/C108005400","wikidata":"https://www.wikidata.org/wiki/Q1305598","display_name":"Facility location problem","level":2,"score":0.622519850730896},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5540534257888794},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.5417419672012329},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5342261791229248},{"id":"https://openalex.org/C2779960059","wikidata":"https://www.wikidata.org/wiki/Q7113681","display_name":"Overhead (engineering)","level":2,"score":0.48372748494148254},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.48331403732299805},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46247637271881104},{"id":"https://openalex.org/C21080849","wikidata":"https://www.wikidata.org/wiki/Q13611879","display_name":"Data point","level":2,"score":0.43903037905693054},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.41373783349990845},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.41101136803627014},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35996881127357483},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3399290442466736},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3100779354572296},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.25609439611434937},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1466619372367859},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3301446","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3301446","pdf_url":null,"source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W1501500081","https://openalex.org/W1529111168","https://openalex.org/W1728268450","https://openalex.org/W1927951443","https://openalex.org/W1970866964","https://openalex.org/W1977541023","https://openalex.org/W1977983731","https://openalex.org/W1998905999","https://openalex.org/W2003207175","https://openalex.org/W2003719999","https://openalex.org/W2004791924","https://openalex.org/W2006514056","https://openalex.org/W2010410498","https://openalex.org/W2011430131","https://openalex.org/W2021640751","https://openalex.org/W2029698681","https://openalex.org/W2045964207","https://openalex.org/W2048974928","https://openalex.org/W2086959852","https://openalex.org/W2091283109","https://openalex.org/W2103718624","https://openalex.org/W2106850014","https://openalex.org/W2110105238","https://openalex.org/W2137130182","https://openalex.org/W2139841919","https://openalex.org/W2150593711","https://openalex.org/W2155429109","https://openalex.org/W2165142526","https://openalex.org/W2165420145","https://openalex.org/W2171125141","https://openalex.org/W2199495299","https://openalex.org/W2313395524","https://openalex.org/W2359462924","https://openalex.org/W2495677458","https://openalex.org/W2562836854","https://openalex.org/W2605029335","https://openalex.org/W2767218854","https://openalex.org/W2951980580","https://openalex.org/W2962858215","https://openalex.org/W2962937493","https://openalex.org/W2963803921","https://openalex.org/W2964283450","https://openalex.org/W4236385439","https://openalex.org/W4243637616","https://openalex.org/W4389615669"],"related_works":["https://openalex.org/W3029224032","https://openalex.org/W3006513224","https://openalex.org/W2046456988","https://openalex.org/W2003719999","https://openalex.org/W2357409937","https://openalex.org/W2293751504","https://openalex.org/W2599747538","https://openalex.org/W2978674666","https://openalex.org/W2074430941","https://openalex.org/W2940991801"],"abstract_inverted_index":{"Clustering":[0],"problems":[1,20,93,322],"are":[2,118,218,365],"well":[3],"studied":[4],"in":[5,62,83,126,323,406],"a":[6,34,63,72,87,120,127,132,255,265,277,293,300,303,337,350,429],"variety":[7],"of":[8,23,75,86,123,135,158,177,229,274,280,354,388,456],"fields,":[9],"such":[10,288],"as":[11,155,264],"data":[12,41,124],"science,":[13],"operations":[14],"research,":[15],"and":[16,29,109,180,203,318,357,390,447,458],"computer":[17],"science.":[18],"Such":[19],"include":[21],"variants":[22],"center":[24,196],"location":[25,103,163],"problems,":[26,116],"k":[27,30,105,110,148,200,204,214,223,315,319,343,393,397,422,445],"-median":[28],"-means":[31],"to":[32,44,70,78,168,174,185,210,213,232,310,418,427],"name":[33],"few.":[35],"In":[36,114,160,199,222],"some":[37,47,56,170],"cases,":[38],"not":[39,384],"all":[40,366],"points":[42,57,77,125,176],"need":[43],"be":[45,49,68,416],"clustered;":[46],"may":[48,58],"discarded":[50],"for":[51,313,328,392,421],"various":[52],"reasons.":[53],"For":[54,282],"instance,":[55],"arise":[59],"from":[60,276],"noise":[61],"dataset":[64],"or":[65,268],"one":[66],"might":[67],"willing":[69],"discard":[71,172],"certain":[73],"fraction":[74],"the":[76,84,156,186,191,227,270,314,324,355,386],"avoid":[79],"incurring":[80],"unnecessary":[81],"overhead":[82],"cost":[85,194,228,346,449],"clustering":[88,92],"solution.":[89],"We":[90,242,374],"study":[91],"with":[94,140,164,285,425],"outliers.":[95,159,362,464],"More":[96],"specifically,":[97],"we":[98,117,166,208,290,307,334,410],"look":[99],"at":[100,348,359,440,451],"uncapacitated":[101,161],"facility":[102,162],"(UFL),":[104],"-":[106,111,201,205,224,316,320,394,398,423],"median":[107,202,317,395],",":[108,149,179,207,226,239],"means":[112,206,225,321,399,424],".":[113],"these":[115],"given":[119],"set":[121,133],"X":[122,178],"metric":[128,257],"space":[129],"\u03b4(.,":[130],".),":[131],"C":[134],"possible":[136],"centers":[137,344],"(each":[138],"maybe":[139,144],"an":[141,145,151,436],"opening":[142,197,220],"cost),":[143],"integer":[146],"parameter":[147,153],"plus":[150,195],"additional":[152],"z":[154,175,361,463],"number":[157,387],"outliers,":[165],"have":[167,209,402],"open":[169,188,211],"centers,":[171,215],"up":[173,212],"assign":[181],"every":[182],"other":[183],"point":[184],"nearest":[187],"center,":[189],"minimizing":[190],"total":[192],"assignment":[193],"costs.":[198,221],"but":[216],"there":[217],"no":[219,460],"assigning":[230],"j":[231,238],"i":[233,240],"is":[234,249,254,269,347,450],"\u03b4":[235,253],"2":[236],"(":[237],").":[241],"present":[243],"several":[244],"results.":[245],"Our":[246,363],"main":[247],"focus":[248],"on":[250,287,368],"cases":[251],"where":[252],"doubling":[256],"(this":[258],"includes":[259],"fixed":[260],"dimensional":[261],"Euclidean":[262,407],"metrics":[263,273,326,420],"special":[266],"case)":[267],"shortest":[271],"path":[272],"graphs":[275],"minor-closed":[278],"family":[279],"graphs.":[281],"uniform-cost":[283],"UFL":[284],"outliers":[286,391,426],"metrics,":[289],"show":[291,376,411],"that":[292,377,382,438],"multiswap":[294,370],"simple":[295],"local":[296,371,379],"search":[297,372,380],"heuristic":[298],"yields":[299],"PTAS.":[301],"With":[302],"bit":[304],"more":[305,461],"work,":[306],"extend":[308],"this":[309],"bicriteria":[311],"approximations":[312],"same":[325],"where,":[327],"any":[329],"constant":[330],"\u03f5":[331,455],">":[332],"0,":[333],"can":[335,415],"find":[336],"solution":[338],"using":[339],"(1":[340,351,442],"+":[341,352,431,434,443,454],"\u03f5)":[342,444],"whose":[345,448],"most":[349,360,441,452],"\u03f5)-factor":[353],"optimum":[356,457],"uses":[358,439,459],"algorithms":[364],"based":[367],"natural":[369,378],"heuristics.":[373],"also":[375],"heuristics":[381],"do":[383],"violate":[385],"clusters":[389,446],"(or":[396],")":[400],"will":[401],"unbounded":[403],"gap":[404],"even":[405],"metrics.":[408],"Furthermore,":[409],"how":[412],"our":[413],"analysis":[414],"extended":[417],"general":[419],"obtain":[428],"(25":[430],"\u03f5,":[432],"1":[433],"\u03f5)-approximation:":[435],"algorithm":[437],"25":[453],"than":[462]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}