{"id":"https://openalex.org/W2964242853","doi":"https://doi.org/10.1145/3392720","title":"The Non-Uniform <i>k</i> -Center Problem","display_name":"The Non-Uniform <i>k</i> -Center Problem","publication_year":2020,"publication_date":"2020-06-21","ids":{"openalex":"https://openalex.org/W2964242853","doi":"https://doi.org/10.1145/3392720","mag":"2964242853"},"language":"en","primary_location":{"id":"doi:10.1145/3392720","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3392720","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/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":false,"raw_author_name":"Deeparnab Chakrabarty","raw_affiliation_strings":["Dartmouth College, Hanover, NH, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dartmouth College, Hanover, NH, USA","institution_ids":["https://openalex.org/I107672454"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110616567","display_name":"Prachi Goyal","orcid":null},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Prachi Goyal","raw_affiliation_strings":["Microsoft, Redmond, WA USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Microsoft, Redmond, WA USA","institution_ids":["https://openalex.org/I1290206253"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060555975","display_name":"Ravishankar Krishnaswamy","orcid":"https://orcid.org/0000-0002-5765-0843"},"institutions":[{"id":"https://openalex.org/I4210124949","display_name":"Microsoft Research (India)","ror":"https://ror.org/02w7f3w92","country_code":"IN","type":"company","lineage":["https://openalex.org/I1290206253","https://openalex.org/I4210124949"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Ravishankar Krishnaswamy","raw_affiliation_strings":["Microsoft Research, Bengaluru, Karnataka, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Microsoft Research, Bengaluru, Karnataka, India","institution_ids":["https://openalex.org/I4210124949"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.3376,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.92647347,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"16","issue":"4","first_page":"1","last_page":"19"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9991999864578247,"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"}},{"id":"https://openalex.org/T11502","display_name":"Facility Location and Emergency Management","score":0.9984999895095825,"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/T12306","display_name":"Urban and Freight Transport Logistics","score":0.9901000261306763,"subfield":{"id":"https://openalex.org/subfields/2215","display_name":"Building and Construction"},"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/mathematics","display_name":"Mathematics","score":0.6710252165794373},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.6005107760429382},{"id":"https://openalex.org/keywords/center","display_name":"Center (category theory)","score":0.5940713882446289},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.5796753168106079},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5679658651351929},{"id":"https://openalex.org/keywords/dilation","display_name":"Dilation (metric space)","score":0.5592644214630127},{"id":"https://openalex.org/keywords/radius","display_name":"RADIUS","score":0.511942982673645},{"id":"https://openalex.org/keywords/minimax-approximation-algorithm","display_name":"Minimax approximation algorithm","score":0.4827944040298462},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.4578626751899719},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3426084816455841},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29568713903427124},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.26499831676483154},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1315467655658722}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6710252165794373},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.6005107760429382},{"id":"https://openalex.org/C2779463800","wikidata":"https://www.wikidata.org/wiki/Q5062222","display_name":"Center (category theory)","level":2,"score":0.5940713882446289},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.5796753168106079},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5679658651351929},{"id":"https://openalex.org/C2780757906","wikidata":"https://www.wikidata.org/wiki/Q5276676","display_name":"Dilation (metric space)","level":2,"score":0.5592644214630127},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.511942982673645},{"id":"https://openalex.org/C117148685","wikidata":"https://www.wikidata.org/wiki/Q6865376","display_name":"Minimax approximation algorithm","level":2,"score":0.4827944040298462},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.4578626751899719},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3426084816455841},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29568713903427124},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.26499831676483154},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1315467655658722},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3392720","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3392720","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":14,"referenced_works":["https://openalex.org/W1973264045","https://openalex.org/W1976619117","https://openalex.org/W1992447230","https://openalex.org/W2015784652","https://openalex.org/W2016973429","https://openalex.org/W2073583237","https://openalex.org/W2085751730","https://openalex.org/W2131687179","https://openalex.org/W2139841919","https://openalex.org/W2258410023","https://openalex.org/W2343942810","https://openalex.org/W2949530173","https://openalex.org/W4236385439","https://openalex.org/W4255005259"],"related_works":["https://openalex.org/W2343942810","https://openalex.org/W1567439696","https://openalex.org/W2405027740","https://openalex.org/W2586212981","https://openalex.org/W2165420145","https://openalex.org/W1579968022","https://openalex.org/W2103946119","https://openalex.org/W2016001296","https://openalex.org/W2950045224","https://openalex.org/W1501105572"],"abstract_inverted_index":{"In":[0],"this":[1,156,259],"article,":[2],"we":[3,228,301,310],"introduce":[4],"and":[5,23,54,146,162,272],"study":[6],"the":[7,39,51,56,62,73,79,103,110,114,128,170,185,194,200,224,249,254,269,273,285,297,306],"Non-Uniform":[8],"k":[9,37,105,111,129,141],"-Center":[10],"(NUkC)":[11],"problem.":[12,260,299],"Given":[13],"a":[14,24,45,89,160,243,266],"finite":[15],"metric":[16,52],"space":[17,53],"(":[18,210],"X":[19,82],",":[20],"d":[21],")":[22],"collection":[25],"of":[26,28,47,64,66,96,143,149,152,233],"balls":[27,65,142,151],"radii":[29,112],"{":[30],"r":[31,36,70],"1":[32,122,145],"\u2265":[33,35],"\u2026":[34],"},":[38],"NUkC":[40,100,195,270,290],"problem":[41,85,93,101,196,251,271],"is":[42,172,188,197,208,265,291,308],"to":[43,120,184,223,241,248,313,324],"find":[44,55],"placement":[46],"their":[48],"centers":[49,232],"in":[50,81,137,284,321],"minimum":[57],"dilation":[58,187],"\u03b1,":[59],"such":[60],"that":[61,180,193,279],"union":[63],"radius":[67,144,153],"\u03b1":[68],"\u22c5":[69],"i":[71,74],"around":[72],"th":[75],"center":[76],"covers":[77],"all":[78,109],"points":[80],".":[83],"This":[84],"naturally":[86],"arises":[87],"as":[88,294,296],"min-max":[90],"vehicle":[91],"routing":[92],"with":[94,131],"fleets":[95],"different":[97],"speeds.":[98],"The":[99],"generalizes":[102,127],"classic":[104],"-center":[106,130],"problem,":[107,136],"wherein":[108],"are":[113,140,311],"same":[115],"(which":[116],"can":[117],"be":[118,121],"assumed":[119],"after":[123],"scaling).":[124],"It":[125],"also":[126,238],"outliers":[132],"(kCwO":[133],"for":[134,166,258],"short)":[135],"which":[138],"there":[139,158],"\u2113":[147],"(number":[148],"outliers)":[150],"0.":[154],"Before":[155],"work,":[157],"was":[159],"2-approximation":[161,247],"3-approximation":[163],"algorithm":[164],"known":[165],"these":[167],"problems,":[168],"respectively;":[169],"former":[171],"best":[173],"possible":[174,189],"unless":[175,190],"P=NP.":[176],"We":[177,218,288],"first":[178],"observe":[179],"no":[181],"O":[182,211,213,221],"(1)-approximation":[183,222],"optimal":[186,225,246],"P=NP,":[191],"implying":[192],"harder":[198],"than":[199],"above":[201],"two":[202],"problems.":[203],"Our":[204,236,261],"main":[205,262],"algorithmic":[206],"result":[207],"an":[209,220],"(1),":[212],"(1))-":[214],"bi-criteria":[215,329],"approximation":[216,257],"result:":[217],"give":[219],"dilation;":[226],"however,":[227],"may":[229],"open":[230],"\u0398(1)":[231],"each":[234],"radii.":[235],"techniques":[237],"allow":[239],"us":[240],"prove":[242],"simple":[244],"(uni-criterion),":[245],"kCwO":[250],"improving":[252],"upon":[253],"long-standing":[255],"3-factor":[256],"technical":[263],"contribution":[264],"connection":[267],"between":[268],"so-called":[274],"firefighter":[275,298],"problems":[276],"on":[277],"trees":[278],"have":[280],"been":[281],"studied":[282],"recently":[283],"TCS":[286],"community.":[287],"show":[289],"at":[292],"least":[293],"hard":[295],"While":[300],"do":[302],"nt":[303],"know":[304],"whether":[305],"converse":[307],"true,":[309],"able":[312],"adapt":[314],"ideas":[315],"from":[316],"recent":[317],"works":[318],"[1,":[319],"3]":[320],"non-trivial":[322],"ways":[323],"obtain":[325],"our":[326],"constant":[327],"factor":[328],"approximation.":[330]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}