{"id":"https://openalex.org/W2064594923","doi":"https://doi.org/10.1137/070698257","title":"A General Approach for Incremental Approximation and Hierarchical Clustering","display_name":"A General Approach for Incremental Approximation and Hierarchical Clustering","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2064594923","doi":"https://doi.org/10.1137/070698257","mag":"2064594923"},"language":"en","primary_location":{"id":"doi:10.1137/070698257","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070698257","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","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/A5109965048","display_name":"Guolong Lin","orcid":"https://orcid.org/0009-0009-9620-8466"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Guolong Lin","raw_affiliation_strings":["glin@akamai.com#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"glin@akamai.com#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050879268","display_name":"Chandrashekhar Nagarajan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chandrashekhar Nagarajan","raw_affiliation_strings":["cn54@yahoo-inc.com#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"cn54@yahoo-inc.com#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103525476","display_name":"Rajmohan Rajaraman","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rajmohan Rajaraman","raw_affiliation_strings":["rraj@ccs.neu.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"rraj@ccs.neu.edu#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043667154","display_name":"David P. Williamson","orcid":"https://orcid.org/0000-0002-2884-0058"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David P. Williamson","raw_affiliation_strings":["dpw@cs.cornell.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"dpw@cs.cornell.edu#TAB#","institution_ids":["https://openalex.org/I205783295"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.8766,"has_fulltext":false,"cited_by_count":53,"citation_normalized_percentile":{"value":0.96337989,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"39","issue":"8","first_page":"3633","last_page":"3669"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11502","display_name":"Facility Location and Emergency Management","score":0.9993000030517578,"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":0.9993000030517578,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9983999729156494,"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"}},{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9944000244140625,"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/cardinality","display_name":"Cardinality (data modeling)","score":0.7751957178115845},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6775163412094116},{"id":"https://openalex.org/keywords/set-cover-problem","display_name":"Set cover problem","score":0.6577024459838867},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6331411600112915},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.5819547176361084},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.5357365608215332},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.4615353047847748},{"id":"https://openalex.org/keywords/vertex-cover","display_name":"Vertex cover","score":0.4541981518268585},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.4519233703613281},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.43036431074142456},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38727861642837524},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3320584297180176},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32134559750556946},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.205938458442688},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.19539234042167664}],"concepts":[{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.7751957178115845},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6775163412094116},{"id":"https://openalex.org/C100808899","wikidata":"https://www.wikidata.org/wiki/Q1192100","display_name":"Set cover problem","level":3,"score":0.6577024459838867},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6331411600112915},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.5819547176361084},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.5357365608215332},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4615353047847748},{"id":"https://openalex.org/C40687702","wikidata":"https://www.wikidata.org/wiki/Q11515519","display_name":"Vertex cover","level":3,"score":0.4541981518268585},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.4519233703613281},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.43036431074142456},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38727861642837524},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3320584297180176},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32134559750556946},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.205938458442688},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.19539234042167664},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/070698257","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070698257","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6299999952316284,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1973264045","https://openalex.org/W1999032440","https://openalex.org/W2003207175","https://openalex.org/W2009279347","https://openalex.org/W2016973429","https://openalex.org/W2041025394","https://openalex.org/W2041645394","https://openalex.org/W2052494364","https://openalex.org/W2055696239","https://openalex.org/W2063852444","https://openalex.org/W2073689249","https://openalex.org/W2121638441","https://openalex.org/W2136442119","https://openalex.org/W2139841919","https://openalex.org/W2143996311","https://openalex.org/W2147258429","https://openalex.org/W2155148197","https://openalex.org/W2161747341","https://openalex.org/W2167112911","https://openalex.org/W2769245605","https://openalex.org/W4243637616"],"related_works":["https://openalex.org/W2950850544","https://openalex.org/W2112112676","https://openalex.org/W2108073487","https://openalex.org/W3159572760","https://openalex.org/W2782292024","https://openalex.org/W2551034790","https://openalex.org/W1502438505","https://openalex.org/W2951888513","https://openalex.org/W4301954754","https://openalex.org/W2019875157"],"abstract_inverted_index":{"We":[0,115,189],"present":[1],"a":[2,107,208],"general":[3],"framework":[4,13,119,194],"and":[5,23,52,87,98,132,137,148],"algorithmic":[6],"approach":[7],"for":[8,40,55,76,95,207],"incremental":[9,89,123,149,180],"approximation":[10],"algorithms.":[11],"The":[12],"handles":[14],"cardinality":[15,72],"constrained":[16],"minimization":[17],"problems,":[18],"such":[19,45,53,93],"as":[20,161,163],"the":[21,47,50,65,77,80,126,152,164,193,212],"k-median":[22,78,127,213],"k-MST":[24,153],"problems.":[25,199],"Given":[26],"some":[27],"notion":[28,81],"of":[29,33,43,67,71,82,103,109,112,125,151,211],"ordering":[30,51,83],"on":[31],"solutions":[32,39,48,92],"different":[34],"cardinalities":[35],"k,":[36,57],"we":[37,176,202],"give":[38,203],"all":[41],"values":[42],"k":[44,97,105],"that":[46,54,94,117,192],"respect":[49],"any":[56,96],"our":[58,88,101,110,118],"solution":[59,70,102,111],"is":[60,84,106,170],"close":[61],"in":[62],"value":[63,66],"to":[64,121,196],"an":[68,204],"optimal":[69],"k.":[73],"For":[74,173],"instance,":[75],"problem,":[79,154,157,160],"set":[85],"inclusion,":[86],"algorithm":[90,206],"produces":[91],"$k'$,":[99],"$k<k'$,":[100],"size":[104,113],"subset":[108],"$k'$.":[114],"show":[116,191],"applies":[120,195],"this":[122],"version":[124,210],"problem":[128,168,214],"(introduced":[129],"by":[130,216],"Mettu":[131,136],"Plaxton":[133,217],"[R.":[134],"R.":[135],"C.":[138],"G.":[139,219],"Plaxton,":[140,220],"SIAM":[141],"J.":[142,221],"Comput.,":[143],"32":[144],"(2003),":[145],"pp.":[146,227],"816\u2013832])":[147],"versions":[150],"k-vertex":[155],"cover":[156,159],"k-set":[158],"well":[162],"uncapacitated":[165],"facility":[166],"location":[167],"(which":[169],"not":[171],"cardinality-constrained).":[172],"these":[174],"problems":[175],"get":[177],"either":[178],"new":[179],"algorithms":[181],"or":[182],"improvements":[183],"over":[184],"what":[185],"was":[186],"previously":[187],"known.":[188],"also":[190],"hierarchical":[197,209],"clustering":[198],"In":[200],"particular,":[201],"improved":[205],"introduced":[215],"[C.":[218],"Comput.":[222],"System":[223],"Sci.,":[224],"72":[225],"(2006),":[226],"425\u2013443].":[228]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
