{"id":"https://openalex.org/W1981479258","doi":"https://doi.org/10.1137/s0097539799361208","title":"A Decomposition Theorem for Maximum Weight Bipartite Matchings","display_name":"A Decomposition Theorem for Maximum Weight Bipartite Matchings","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W1981479258","doi":"https://doi.org/10.1137/s0097539799361208","mag":"1981479258"},"language":"en","primary_location":{"id":"doi:10.1137/s0097539799361208","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539799361208","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/A5109219665","display_name":"Ming\u2010Yang Kao","orcid":null},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ming-Yang Kao","raw_affiliation_strings":["Yale University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Yale University","institution_ids":["https://openalex.org/I32971472"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077116003","display_name":"Tak\u2010Wah Lam","orcid":"https://orcid.org/0000-0003-4676-8587"},"institutions":[{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Tak-Wah Lam","raw_affiliation_strings":["University of Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Hong Kong","institution_ids":["https://openalex.org/I889458895"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012563463","display_name":"Wing\u2010Kin Sung","orcid":"https://orcid.org/0000-0001-7806-7086"},"institutions":[{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Wing-Kin Sung","raw_affiliation_strings":["University of Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Hong Kong","institution_ids":["https://openalex.org/I889458895"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033934413","display_name":"Hing\u2010Fung Ting","orcid":"https://orcid.org/0000-0002-2807-2351"},"institutions":[{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Hing-Fung Ting","raw_affiliation_strings":["University of Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Hong Kong","institution_ids":["https://openalex.org/I889458895"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.2053,"has_fulltext":false,"cited_by_count":57,"citation_normalized_percentile":{"value":0.91202174,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"31","issue":"1","first_page":"18","last_page":"26"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9995999932289124,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9994999766349792,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9945999979972839,"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/bipartite-graph","display_name":"Bipartite graph","score":0.9133762121200562},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8136563301086426},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7535371780395508},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.6881837844848633},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.6271897554397583},{"id":"https://openalex.org/keywords/minimum-weight","display_name":"Minimum weight","score":0.5264975428581238},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5205941200256348},{"id":"https://openalex.org/keywords/decomposition-theorem","display_name":"Decomposition theorem","score":0.5158481001853943},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.45810508728027344},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4506136476993561},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.38398277759552},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07520723342895508},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06710603833198547}],"concepts":[{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.9133762121200562},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8136563301086426},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7535371780395508},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.6881837844848633},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.6271897554397583},{"id":"https://openalex.org/C2778945305","wikidata":"https://www.wikidata.org/wiki/Q6865502","display_name":"Minimum weight","level":2,"score":0.5264975428581238},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5205941200256348},{"id":"https://openalex.org/C2779182943","wikidata":"https://www.wikidata.org/wiki/Q25345219","display_name":"Decomposition theorem","level":2,"score":0.5158481001853943},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.45810508728027344},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4506136476993561},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.38398277759552},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07520723342895508},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06710603833198547},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s0097539799361208","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539799361208","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.32.3053","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.32.3053","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.hku.hk/~twlam/papers/matchings.ps","raw_type":"text"},{"id":"pmh:oai:hub.hku.hk:10722/43656","is_oa":false,"landing_page_url":"http://hdl.handle.net/10722/43656","pdf_url":null,"source":{"id":"https://openalex.org/S4377196271","display_name":"The HKU Scholars Hub (University of Hong Kong)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I889458895","host_organization_name":"University of Hong Kong","host_organization_lineage":["https://openalex.org/I889458895"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"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/W1484040084","https://openalex.org/W1507231083","https://openalex.org/W1577048928","https://openalex.org/W1969357318","https://openalex.org/W1969781519","https://openalex.org/W1972978715","https://openalex.org/W2080090262","https://openalex.org/W2084224084","https://openalex.org/W2086974119","https://openalex.org/W2139559590","https://openalex.org/W2157529519","https://openalex.org/W2222512263","https://openalex.org/W2752885492","https://openalex.org/W2888871578"],"related_works":["https://openalex.org/W2371352078","https://openalex.org/W2953461625","https://openalex.org/W4301329442","https://openalex.org/W2953390393","https://openalex.org/W2151412766","https://openalex.org/W4301055422","https://openalex.org/W2408555533","https://openalex.org/W2950628401","https://openalex.org/W1981479258","https://openalex.org/W103840660"],"abstract_inverted_index":{"Let":[0,17,36],"G":[1,103,123],"be":[2,22,39],"a":[3,48,70,79,90,98,105,118],"bipartite":[4,55],"graph":[5],"with":[6],"positive":[7],"integer":[8],"weights":[9],"on":[10],"the":[11,23,26,31,83,115],"edges":[12],"and":[13,20,30,57,94,104],"without":[14],"isolated":[15],"nodes.":[16],"n,":[18],"N,":[19],"W":[21],"node":[24],"count,":[25],"largest":[27],"edge":[28],"weight,":[29],"total":[32],"weight":[33,54,72,92,107,116,120],"of":[34,74,88,96,109,117,122],"G.":[35,75],"k(x,":[37],"y)":[38],"log":[40,43],"x":[41],"/":[42,64],"(x2":[44],"/y).":[45],"We":[46],"present":[47],"new":[49],"decomposition":[50],"theorem":[51],"for":[52,68,126],"maximum":[53,71,91,99,106,119],"matchings":[56],"use":[58],"it":[59],"to":[60],"design":[61],"an":[62],"$O(\\sqrt{n}W":[63],"k(n,":[65],"W/N))$-time":[66],"algorithm":[67,77],"computing":[69,89,97],"matching":[73,93,108,121],"This":[76],"bridges":[78],"long-standing":[80],"gap":[81],"between":[82],"best":[84],"known":[85],"time":[86],"complexity":[87],"that":[95],"cardinality":[100],"matching.":[101],"Given":[102],"G,":[110],"we":[111],"can":[112],"further":[113],"compute":[114],"-":[124],"{u}":[125],"all":[127],"nodes":[128],"u":[129],"in":[130],"O(W)":[131],"time.":[132]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":5}],"updated_date":"2026-06-13T07:54:00.901334","created_date":"2025-10-10T00:00:00"}