{"id":"https://openalex.org/W3142718897","doi":"https://doi.org/10.1137/16m1106195","title":"Algorithms for Weighted Matching Generalizations I: Bipartite Graphs, <i>b</i>-matching, and Unweighted <i>f</i>-factors","display_name":"Algorithms for Weighted Matching Generalizations I: Bipartite Graphs, <i>b</i>-matching, and Unweighted <i>f</i>-factors","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3142718897","doi":"https://doi.org/10.1137/16m1106195","mag":"3142718897"},"language":"en","primary_location":{"id":"doi:10.1137/16m1106195","is_oa":true,"landing_page_url":"https://doi.org/10.1137/16m1106195","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/16M1106195","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":true,"oa_status":"hybrid","oa_url":"https://epubs.siam.org/doi/pdf/10.1137/16M1106195","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001013961","display_name":"Harold N. Gabow","orcid":"https://orcid.org/0000-0002-9775-3492"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Harold N. Gabow","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5025494465","display_name":"Piotr Sankowski","orcid":"https://orcid.org/0000-0002-0907-3754"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Piotr Sankowski","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5001013961"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3014,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.59500315,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"50","issue":"2","first_page":"440","last_page":"486"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998000264167786,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9998000264167786,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998000264167786,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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":0.8327500820159912},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.7202925682067871},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6898022890090942},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6214890480041504},{"id":"https://openalex.org/keywords/3-dimensional-matching","display_name":"3-dimensional matching","score":0.5796276926994324},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3788434565067291},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.21458303928375244},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.17830690741539001}],"concepts":[{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.8327500820159912},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.7202925682067871},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6898022890090942},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6214890480041504},{"id":"https://openalex.org/C72545166","wikidata":"https://www.wikidata.org/wiki/Q10866593","display_name":"3-dimensional matching","level":4,"score":0.5796276926994324},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3788434565067291},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.21458303928375244},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.17830690741539001}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/16m1106195","is_oa":true,"landing_page_url":"https://doi.org/10.1137/16m1106195","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/16M1106195","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1137/16m1106195","is_oa":true,"landing_page_url":"https://doi.org/10.1137/16m1106195","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/16M1106195","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2464966296","display_name":null,"funder_award_id":"772346","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"}],"funders":[{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3142718897.pdf","grobid_xml":"https://content.openalex.org/works/W3142718897.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W15553240","https://openalex.org/W37994088","https://openalex.org/W1494735819","https://openalex.org/W1599026900","https://openalex.org/W1969357318","https://openalex.org/W1995653528","https://openalex.org/W1999848117","https://openalex.org/W2001274023","https://openalex.org/W2005633226","https://openalex.org/W2008816808","https://openalex.org/W2023810039","https://openalex.org/W2066470474","https://openalex.org/W2080132708","https://openalex.org/W2082180697","https://openalex.org/W2084990336","https://openalex.org/W2089939118","https://openalex.org/W2094090625","https://openalex.org/W2098939045","https://openalex.org/W2099463627","https://openalex.org/W2149342630","https://openalex.org/W2151827175","https://openalex.org/W2327315803","https://openalex.org/W2913445149","https://openalex.org/W2950975603"],"related_works":["https://openalex.org/W1725047827","https://openalex.org/W2798321768","https://openalex.org/W2372768926","https://openalex.org/W2381564394","https://openalex.org/W2551344807","https://openalex.org/W2748469983","https://openalex.org/W2579720493","https://openalex.org/W2765379809","https://openalex.org/W1968325900","https://openalex.org/W2364074136"],"abstract_inverted_index":{"Let":[0],"$G=(V,E)$":[1],"be":[2],"a":[3,12,15,24,31,35,64,199],"weighted":[4,129],"graph":[5,39],"or":[6,10],"multigraph,":[7],"with":[8,69,223],"$f$":[9],"$b$":[11],"function":[13,28],"assigning":[14],"nonnegative":[16],"integer":[17],"to":[18,62,122,157,175,181],"each":[19,51],"vertex.":[20],"An":[21,108,154],"$f$-factor":[22,68,87,173],"is":[23,29,34,119,133,163,205,221,231],"subgraph":[25],"whose":[26],"degree":[27],"$f$;":[30],"perfect":[32],"$b$-matching":[33],"$b$-factor":[36],"in":[37,57,96],"the":[38,73,85,90,137,149,172,187,212,219,229],"formed":[40],"from":[41],"$G$":[42],"by":[43],"adding":[44],"an":[45,58,141,159],"unlimited":[46],"number":[47],"of":[48,50,80,93,140,151,171,201],"copies":[49],"edge.":[52],"This":[53,185],"two-part":[54],"paper":[55],"culminates":[56],"efficient":[59],"algebraic":[60,109,155],"algorithm":[61,88,110,156,174,204,220,230],"find":[63,158],"maximum":[65,70,86,112,115,138],"$f$-factor,":[66],"i.e.,":[67,114],"weight.":[71],"Along":[72],"way":[74],"it":[75],"presents":[76,84,105],"simpler":[77],"special":[78,91,124],"cases":[79],"interest.":[81],"Part":[82,103],"II":[83],"and":[89,147,178,195,207],"case":[92,125],"shortest":[94],"paths":[95],"conservative":[97],"undirected":[98],"graphs":[99,177],"(negative":[100],"edges":[101],"allowed).":[102],"I":[104],"these":[106],"results:":[107],"for":[111,135,165,191],"$b$-matching,":[113],"weight":[116],"$b$-matching.":[117],"It":[118],"almost":[120],"identical":[121],"its":[123,179],"$b\\equiv":[126],"1$,":[127],"ordinary":[128],"matching.":[130],"The":[131,161,169],"time":[132,162,214,218,228],"$O(Wb(V)^{\\omega})$":[134],"$W$":[136],"magnitude":[139],"edge":[142],"weight,":[143],"$b(V)=\\sum_{v\\in":[144],"V}":[145,167],"b(v)$,":[146],"$\\omega<2.373$":[148],"exponent":[150],"matrix":[152],"multiplication.":[153],"$f$-factor.":[160],"$O(f(V)^{\\omega})$":[164],"$f(V)=\\sum_{v\\in":[166],"f(v)$.":[168],"specialization":[170],"bipartite":[176,183],"extension":[180],"maximum/minimum":[182],"$f$-factors.":[184],"improves":[186],"known":[188],"complexity":[189],"bounds":[190],"vertex":[192],"capacitated":[193],"max-flow":[194,197],"min-cost":[196],"on":[198],"subclass":[200],"graphs.":[202],"Each":[203],"randomized":[206],"has":[208],"two":[209],"versions":[210],"achieving":[211],"above":[213],"bound:":[215],"For":[216,226],"worst-case":[217],"correct":[222],"high":[224],"probability.":[225],"expected":[227],"Las":[232],"Vegas.":[233]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-03-12T08:34:05.389933","created_date":"2025-10-10T00:00:00"}