{"id":"https://openalex.org/W4402745972","doi":"https://doi.org/10.1145/3696668","title":"Maximum Cardinality <i>f</i> -Matching in Time <i>O</i> ( <i>n</i> <sup>2/3</sup> <i>m</i> )","display_name":"Maximum Cardinality <i>f</i> -Matching in Time <i>O</i> ( <i>n</i> <sup>2/3</sup> <i>m</i> )","publication_year":2024,"publication_date":"2024-09-23","ids":{"openalex":"https://openalex.org/W4402745972","doi":"https://doi.org/10.1145/3696668"},"language":"en","primary_location":{"id":"doi:10.1145/3696668","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3696668","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/A5001013961","display_name":"Harold N. Gabow","orcid":"https://orcid.org/0000-0002-9775-3492"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]},{"id":"https://openalex.org/I2802236040","display_name":"University of Colorado System","ror":"https://ror.org/00jc20583","country_code":"US","type":"education","lineage":["https://openalex.org/I2802236040"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Harold N. Gabow","raw_affiliation_strings":["Department of Computer Science, University of Colorado, Boulder, CO, USA","University of Colorado, USA"],"raw_orcid":"https://orcid.org/0000-0002-9775-3492","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Colorado, Boulder, CO, USA","institution_ids":["https://openalex.org/I188538660"]},{"raw_affiliation_string":"University of Colorado, USA","institution_ids":["https://openalex.org/I2802236040"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5001013961"],"corresponding_institution_ids":["https://openalex.org/I188538660","https://openalex.org/I2802236040"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.18735436,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"21","issue":"1","first_page":"1","last_page":"28"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9997000098228455,"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":0.9997000098228455,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.9987999796867371,"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/cardinality","display_name":"Cardinality (data modeling)","score":0.7869153022766113},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.687980592250824},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6610985994338989},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.6236891746520996},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3419575095176697},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28347697854042053},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.15028157830238342},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.06683176755905151}],"concepts":[{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.7869153022766113},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.687980592250824},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6610985994338989},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.6236891746520996},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3419575095176697},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28347697854042053},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.15028157830238342},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.06683176755905151}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3696668","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3696668","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":20,"referenced_works":["https://openalex.org/W1499313444","https://openalex.org/W1791617053","https://openalex.org/W1969357318","https://openalex.org/W2008292658","https://openalex.org/W2090010485","https://openalex.org/W2149342630","https://openalex.org/W2157529519","https://openalex.org/W2327315803","https://openalex.org/W2551688242","https://openalex.org/W2605161051","https://openalex.org/W2782000683","https://openalex.org/W2988480584","https://openalex.org/W3014094413","https://openalex.org/W3090768320","https://openalex.org/W4210431029","https://openalex.org/W4213060235","https://openalex.org/W4214659657","https://openalex.org/W4233756358","https://openalex.org/W4376505282","https://openalex.org/W4396690120"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2002177687","https://openalex.org/W2950751300","https://openalex.org/W4301272096","https://openalex.org/W24519920","https://openalex.org/W2087778462"],"abstract_inverted_index":{"We":[0,105,121],"present":[1],"an":[2,26],"algorithm":[3,153],"that":[4,49],"finds":[5],"a":[6,12,22,30,45],"maximum":[7,160],"cardinality":[8,161],"\\(f\\)":[9,27],"-matching":[10,28],"of":[11,47,63,112],"simple":[13,52],"graph":[14,96],"in":[15],"time":[16,129,140,157],"\\(O(n^{2/3}m)\\)":[17],".":[18,41,145,165],"Here,":[19],"\\(f:V\\to\\mathbb{N}\\)":[20],"is":[21,29,58,134],"given":[23],"function":[24],"and":[25,85],"subgraph":[31],"wherein":[32],"each":[33],"vertex":[34],"\\(v\\in":[35],"V\\)":[36],"has":[37],"degree":[38],"\\(\\leq":[39],"f(v)\\)":[40],"This":[42],"result":[43],"generalizes":[44],"string":[46],"algorithms":[48],"concentrate":[50],"on":[51,60,137],"bipartite":[53,56,98],"graphs.":[54],"The":[55,131,146],"case":[57,148],"based":[59],"the":[61,93,127,152,155],"notion":[62,76],"level":[64,95],"graph,":[65],"introduced":[66],"by":[67],"Dinic":[68],"for":[69,118,143,159],"network":[70],"flow.":[71],"In":[72],"general":[73],"graphs":[74,99],"this":[75],"breaks":[77],"down:":[78],"Vertices":[79],"no":[80],"longer":[81],"have":[82],"unique":[83],"levels,":[84],"there":[86],"are":[87],"too":[88],"many":[89],"levels":[90,108,124],"to":[91,109,125],"analyze":[92],"corresponding":[94],"like":[97],"(":[100],"\\(\\Theta(n^{2})\\)":[101],"vs.":[102],"\\(n\\)":[103],").":[104],"use":[106,122],"\u201cnatural\u201d":[107],"prove":[110],"properties":[111],"shortest":[113],"augmenting":[114],"trails":[115],"(e.g.,":[116],"formulas":[117],"trail":[119],"length).":[120],"\u201cshortened\u201d":[123],"derive":[126],"algorithm\u2019s":[128],"bound.":[130],"algorithm,":[132],"unmodified,":[133],"also":[135],"efficient":[136],"multigraphs,":[138],"achieving":[139],"\\(O(\\min\\{\\sqrt{f(V)},n\\}":[141],"m)\\)":[142,164],"\\(f(V)=\\sum_{v}f(v)\\)":[144],"special":[147],"\\(f\\equiv":[149],"1\\)":[150],"shows":[151],"duplicates":[154],"classic":[156],"bound":[158],"matching,":[162],"\\(O(\\sqrt{n}":[163]},"counts_by_year":[],"updated_date":"2025-12-23T23:11:35.936235","created_date":"2024-09-24T00:00:00"}
