{"id":"https://openalex.org/W1981139087","doi":"https://doi.org/10.1137/0215048","title":"The Complexity of Counting Stable Marriages","display_name":"The Complexity of Counting Stable Marriages","publication_year":1986,"publication_date":"1986-08-01","ids":{"openalex":"https://openalex.org/W1981139087","doi":"https://doi.org/10.1137/0215048","mag":"1981139087"},"language":"en","primary_location":{"id":"doi:10.1137/0215048","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0215048","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/A5030437633","display_name":"Robert W. Irving","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Robert W. Irving","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5001137742","display_name":"P.S.H. Leather","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Paul Leather","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5030437633"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":10.5979,"has_fulltext":false,"cited_by_count":224,"citation_normalized_percentile":{"value":0.98086309,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"15","issue":"3","first_page":"655","last_page":"667"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9793000221252441,"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":0.9713000059127808,"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/stable-marriage-problem","display_name":"Stable marriage problem","score":0.8905487060546875},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.7853755950927734},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7667646408081055},{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.6519491076469421},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6494479179382324},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6219461560249329},{"id":"https://openalex.org/keywords/preference","display_name":"Preference","score":0.5668720006942749},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5362083315849304},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5191806554794312},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.44714459776878357},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3871978223323822},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21394839882850647},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1003560721874237}],"concepts":[{"id":"https://openalex.org/C146393371","wikidata":"https://www.wikidata.org/wiki/Q620702","display_name":"Stable marriage problem","level":3,"score":0.8905487060546875},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.7853755950927734},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7667646408081055},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.6519491076469421},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6494479179382324},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6219461560249329},{"id":"https://openalex.org/C2781249084","wikidata":"https://www.wikidata.org/wiki/Q908656","display_name":"Preference","level":2,"score":0.5668720006942749},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5362083315849304},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5191806554794312},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.44714459776878357},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3871978223323822},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21394839882850647},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1003560721874237},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0215048","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0215048","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":0.6399999856948853,"display_name":"Gender equality","id":"https://metadata.un.org/sdg/5"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1998076865","https://openalex.org/W2003494253","https://openalex.org/W2006912660","https://openalex.org/W2017008045","https://openalex.org/W2068574579","https://openalex.org/W2115826669","https://openalex.org/W4235234911","https://openalex.org/W4300890427"],"related_works":["https://openalex.org/W4236362086","https://openalex.org/W4322508012","https://openalex.org/W2145824340","https://openalex.org/W3123407378","https://openalex.org/W3200900840","https://openalex.org/W2072430061","https://openalex.org/W2044621860","https://openalex.org/W2054731762","https://openalex.org/W2593419644","https://openalex.org/W4236298560"],"abstract_inverted_index":{"In":[0],"an":[1,142],"instance":[2,128],"of":[3,6,12,21,27,36,82,98,108,119,122,129,139,141,153,158],"size":[4],"n":[5,13,16],"the":[7,19,22,59,79,83,96,105,109,117,120,130,137,150,154,156],"stable":[8,30,69,74,101,123,159],"marriage":[9,75],"problem,":[10,131],"each":[11,52],"men":[14,37],"and":[15,38,44,132,163],"women":[17,39],"ranks":[18],"members":[20],"opposite":[23],"sex":[24],"in":[25,168],"order":[26],"preference.":[28],"A":[29],"matching":[31,35,70],"is":[32,62,111],"a":[33,87,100],"complete":[34],"such":[40,99],"that":[41,65,78,104,149],"no":[42],"man":[43],"woman":[45],"who":[46],"are":[47,93],"not":[48],"partners":[49,57],"both":[50],"prefer":[51],"other":[53],"to":[54],"their":[55],"actual":[56],"under":[58],"matching.":[60],"It":[61],"well":[63],"known":[64,94],"at":[66],"least":[67],"one":[68],"exists":[71],"for":[72,95,125],"every":[73],"instance,":[76],"so":[77,103],"decision":[80],"version":[81,107,152],"problem":[84,110],"always":[85],"has":[86],"\u201cyes\u201d":[88],"answer.":[89],"Furthermore,":[90],"efficient":[91],"algorithms":[92],"determination":[97],"matching,":[102],"search":[106],"polynomially":[112],"solvable.":[113],"However,":[114],"by":[115],"exploring":[116],"structure":[118],"set":[121,138],"matchings":[124],"any":[126],"particular":[127],"exploiting":[133],"its":[134],"relationship":[135],"with":[136],"antichains":[140],"associated":[143],"partially":[144],"ordered":[145],"set,":[146],"we":[147],"prove":[148],"enumeration":[151],"problem\u2014determining":[155],"number":[157],"matchings\u2014is":[160],"#":[161],"P-complete,":[162],"therefore":[164],"cannot":[165],"be":[166],"solved":[167],"polynomial":[169],"time":[170],"if":[171],"${\\bf":[172],"P}":[173],"\\ne":[174],"{\\bf":[175],"NP}$.":[176]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":14},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":14},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":15},{"year":2018,"cited_by_count":11},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":11},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":7}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
