{"id":"https://openalex.org/W4224297439","doi":"https://doi.org/10.1142/s1793830922500951","title":"Minimal instances with no weakly stable matching for three-sided problem with cyclic incomplete preferences","display_name":"Minimal instances with no weakly stable matching for three-sided problem with cyclic incomplete preferences","publication_year":2022,"publication_date":"2022-04-19","ids":{"openalex":"https://openalex.org/W4224297439","doi":"https://doi.org/10.1142/s1793830922500951"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830922500951","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830922500951","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","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/A5055448513","display_name":"\u00c9. Yu. Lerner","orcid":"https://orcid.org/0000-0001-5129-5820"},"institutions":[{"id":"https://openalex.org/I21203515","display_name":"Kazan Federal University","ror":"https://ror.org/05256ym39","country_code":"RU","type":"education","lineage":["https://openalex.org/I21203515"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Eduard Yu. Lerner","raw_affiliation_strings":["Department of Data Analysis and Programming Technologies, Institute of Computational Mathematics and Information Technologies, Kazan Federal University, Russia"],"raw_orcid":"https://orcid.org/0000-0001-5129-5820","affiliations":[{"raw_affiliation_string":"Department of Data Analysis and Programming Technologies, Institute of Computational Mathematics and Information Technologies, Kazan Federal University, Russia","institution_ids":["https://openalex.org/I21203515"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058369048","display_name":"Regina E. Lerner","orcid":null},"institutions":[{"id":"https://openalex.org/I153845743","display_name":"Moscow Institute of Physics and Technology","ror":"https://ror.org/00v0z9322","country_code":"RU","type":"education","lineage":["https://openalex.org/I153845743"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Regina E. Lerner","raw_affiliation_strings":["Phystech School of Applied Mathematics and Informatics, Moscow Institute of Physics and Technology, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Phystech School of Applied Mathematics and Informatics, Moscow Institute of Physics and Technology, Russia","institution_ids":["https://openalex.org/I153845743"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5055448513"],"corresponding_institution_ids":["https://openalex.org/I21203515"],"apc_list":null,"apc_paid":null,"fwci":1.3712,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.87163285,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"15","issue":"03","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":1.0,"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":1.0,"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/T11182","display_name":"Auction Theory and Applications","score":0.980400025844574,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9318000078201294,"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/preference","display_name":"Preference","score":0.8698267936706543},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.7931404113769531},{"id":"https://openalex.org/keywords/stable-marriage-problem","display_name":"Stable marriage problem","score":0.739957332611084},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6291384100914001},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5274755358695984},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.4478873312473297},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.329393208026886},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.17532014846801758}],"concepts":[{"id":"https://openalex.org/C2781249084","wikidata":"https://www.wikidata.org/wiki/Q908656","display_name":"Preference","level":2,"score":0.8698267936706543},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.7931404113769531},{"id":"https://openalex.org/C146393371","wikidata":"https://www.wikidata.org/wiki/Q620702","display_name":"Stable marriage problem","level":3,"score":0.739957332611084},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6291384100914001},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5274755358695984},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.4478873312473297},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.329393208026886},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.17532014846801758}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830922500951","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830922500951","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/5","score":0.46000000834465027,"display_name":"Gender equality"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1991220215","https://openalex.org/W1992351112","https://openalex.org/W2068115726","https://openalex.org/W2131227819","https://openalex.org/W2947370633","https://openalex.org/W3027769782","https://openalex.org/W4213094076","https://openalex.org/W4254572365"],"related_works":["https://openalex.org/W4236362086","https://openalex.org/W1976524344","https://openalex.org/W4322508012","https://openalex.org/W2145824340","https://openalex.org/W3123407378","https://openalex.org/W3200900840","https://openalex.org/W2054731762","https://openalex.org/W2072430061","https://openalex.org/W2593419644","https://openalex.org/W4236298560"],"abstract_inverted_index":{"Given":[0],"n":[1,3,6],"men,":[2],"women,":[4,16],"and":[5,26,49,116,189,224],"dogs,":[7,25],"each":[8,17,27,126],"man":[9],"has":[10,19,29],"an":[11,20,30,149,170,177],"incomplete":[12,21,31],"preference":[13,22,32,59,70,81,220],"list":[14,23,33,60,71,82],"of":[15,24,34,44,61,72,83,93,127,151,168,212,230],"woman":[18],"dog":[28,51,55,118],"men.":[35],"We":[36,86,147],"understand":[37,87],"a":[38,41,88,91,112,114,117],"family":[39],"as":[40,90],"triple":[42],"consisting":[43],"one":[45,47,50,109,207],"man,":[46,74,113],"woman,":[48,63,115],"such":[52,169],"that":[53],"the":[54,58,62,69,73,76,80,84,136,166,210,213,228],"belongs":[56,67,78],"to":[57,68,79,105,140,208],"who,":[64],"in":[65,237,243],"turn,":[66],"while":[75],"latter":[77],"dog.":[85],"matching":[89,102,137,161],"collection":[92],"nonintersecting":[94],"families":[95],"(some":[96],"agents,":[97],"possibly,":[98],"remain":[99],"single).":[100],"A":[101],"is":[103,138],"said":[104,139],"be":[106,141],"nonstable,":[107],"if":[108,132],"can":[110],"find":[111],"who":[119],"do":[120],"not":[121],"live":[122],"together":[123],"currently":[124],"but":[125],"them":[128],"would":[129],"become":[130],"\u201chappier\u201d":[131],"they":[133],"do.":[134],"Otherwise,":[135],"stable":[142,145,160,193,232],"(a":[143],"weakly":[144],"matching).":[146],"give":[148],"example":[150,171,178,217],"this":[152],"problem":[153],"for":[154,172,183,218],"[Formula:":[155,173,184],"see":[156,174,185],"text]":[157,186],"where":[158],"no":[159],"exists.":[162],"Moreover,":[163],"we":[164],"prove":[165],"absence":[167],"text].":[175],"Such":[176],"was":[179],"known":[180],"earlier":[181],"only":[182],"[P.":[187],"Bir\u00f3":[188],"E.":[190],"McDermid,":[191],"Three-sided":[192],"matchings":[194,233],"with":[195,234],"cyclic":[196,235],"preferences,":[197,236],"Algorithmica":[198],"58":[199],"(2010)":[200],"5\u201318].":[201],"The":[202],"constructed":[203,215],"examples":[204],"also":[205],"allow":[206],"halve":[209],"size":[211],"recently":[214],"analogous":[216],"complete":[219],"lists":[221],"[C.-K.":[222],"Lam":[223],"C.G.":[225],"Plaxton,":[226],"On":[227],"existence":[229],"three-dimensional":[231],"Algorithmic":[238],"Game":[239],"Theory,":[240],"Lecture":[241],"Notes":[242],"Computer":[244],"Science,":[245],"Vol.":[246],"11801":[247],"(Springer,":[248],"2019),":[249],"pp.":[250],"329\u2013342].":[251]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
