{"id":"https://openalex.org/W2141890533","doi":"https://doi.org/10.1137/090750299","title":"Stable Roommates Matchings, Mirror Posets, Median Graphs, and the Local/Global Median Phenomenon in Stable Matchings","display_name":"Stable Roommates Matchings, Mirror Posets, Median Graphs, and the Local/Global Median Phenomenon in Stable Matchings","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2141890533","doi":"https://doi.org/10.1137/090750299","mag":"2141890533"},"language":"en","primary_location":{"id":"doi:10.1137/090750299","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090750299","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"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 Discrete Mathematics","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/A5101427454","display_name":"Christine T. Cheng","orcid":"https://orcid.org/0000-0003-0524-5368"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christine T. Cheng","raw_affiliation_strings":["ccheng@cs.uwm.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ccheng@cs.uwm.edu#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001006671","display_name":"Anhua Lin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Anhua Lin","raw_affiliation_strings":["alin@mtsu.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"alin@mtsu.edu#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1575,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.92203679,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"25","issue":"1","first_page":"72","last_page":"94"},"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/T11031","display_name":"Game Theory and Applications","score":0.9815000295639038,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9710000157356262,"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/combinatorics","display_name":"Combinatorics","score":0.8396831750869751},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.76874840259552},{"id":"https://openalex.org/keywords/stable-marriage-problem","display_name":"Stable marriage problem","score":0.5981490015983582},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.47168758511543274},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4351480007171631},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.3912135362625122}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8396831750869751},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.76874840259552},{"id":"https://openalex.org/C146393371","wikidata":"https://www.wikidata.org/wiki/Q620702","display_name":"Stable marriage problem","level":3,"score":0.5981490015983582},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.47168758511543274},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4351480007171631},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.3912135362625122},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/090750299","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090750299","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"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 Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.186.7069","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.186.7069","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.uwm.edu/%7Eccheng/papers/rm19.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.209.1036","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.209.1036","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.uwm.edu/~ccheng/papers/rm17.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6800000071525574,"display_name":"Gender equality","id":"https://metadata.un.org/sdg/5"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W71943752","https://openalex.org/W1571542312","https://openalex.org/W1981139087","https://openalex.org/W1994784589","https://openalex.org/W2006242427","https://openalex.org/W2008810423","https://openalex.org/W2022287675","https://openalex.org/W2033701176","https://openalex.org/W2040506884","https://openalex.org/W2047631336","https://openalex.org/W2068115726","https://openalex.org/W2068574579","https://openalex.org/W2082363232","https://openalex.org/W2084501762","https://openalex.org/W2085944695","https://openalex.org/W2091887239","https://openalex.org/W2098850032","https://openalex.org/W2114200231","https://openalex.org/W2128340555","https://openalex.org/W2143529993","https://openalex.org/W2162195070","https://openalex.org/W2752853835","https://openalex.org/W2952126919","https://openalex.org/W3123388428","https://openalex.org/W3125517159","https://openalex.org/W4235234911"],"related_works":["https://openalex.org/W2010725720","https://openalex.org/W4310066305","https://openalex.org/W2137180285","https://openalex.org/W3200900840","https://openalex.org/W4322508012","https://openalex.org/W2145824340","https://openalex.org/W3123407378","https://openalex.org/W2593419644","https://openalex.org/W3125506481","https://openalex.org/W3125260373"],"abstract_inverted_index":{"For":[0],"stable":[1,6,16,28,35,56,73,79,83,125,154,176],"marriage":[2],"(SM)":[3],"and":[4,41,115,118,127,174,198],"solvable":[5],"roommates":[7],"(SR)":[8],"instances,":[9,33],"it":[10,44],"is":[11,45,143,156],"known":[12,169],"that":[13,18,63,98,133],"there":[14,142],"are":[15,103,162,201],"matchings":[17,74,80,84,126,155],"assign":[19],"each":[20,107],"participant":[21],"to":[22,77,112,123,158,164],"his":[23],"or":[24],"her":[25],"(lower/upper)":[26],"median":[27,47,67,87,136],"partner.":[29],"Moreover,":[30],"for":[31,134,170,208],"SM":[32,72,175,209],"a":[34,46,86],"matching":[36],"has":[37],"this":[38,59],"property":[39],"if":[40,43],"only":[42],"of":[48,92,106,153,180,190,205],"the":[49,54,64,90,165,188,193],"distributive":[50,171],"lattice":[51],"formed":[52],"by":[53],"instance's":[55],"matchings.":[57,177],"In":[58,89],"paper,":[60],"we":[61,95],"show":[62],"above":[65],"local/global":[66],"phenomenon":[68],"first":[69],"observed":[70],"in":[71,192],"also":[75,96,184],"extends":[76],"SR":[78,82,124,145],"because":[81],"form":[85],"graph.":[88],"course":[91],"our":[93],"investigations,":[94],"prove":[97],"three":[99],"seemingly":[100],"different":[101],"structures":[102],"pairwise":[104,166],"duals":[105],"other\u2014median":[108],"graphs":[109],"give":[110,121],"rise":[111,122],"mirror":[113,119],"posets":[114,120],"vice":[116,128],"versa,":[117],"versa.":[129],"Together,":[130],"they":[131],"imply":[132],"every":[135],"graph":[137,152],"G":[138],"with":[139,148],"n":[140],"vertices,":[141],"an":[144],"instance":[146],"$I(G)$":[147],"$O(n^2)$":[149],"participants":[150],"whose":[151],"isomorphic":[157],"G.":[159],"Our":[160,196],"results":[161,168,182],"analogous":[163],"duality":[167],"lattices,":[172],"posets,":[173],"Interestingly,":[178],"some":[179],"these":[181],"can":[183],"be":[185],"inferred":[186],"from":[187],"work":[189],"Feder":[191],"early":[194],"1990s.":[195],"constructions":[197],"proofs,":[199],"however,":[200],"more":[202],"natural":[203],"generalizations":[204],"those":[206],"used":[207],"instances.":[210]},"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}