{"id":"https://openalex.org/W4220735480","doi":"https://doi.org/10.1137/19m130491x","title":"On Treewidth and Stable Marriage: Parameterized Algorithms and Hardness Results (Complete Characterization)","display_name":"On Treewidth and Stable Marriage: Parameterized Algorithms and Hardness Results (Complete Characterization)","publication_year":2022,"publication_date":"2022-03-01","ids":{"openalex":"https://openalex.org/W4220735480","doi":"https://doi.org/10.1137/19m130491x"},"language":"en","primary_location":{"id":"doi:10.1137/19m130491x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m130491x","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/A5076062797","display_name":"Sushmita Gupta","orcid":"https://orcid.org/0000-0003-1255-8266"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sushmita Gupta","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015806060","display_name":"Saket Saurabh","orcid":"https://orcid.org/0000-0001-7847-6402"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Saket Saurabh","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5082025487","display_name":"Meirav Zehavi","orcid":"https://orcid.org/0000-0002-3636-5322"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Meirav Zehavi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2874,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.55083259,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"36","issue":"1","first_page":"596","last_page":"681"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9994000196456909,"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":0.9994000196456909,"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/T10991","display_name":"Game Theory and Voting Systems","score":0.9803000092506409,"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":0.9469000101089478,"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/treewidth","display_name":"Treewidth","score":0.9702484011650085},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.8998812437057495},{"id":"https://openalex.org/keywords/exponential-time-hypothesis","display_name":"Exponential time hypothesis","score":0.755286693572998},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7119623422622681},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6609729528427124},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4680492579936981},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.42786848545074463},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3848060369491577},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.3110979199409485},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.06641855835914612}],"concepts":[{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.9702484011650085},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.8998812437057495},{"id":"https://openalex.org/C71017364","wikidata":"https://www.wikidata.org/wiki/Q5421532","display_name":"Exponential time hypothesis","level":3,"score":0.755286693572998},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7119623422622681},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6609729528427124},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4680492579936981},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.42786848545074463},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3848060369491577},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.3110979199409485},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.06641855835914612},{"id":"https://openalex.org/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/19m130491x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m130491x","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"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/5","display_name":"Gender equality","score":0.47999998927116394}],"awards":[{"id":"https://openalex.org/G6193796531","display_name":"Lossy Preprocessing","funder_award_id":"819416","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"}],"funders":[{"id":"https://openalex.org/F4320338335","display_name":"H2020 European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W881461489","https://openalex.org/W1518887068","https://openalex.org/W1964590038","https://openalex.org/W1981139087","https://openalex.org/W1985572324","https://openalex.org/W1995725694","https://openalex.org/W1996180590","https://openalex.org/W2000321198","https://openalex.org/W2011268914","https://openalex.org/W2014455522","https://openalex.org/W2042544885","https://openalex.org/W2046229127","https://openalex.org/W2048888597","https://openalex.org/W2051627428","https://openalex.org/W2059209074","https://openalex.org/W2059372025","https://openalex.org/W2068115726","https://openalex.org/W2073547397","https://openalex.org/W2133312780","https://openalex.org/W2144220809","https://openalex.org/W2154426512","https://openalex.org/W2404960361","https://openalex.org/W2791358809","https://openalex.org/W2952126919","https://openalex.org/W2963079722","https://openalex.org/W4253633138"],"related_works":["https://openalex.org/W2113684989","https://openalex.org/W1511821218","https://openalex.org/W4389814085","https://openalex.org/W1531868704","https://openalex.org/W4285659194","https://openalex.org/W3031065515","https://openalex.org/W2810116196","https://openalex.org/W2964032063","https://openalex.org/W4288110151","https://openalex.org/W2956577062"],"abstract_inverted_index":{"Stable":[0,23,27,70,118,144,320],"Marriage":[1,24,28,31,37,71,145,321],"is":[2,87,164,216,238,294],"a":[3,159,312],"fundamental":[4],"problem":[5,19],"to":[6,69,76,102,107,117,128,143,218,324],"both":[7,187,266,282],"computer":[8],"science":[9],"and":[10,35,65,191,260,268,284],"economics.":[11],"Four":[12],"well-known":[13],"NP-hard":[14],"optimization":[15],"versions":[16],"of":[17,52,60,66,85,134,137,140,154,186,200,241,252,316,319],"this":[18,43,257],"are":[20,113,210,244,262],"the":[21,50,57,77,83,121,135,165,184,197,201,235,249,253,290,317],"Sex-Equal":[22],"(SESMI),":[25],"Balanced":[26],"(BSMI),":[29],"max-Stable":[30],"with":[32,38,74,100,322],"Ties":[33,39],"(max-SMTI),":[34],"min-Stable":[36],"(min-SMTI)":[40],"problems.":[41],"In":[42,212,256],"paper,":[44],"we":[45,195,231,247,270,286],"analyze":[46],"these":[47,61,108,124,155,242],"problems":[48,62,67,91,109,182,209,223],"from":[49],"viewpoint":[51],"parameterized":[53,172,177],"complexity.":[54,173],"We":[55,174,204,309],"conduct":[56],"first":[58],"study":[59,196,248],"in":[63,72,92,171,228,277,299],"particular,":[64,213],"related":[68],"general,":[73],"respect":[75,101,323],"parameter":[78,170],"treewidth.":[79,103,325],"The":[80,104],"motivation":[81,122],"behind":[82],"choice":[84,94],"treewidth":[86,136,163,185,198,250],"threefold.":[88],"First,":[89,194],"several":[90,138],"social":[93,111],"theory":[95],"have":[96,146,158],"already":[97,148],"been":[98,149],"studied":[99,168],"networks":[105,141,156],"relevant":[106,116,142],"(say,":[110],"networks)":[112],"clearly":[114],"also":[115,147],"Marriage.":[119],"Thus,":[120],"underlying":[123],"studies":[125,133],"directly":[126],"extends":[127],"our":[129],"study.":[130],"Second,":[131],"empirical":[132],"types":[139],"undertaken,":[150],"identifying":[151],"that":[152,206,220,226,233,275,288,297],"some":[153],"indeed":[157],"treelike":[160],"structure.":[161],"Third,":[162],"most":[166],"well":[167],"structural":[169],"design":[175,271],"optimal":[176],"algorithms":[178,225,243,274,296],"for":[179,281,305],"all":[180,207,221,240],"four":[181,208,222],"under":[183],"their":[188],"primal":[189,202],"graphs":[190],"rotation":[192,254],"digraphs.":[193],"${\\mathtt{tw}}$":[199,251],"graph.":[203],"establish":[205],"W[1]-hard.":[211],"while":[214],"it":[215],"easy":[217],"show":[219],"admit":[224],"run":[227,276,298],"time":[229,278,300],"$n^{{\\mathcal{O}}({\\mathtt{tw}})}$,":[230],"prove":[232,287],"unless":[234,289],"exponential-time":[236,292],"hypothesis":[237,293],"false,":[239,295],"optimal.":[245],"Next,":[246],"digraph.":[255],"context,":[258],"max-SMTI":[259],"min-SMTI":[261],"not":[263,303],"defined.":[264],"For":[265],"SESMI":[267,283],"BSMI,":[269,285],"(highly":[272],"nontrivial)":[273],"$2^{{\\mathtt{tw}}}n^{{\\mathcal{O}}(1)}$.":[279],"Then,":[280],"strong":[291],"$(2-\\epsilon)^{{\\mathtt{tw}}}n^{{\\mathcal{O}}(1)}$":[301],"do":[302],"exist":[304],"any":[306],"fixed":[307],"$\\epsilon>0$.":[308],"thus":[310],"present":[311],"comprehensive,":[313],"complete":[314],"picture":[315],"behavior":[318]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}