{"id":"https://openalex.org/W2759253428","doi":"https://doi.org/10.1145/3127497","title":"The Matching Polytope has Exponential Extension Complexity","display_name":"The Matching Polytope has Exponential Extension Complexity","publication_year":2017,"publication_date":"2017-09-28","ids":{"openalex":"https://openalex.org/W2759253428","doi":"https://doi.org/10.1145/3127497","mag":"2759253428"},"language":"en","primary_location":{"id":"doi:10.1145/3127497","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3127497","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"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":"Journal of the ACM","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/A5008952420","display_name":"Thomas Rothvo\u00df","orcid":"https://orcid.org/0009-0007-8314-0963"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Thomas Rothvoss","raw_affiliation_strings":["University of Washington, Padelford, Seattle, WA"],"affiliations":[{"raw_affiliation_string":"University of Washington, Padelford, Seattle, WA","institution_ids":["https://openalex.org/I201448701"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5008952420"],"corresponding_institution_ids":["https://openalex.org/I201448701"],"apc_list":null,"apc_paid":null,"fwci":7.3438,"has_fulltext":false,"cited_by_count":91,"citation_normalized_percentile":{"value":0.97708006,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"64","issue":"6","first_page":"1","last_page":"19"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9991999864578247,"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":0.9991999864578247,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9991000294685364,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9977999925613403,"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/polytope","display_name":"Polytope","score":0.9308788776397705},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7480586767196655},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.652449905872345},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.6259509325027466},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.6249357461929321},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5759385824203491},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5005178451538086},{"id":"https://openalex.org/keywords/polyhedral-combinatorics","display_name":"Polyhedral combinatorics","score":0.4664587080478668},{"id":"https://openalex.org/keywords/birkhoff-polytope","display_name":"Birkhoff polytope","score":0.450670063495636},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43540728092193604},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4185160994529724},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23912790417671204}],"concepts":[{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.9308788776397705},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7480586767196655},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.652449905872345},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.6259509325027466},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.6249357461929321},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5759385824203491},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5005178451538086},{"id":"https://openalex.org/C174248988","wikidata":"https://www.wikidata.org/wiki/Q8348314","display_name":"Polyhedral combinatorics","level":5,"score":0.4664587080478668},{"id":"https://openalex.org/C206304794","wikidata":"https://www.wikidata.org/wiki/Q4916482","display_name":"Birkhoff polytope","level":5,"score":0.450670063495636},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43540728092193604},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4185160994529724},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23912790417671204},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.0},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3127497","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3127497","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"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":"Journal of the ACM","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8281068745","display_name":null,"funder_award_id":"1115849","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1599370812","https://openalex.org/W1816633297","https://openalex.org/W1965650902","https://openalex.org/W1967232806","https://openalex.org/W1972997295","https://openalex.org/W1985123706","https://openalex.org/W1991528957","https://openalex.org/W2009377295","https://openalex.org/W2031923588","https://openalex.org/W2038907843","https://openalex.org/W2061987651","https://openalex.org/W2066620631","https://openalex.org/W2068066892","https://openalex.org/W2070982319","https://openalex.org/W2081052967","https://openalex.org/W2091039687","https://openalex.org/W2095405086","https://openalex.org/W2111517082","https://openalex.org/W2119368733","https://openalex.org/W2123805664","https://openalex.org/W2134443705","https://openalex.org/W2159584454","https://openalex.org/W2160416472","https://openalex.org/W2161226285","https://openalex.org/W2327315803","https://openalex.org/W2400109196","https://openalex.org/W2534717833","https://openalex.org/W2568023417","https://openalex.org/W2949885909","https://openalex.org/W2951693280","https://openalex.org/W2951982454","https://openalex.org/W2988480584"],"related_works":["https://openalex.org/W2953076628","https://openalex.org/W2016944804","https://openalex.org/W4288417334","https://openalex.org/W3088865259","https://openalex.org/W2069107464","https://openalex.org/W2056010966","https://openalex.org/W2089946268","https://openalex.org/W2346823476","https://openalex.org/W4299594889","https://openalex.org/W3016111003"],"abstract_inverted_index":{"A":[0],"popular":[1],"method":[2],"in":[3,50,90,125],"combinatorial":[4],"optimization":[5],"is":[6,131],"to":[7,29,36,72,162],"express":[8],"polytopes":[9],"P":[10,64,84],",":[11,59],"which":[12,60],"may":[13],"potentially":[14],"have":[15,46],"exponentially":[16],"many":[17,108],"facets,":[18],"as":[19,103],"solutions":[20],"of":[21,33,42,69,120],"linear":[22],"programs":[23],"that":[24,78],"use":[25],"few":[26],"extra":[27],"variables":[28],"reduce":[30],"the":[31,55,66,87,97,117,121,145,149,153],"number":[32,68],"constraints":[34],"down":[35],"a":[37,62,74,126,139],"polynomial.":[38],"After":[39],"two":[40],"decades":[41],"standstill,":[43],"recent":[44],"years":[45],"brought":[47],"amazing":[48],"progress":[49],"showing":[51],"lower":[52,146],"bounds":[53],"for":[54,61,152],"so-called":[56],"extension":[57,118,150],"complexity":[58,119,151],"polytope":[63,76,100,124,155],"denotes":[65],"smallest":[67],"inequalities":[70],"necessary":[71],"describe":[73],"higher-dimensional":[75],"Q":[77],"can":[79,96],"be":[80,101],"linearly":[81],"projected":[82],"on":[83,148],".":[85,137,168],"However,":[86],"central":[88],"question":[89,113],"this":[91,112,142],"field":[92],"remained":[93],"wide":[94],"open:":[95],"perfect":[98,122],"matching":[99,123],"written":[102],"an":[104],"LP":[105],"with":[106],"polynomially":[107],"constraints?":[109],"We":[110],"answer":[111],"negatively.":[114],"In":[115],"fact,":[116],"complete":[127],"n":[128,135,160,166],"-node":[129],"graph":[130],"2":[132,157,163],"\u03a9":[133,158,164],"(":[134,165],")":[136,161,167],"By":[138],"known":[140],"reduction,":[141],"also":[143],"improves":[144],"bound":[147],"TSP":[154],"from":[156],"(\u221a":[159]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":26},{"year":2020,"cited_by_count":13},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
