{"id":"https://openalex.org/W2079485638","doi":"https://doi.org/10.1137/100812513","title":"Perfect Matchings in $O(n\\log n)$ Time in Regular Bipartite Graphs","display_name":"Perfect Matchings in $O(n\\log n)$ Time in Regular Bipartite Graphs","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2079485638","doi":"https://doi.org/10.1137/100812513","mag":"2079485638"},"language":"en","primary_location":{"id":"doi:10.1137/100812513","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100812513","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/A5101748190","display_name":"Ashish Goel","orcid":"https://orcid.org/0000-0003-0938-0401"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ashish Goel","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086773451","display_name":"Michael Kapralov","orcid":"https://orcid.org/0009-0006-2882-0459"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael Kapralov","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5039619350","display_name":"Sanjeev Khanna","orcid":"https://orcid.org/0009-0000-2601-1689"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sanjeev Khanna","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101748190"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.9588,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.91084536,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"42","issue":"3","first_page":"1392","last_page":"1404"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9997000098228455,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9997000098228455,"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":0.9988999962806702,"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/T12288","display_name":"Optimization and Search Problems","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.7969536185264587},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.7605084180831909},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7498127818107605},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.5816145539283752},{"id":"https://openalex.org/keywords/randomized-algorithm","display_name":"Randomized algorithm","score":0.5657954812049866},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.49062982201576233},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.48494985699653625},{"id":"https://openalex.org/keywords/deterministic-algorithm","display_name":"Deterministic algorithm","score":0.4749099016189575},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4526725113391876},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4143722653388977},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3360569477081299}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7969536185264587},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.7605084180831909},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7498127818107605},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.5816145539283752},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.5657954812049866},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.49062982201576233},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48494985699653625},{"id":"https://openalex.org/C13533509","wikidata":"https://www.wikidata.org/wiki/Q1064349","display_name":"Deterministic algorithm","level":2,"score":0.4749099016189575},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4526725113391876},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4143722653388977},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3360569477081299},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":8,"locations":[{"id":"doi:10.1137/100812513","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100812513","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"},{"id":"pmh:oai:repository.upenn.edu:cis_papers-1703","is_oa":false,"landing_page_url":"https://repository.upenn.edu/cgi/viewcontent.cgi?article=1703&context=cis_papers","pdf_url":null,"source":{"id":"https://openalex.org/S4306402083","display_name":"ScholarlyCommons (University of Pennsylvania)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79576946","host_organization_name":"University of Pennsylvania","host_organization_lineage":["https://openalex.org/I79576946"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Departmental Papers (CIS)","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.226.73","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.226.73","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.stanford.edu/%7Ekapralov/papers/match-linear.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.246.660","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.246.660","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0909.3346v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.308.6467","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.308.6467","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cis.upenn.edu/~sanjeev/papers/STOC10_PerfectMatchings.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.756.6763","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.756.6763","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0909.3346.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.905.4371","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.905.4371","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://repository.upenn.edu/cgi/viewcontent.cgi?article%3D1703%26context%3Dcis_papers","raw_type":"text"},{"id":"pmh:oai:repository.upenn.edu:20.500.14332/6731","is_oa":false,"landing_page_url":"https://repository.upenn.edu/handle/20.500.14332/6731","pdf_url":null,"source":{"id":"https://openalex.org/S4306402083","display_name":"ScholarlyCommons (University of Pennsylvania)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79576946","host_organization_name":"University of Pennsylvania","host_organization_lineage":["https://openalex.org/I79576946"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"published","raw_type":"Presentation"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1971663478","https://openalex.org/W2004308928","https://openalex.org/W2019496833","https://openalex.org/W2036575499","https://openalex.org/W2047825085","https://openalex.org/W2053050060","https://openalex.org/W2067692201","https://openalex.org/W2120729889","https://openalex.org/W2124624165","https://openalex.org/W2134167260","https://openalex.org/W2145192475","https://openalex.org/W2157529519","https://openalex.org/W2165076510","https://openalex.org/W2170198451","https://openalex.org/W2295428206","https://openalex.org/W2493312408","https://openalex.org/W2952325666","https://openalex.org/W3017089570"],"related_works":["https://openalex.org/W2279830512","https://openalex.org/W3046990805","https://openalex.org/W3097369619","https://openalex.org/W4287691960","https://openalex.org/W2007715402","https://openalex.org/W2004524662","https://openalex.org/W2963181990","https://openalex.org/W2913663107","https://openalex.org/W2960354271","https://openalex.org/W2565109825"],"abstract_inverted_index":{"In":[0,40,61,89],"this":[1,90,187],"paper":[2],"we":[3,92],"consider":[4],"the":[5,72,149,171,197],"well-studied":[6],"problem":[7],"of":[8,65,151,173,201],"finding":[9,196],"a":[10,14,45,62,94,99,103,168,174,189,202,234,239,242],"perfect":[11,100],"matching":[12,46,101,169,240],"in":[13,52,102,108,113,156,170,178,241],"$d$-regular":[15,104],"bipartite":[16,30,42,244],"graph":[17,105],"on":[18],"$2n$":[19],"nodes":[20],"with":[21,116,183,251],"$m=nd$":[22],"edges.":[23],"The":[24,119],"best":[25],"known":[26,48],"algorithm":[27,96,120,134,164,194,236],"for":[28,195,212,223],"general":[29],"graphs":[31],"(due":[32,55],"to":[33,49,56,79,85,128,147],"Hopcroft":[34],"and":[35,59,70,83,106,115,143,246],"Karp)":[36],"takes":[37,247],"time":[38,54,74,111,180,193,215,250],"$O(m\\sqrt{n})$.":[39],"regular":[41,243],"graphs,":[43],"however,":[44],"is":[47,144,210],"be":[50,136],"computable":[51],"$O(m)$":[53,73,184],"Cole,":[57],"Ost,":[58],"Schirra).":[60],"recent":[63],"line":[64],"work":[66],"by":[67,217],"Goel,":[68],"Kapralov,":[69],"Khanna":[71],"bound":[75,222],"was":[76],"improved":[77],"first":[78],"$\\tilde":[80,86],"O\\left(\\min\\{m,":[81,87],"n^{2.5}/d\\}\\right)$":[82],"then":[84],"n^2/d\\}\\right)$.":[88],"paper,":[91],"give":[93,162],"randomized":[95,235],"that":[97,165,208,229,237],"finds":[98,167,238],"runs":[107],"$O(n\\log":[109],"n)$":[110,192,249],"(both":[112],"expectation":[114],"high":[117,252],"probability).":[118],"performs":[121],"an":[122,163,219],"appropriately":[123],"truncated":[124],"alternating":[125],"random":[126],"walk":[127],"successively":[129,166],"find":[130],"augmenting":[131],"paths.":[132],"Our":[133,159],"may":[135],"viewed":[137],"as":[138],"using":[139],"adaptive":[140],"uniform":[141,153],"sampling,":[142],"thus":[145],"able":[146],"bypass":[148],"limitations":[150],"(nonadaptive)":[152],"sampling":[154],"established":[155],"earlier":[157],"work.":[158],"techniques":[160],"also":[161,227],"support":[172],"doubly":[175,203],"stochastic":[176,204],"matrix":[177],"expected":[179],"$O(n\\log^2":[181],"n)$,":[182],"preprocessing":[185],"time;":[186],"gives":[188],"simple":[190],"$O(m+mn\\log^2":[191],"Birkhoff--von":[198],"Neumann":[199],"decomposition":[200],"matrix.":[205],"We":[206,226],"show":[207,228],"randomization":[209],"crucial":[211],"obtaining":[213],"$o(nd)$":[214],"algorithms":[216],"establishing":[218],"$\\Omega(nd)$":[220],"lower":[221],"deterministic":[224],"algorithms.":[225],"there":[230],"does":[231],"not":[232],"exist":[233],"multigraph":[245],"$o(n\\log":[248],"probability.":[253]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}