{"id":"https://openalex.org/W1987197912","doi":"https://doi.org/10.1137/0214045","title":"An $O(n\\log ^2 n)$ Algorithm for Maximum Flow in Undirected Planar Networks","display_name":"An $O(n\\log ^2 n)$ Algorithm for Maximum Flow in Undirected Planar Networks","publication_year":1985,"publication_date":"1985-08-01","ids":{"openalex":"https://openalex.org/W1987197912","doi":"https://doi.org/10.1137/0214045","mag":"1987197912"},"language":"en","primary_location":{"id":"doi:10.1137/0214045","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0214045","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/A5022008503","display_name":"Refael Hassin","orcid":"https://orcid.org/0000-0001-9631-6162"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Refael Hassin","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5103328212","display_name":"D. Barton Johnson","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Donald B. Johnson","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5022008503"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.644,"has_fulltext":false,"cited_by_count":57,"citation_normalized_percentile":{"value":0.82453638,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"14","issue":"3","first_page":"612","last_page":"624"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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":0.9927999973297119,"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/T11106","display_name":"Data Management and Algorithms","score":0.97079998254776,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/maximum-flow-problem","display_name":"Maximum flow problem","score":0.7512115240097046},{"id":"https://openalex.org/keywords/dijkstras-algorithm","display_name":"Dijkstra's algorithm","score":0.7330855131149292},{"id":"https://openalex.org/keywords/shortest-path-problem","display_name":"Shortest path problem","score":0.7292662262916565},{"id":"https://openalex.org/keywords/shortest-path-faster-algorithm","display_name":"Shortest Path Faster Algorithm","score":0.6768781542778015},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6578415632247925},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6210510730743408},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5576298236846924},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5502323508262634},{"id":"https://openalex.org/keywords/yens-algorithm","display_name":"Yen's algorithm","score":0.5384231805801392},{"id":"https://openalex.org/keywords/flow-network","display_name":"Flow network","score":0.5362038016319275},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.5194122791290283},{"id":"https://openalex.org/keywords/suurballes-algorithm","display_name":"Suurballe's algorithm","score":0.49487370252609253},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.4930269420146942},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4928405284881592},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.475471168756485},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.4566788077354431},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.4481578469276428},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.4363551139831543},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22191137075424194},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.14752915501594543},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07427659630775452}],"concepts":[{"id":"https://openalex.org/C157469704","wikidata":"https://www.wikidata.org/wiki/Q2585642","display_name":"Maximum flow problem","level":2,"score":0.7512115240097046},{"id":"https://openalex.org/C173870130","wikidata":"https://www.wikidata.org/wiki/Q8548","display_name":"Dijkstra's algorithm","level":4,"score":0.7330855131149292},{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.7292662262916565},{"id":"https://openalex.org/C168451585","wikidata":"https://www.wikidata.org/wiki/Q7502159","display_name":"Shortest Path Faster Algorithm","level":5,"score":0.6768781542778015},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6578415632247925},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6210510730743408},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5576298236846924},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5502323508262634},{"id":"https://openalex.org/C119971455","wikidata":"https://www.wikidata.org/wiki/Q8052172","display_name":"Yen's algorithm","level":5,"score":0.5384231805801392},{"id":"https://openalex.org/C114809511","wikidata":"https://www.wikidata.org/wiki/Q1412924","display_name":"Flow network","level":2,"score":0.5362038016319275},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.5194122791290283},{"id":"https://openalex.org/C98779529","wikidata":"https://www.wikidata.org/wiki/Q7650417","display_name":"Suurballe's algorithm","level":5,"score":0.49487370252609253},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.4930269420146942},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4928405284881592},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.475471168756485},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.4566788077354431},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.4481578469276428},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.4363551139831543},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22191137075424194},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.14752915501594543},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07427659630775452},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","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},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0214045","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0214045","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W2018804864","https://openalex.org/W2022980325","https://openalex.org/W2039086323","https://openalex.org/W2068595367","https://openalex.org/W2070505654","https://openalex.org/W2113679823","https://openalex.org/W2125690626","https://openalex.org/W2141038472","https://openalex.org/W2169528473","https://openalex.org/W4213060883"],"related_works":["https://openalex.org/W4253588386","https://openalex.org/W2810620529","https://openalex.org/W2147862592","https://openalex.org/W1562631103","https://openalex.org/W2382831994","https://openalex.org/W1508906807","https://openalex.org/W2381419702","https://openalex.org/W2371042914","https://openalex.org/W3015233512","https://openalex.org/W2314157120"],"abstract_inverted_index":{"A":[0],"new":[1],"algorithm":[2,39,81,146,156],"is":[3,22,117,150],"given":[4,48,68],"to":[5,63,120],"find":[6,121],"a":[7,31,41,77,102,113,134,141],"maximum":[8,78],"flow":[9,14,49,124],"in":[10,16,51,66,107,152,157],"an":[11],"undirected":[12],"planar":[13,148],"network":[15,50],"$O(n\\log":[17,108],"^2":[18,109],"n)$":[19,110],"time,":[20],"which":[21,52,116],"faster":[23],"than":[24],"the":[25,44,47,67,74,84,95,122],"best":[26],"method":[27,115],"previously":[28],"known":[29,114],"by":[30,89,112,133],"factor":[32,135],"of":[33,43,46,76,94,104,136,154],"$\\sqrt":[34],"n":[35],"/\\log":[36],"n$.":[37],"The":[38,70,80,126],"constructs":[40],"transformation":[42,71],"dual":[45],"differences":[53],"between":[54],"shortest":[55,85,144,161],"distances":[56,86],"are":[57,163],"equal,":[58],"under":[59],"suitable":[60],"edge":[61,64],"correspondences,":[62],"flows":[65],"network.":[69],"depends":[72],"on":[73],"value":[75],"flow.":[79],"then":[82],"solves":[83],"problem":[87],"efficiently":[88],"exploiting":[90],"certain":[91],"structural":[92],"properties":[93],"transformed":[96],"dual,":[97],"as":[98,100],"well":[99],"using":[101],"set":[103],"cuts":[105],"constructible":[106],"time":[111],"also":[118],"used":[119,151],"requisite":[123],"value.":[125],"main":[127],"result":[128],"can":[129],"be":[130],"further":[131],"improved":[132],"$\\log":[137],"n/\\log^*":[138],"n$":[139],"if":[140],"recently":[142],"developed":[143],"path":[145],"for":[147],"networks":[149],"place":[153],"Dijkstra\u2019s":[155],"each":[158],"step":[159],"where":[160],"paths":[162],"computed.":[164]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}