{"id":"https://openalex.org/W2080488179","doi":"https://doi.org/10.1137/s0097539791278376","title":"An $o(n^3 )$-Time Maximum-Flow Algorithm","display_name":"An $o(n^3 )$-Time Maximum-Flow Algorithm","publication_year":1996,"publication_date":"1996-12-01","ids":{"openalex":"https://openalex.org/W2080488179","doi":"https://doi.org/10.1137/s0097539791278376","mag":"2080488179"},"language":"en","primary_location":{"id":"doi:10.1137/s0097539791278376","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539791278376","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":true,"oa_status":"green","oa_url":"http://hdl.handle.net/11858/00-001M-0000-0014-B08A-3","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046805470","display_name":"Joseph Cheriyan","orcid":"https://orcid.org/0000-0003-0316-7650"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Joseph Cheriyan","raw_affiliation_strings":["School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14853, USA"],"affiliations":[{"raw_affiliation_string":"School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14853, USA","institution_ids":["https://openalex.org/I205783295"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059236728","display_name":"Torben Hagerup","orcid":"https://orcid.org/0000-0001-6974-2473"},"institutions":[{"id":"https://openalex.org/I149899117","display_name":"Max Planck Society","ror":"https://ror.org/01hhn8329","country_code":"DE","type":"funder","lineage":["https://openalex.org/I149899117"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Torben Hagerup","raw_affiliation_strings":["Algorithms and Complexity, MPI for Informatics, Max Planck Society"],"affiliations":[{"raw_affiliation_string":"Algorithms and Complexity, MPI for Informatics, Max Planck Society","institution_ids":["https://openalex.org/I149899117"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010961023","display_name":"Kurt Mehlhorn","orcid":"https://orcid.org/0000-0003-4020-4334"},"institutions":[{"id":"https://openalex.org/I149899117","display_name":"Max Planck Society","ror":"https://ror.org/01hhn8329","country_code":"DE","type":"funder","lineage":["https://openalex.org/I149899117"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Kurt Mehlhorn","raw_affiliation_strings":["Algorithms and Complexity, MPI for Informatics, Max Planck Society"],"affiliations":[{"raw_affiliation_string":"Algorithms and Complexity, MPI for Informatics, Max Planck Society","institution_ids":["https://openalex.org/I149899117"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5046805470"],"corresponding_institution_ids":["https://openalex.org/I205783295"],"apc_list":null,"apc_paid":null,"fwci":2.0612,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.87405542,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"25","issue":"6","first_page":"1144","last_page":"1170"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9988999962806702,"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"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9980999827384949,"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":0.6971315145492554},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.6497517824172974},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.577675461769104},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.542073667049408},{"id":"https://openalex.org/keywords/maximum-flow-problem","display_name":"Maximum flow problem","score":0.5260624289512634},{"id":"https://openalex.org/keywords/log-log-plot","display_name":"Log-log plot","score":0.48389872908592224},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.47525617480278015},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.45266517996788025},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4263775944709778},{"id":"https://openalex.org/keywords/bottleneck","display_name":"Bottleneck","score":0.41853955388069153},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41301143169403076},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35941314697265625},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17259129881858826},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10319653153419495}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6971315145492554},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.6497517824172974},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.577675461769104},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.542073667049408},{"id":"https://openalex.org/C157469704","wikidata":"https://www.wikidata.org/wiki/Q2585642","display_name":"Maximum flow problem","level":2,"score":0.5260624289512634},{"id":"https://openalex.org/C195292467","wikidata":"https://www.wikidata.org/wiki/Q2091879","display_name":"Log-log plot","level":3,"score":0.48389872908592224},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.47525617480278015},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.45266517996788025},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4263775944709778},{"id":"https://openalex.org/C2780513914","wikidata":"https://www.wikidata.org/wiki/Q18210350","display_name":"Bottleneck","level":2,"score":0.41853955388069153},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41301143169403076},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35941314697265625},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17259129881858826},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10319653153419495},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/s0097539791278376","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539791278376","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:pure.mpg.de:item_1331654","is_oa":false,"landing_page_url":"http://hdl.handle.net/11858/00-001M-0000-0014-AB1F-9","pdf_url":null,"source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Computing","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pure.mpg.de:item_1834979","is_oa":true,"landing_page_url":"http://hdl.handle.net/11858/00-001M-0000-0014-B08A-3","pdf_url":null,"source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Research Report / Max-Planck-Institut f\u00fcr Informatik","raw_type":"info:eu-repo/semantics/report"},{"id":"pmh:oai:uni-augsburg.opus-bayern.de:46286","is_oa":false,"landing_page_url":"https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/46286","pdf_url":null,"source":{"id":"https://openalex.org/S4306400930","display_name":"OPUS (Augsburg University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119916105","host_organization_name":"Augsburg University","host_organization_lineage":["https://openalex.org/I119916105"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:pure.mpg.de:item_1834979","is_oa":true,"landing_page_url":"http://hdl.handle.net/11858/00-001M-0000-0014-B08A-3","pdf_url":null,"source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Research Report / Max-Planck-Institut f\u00fcr Informatik","raw_type":"info:eu-repo/semantics/report"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1655990431","https://openalex.org/W1992170089","https://openalex.org/W2007470648","https://openalex.org/W2018804864","https://openalex.org/W2025830455","https://openalex.org/W2046043928","https://openalex.org/W2050034390","https://openalex.org/W2056800373","https://openalex.org/W2057059776","https://openalex.org/W2057399436","https://openalex.org/W2059378738","https://openalex.org/W2090359754","https://openalex.org/W2100440346","https://openalex.org/W2109567578","https://openalex.org/W2130055503","https://openalex.org/W2145532166","https://openalex.org/W2752885492"],"related_works":["https://openalex.org/W2035522910","https://openalex.org/W2005615533","https://openalex.org/W4243665620","https://openalex.org/W1529311266","https://openalex.org/W2047234016","https://openalex.org/W2052169362","https://openalex.org/W1608733163","https://openalex.org/W2623150993","https://openalex.org/W2055932080","https://openalex.org/W3127082728"],"abstract_inverted_index":{"We":[0,182],"show":[1,137],"that":[2,138,185],"a":[3,7,24,45,139],"maximum":[4,140],"flow":[5,57,73,118,141,162],"in":[6,16,41,68,86,127],"network":[8],"with":[9,70,120,193],"n":[10,103],"vertices":[11],"can":[12,142],"be":[13,143],"computed":[14,144],"deterministically":[15,145],"$O({{n^3":[17],"}":[18,108,115,168],"/":[19,61,65,97,100,109,116,148,151,157,169,176],"{\\log":[20,110,170],"n}})$":[21],"time":[22],"on":[23,48,56],"uniform-cost":[25],"RAM.":[26],"For":[27,123],"dense":[28],"graphs,":[29],"this":[30],"improves":[31],"the":[32,82,87,124],"previous":[33,77],"best":[34],"bound":[35],"of":[36,53,84,92,187],"$O(n^3":[37],")$.":[38],"The":[39,51],"bottleneck":[40],"our":[42,93,188],"algorithm":[43,94],"is":[44,59],"combinatorial":[46],"problem":[47],"(unweighted)":[49],"graphs.":[50],"number":[52,83],"operations":[54,74,119,163],"executed":[55],"variables":[58],"$O(n^{{8":[60],"3}}":[62,66],"(\\log":[63,106,155],"n)^{{4":[64],")$,":[67],"contrast":[69],"$\\Omega":[71],"(nm)$":[72],"for":[75],"all":[76,129],"algorithms,":[78],"where":[79],"m":[80],"denotes":[81],"edges":[85],"network.":[88],"A":[89],"randomized":[90],"version":[91],"executes":[95],"$O(n^{{3":[96,147],"2}}":[98,101,149,152,158,177],"m^{{1":[99,150],"\\log":[102,160,179],"+":[104,112,153,159,172,178],"{{n^2":[105],"n)^2":[107,114],"}}(2":[111],"{{n(\\log":[113],"m})$":[117],"high":[121],"probability.":[122],"special":[125],"case":[126],"which":[128],"capacities":[130],"are":[131],"integers":[132],"bounded":[133],"by":[134],"U,":[135],"we":[136],"using":[146],"n^2":[154,173],"U)^{{1":[156,175],"U$":[161],"and":[164],"$O(\\min":[165],"\\{":[166],"{{nm,n^3":[167],"n\\}":[171],"}}(\\log":[174],"U)$":[180],"time.":[181],"finally":[183],"argue":[184],"several":[186],"results":[189],"yield":[190],"parallel":[191],"algorithms":[192],"optimal":[194],"speedup.":[195]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}