{"id":"https://openalex.org/W2466314701","doi":"https://doi.org/10.1007/978-1-349-16675-6_9","title":"Flows in Networks: Basic Model","display_name":"Flows in Networks: Basic Model","publication_year":1982,"publication_date":"1982-01-01","ids":{"openalex":"https://openalex.org/W2466314701","doi":"https://doi.org/10.1007/978-1-349-16675-6_9","mag":"2466314701"},"language":"en","primary_location":{"id":"doi:10.1007/978-1-349-16675-6_9","doi":"https://doi.org/10.1007/978-1-349-16675-6_9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-1-349-16675-6_9","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graph Theory in Operations Research","raw_type":"book-chapter"},"volume":{"id":"https://openalex.org/W4210850639","display_name":"Graph Theory in Operations Research"},"type":"book-chapter","is_traditional":true,"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/A5012267335","display_name":"T. Brian Boffey","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"T. B. Boffey","raw_affiliation_strings":["University of Liverpool, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Liverpool, UK","institution_ids":["https://openalex.org/I146655781"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5012267335"],"corresponding_institution_ids":["https://openalex.org/I146655781"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"196","last_page":"213"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9994999766349792,"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":0.9994999766349792,"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/T12709","display_name":"Optimization and Mathematical Programming","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/network-flow","display_name":"network flow","score":0.8009999990463257},{"id":"https://openalex.org/keywords/max-flow-min-cut-theorem","display_name":"max-flow min-cut theorem","score":0.8939999938011169},{"id":"https://openalex.org/keywords/ford-fulkerson-algorithm","display_name":"Ford-Fulkerson algorithm","score":0.9950000047683716},{"id":"https://openalex.org/keywords/dinic-s-algorithm","display_name":"Dinic's algorithm","score":0.925000011920929},{"id":"https://openalex.org/keywords/capacity-constraints","display_name":"capacity constraints","score":0.47099998593330383},{"id":"https://openalex.org/keywords/flow-networks","display_name":"flow networks","score":0.4129999876022339},{"id":"https://openalex.org/keywords/flow-conservation","display_name":"flow conservation","score":0.32199999690055847},{"id":"https://openalex.org/keywords/maximum-flow","display_name":"maximum flow","score":0.30300000309944153}],"concepts":[{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6716306209564209},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.6655086278915405},{"id":"https://openalex.org/C2780129039","wikidata":"https://www.wikidata.org/wiki/Q1931107","display_name":"Section (typography)","level":2,"score":0.6605156660079956},{"id":"https://openalex.org/C114809511","wikidata":"https://www.wikidata.org/wiki/Q1412924","display_name":"Flow network","level":2,"score":0.5433921813964844},{"id":"https://openalex.org/C157469704","wikidata":"https://www.wikidata.org/wiki/Q2585642","display_name":"Maximum flow problem","level":2,"score":0.5205672383308411},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.518376886844635},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49533382058143616},{"id":"https://openalex.org/C190839683","wikidata":"https://www.wikidata.org/wiki/Q2448197","display_name":"Train","level":2,"score":0.4506152868270874},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.33283305168151855},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.29011571407318115},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.21982058882713318},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12610885500907898},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.1078188419342041},{"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C58640448","wikidata":"https://www.wikidata.org/wiki/Q42515","display_name":"Cartography","level":1,"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:10.1007/978-1-349-16675-6_9","doi":"https://doi.org/10.1007/978-1-349-16675-6_9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-1-349-16675-6_9","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graph Theory in Operations Research","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7208763877","https://openalex.org/W7117452722","https://openalex.org/W2794016876","https://openalex.org/W267630425","https://openalex.org/W2150815458","https://openalex.org/W3136340482","https://openalex.org/W1898105657","https://openalex.org/W7220595475","https://openalex.org/W2171251575","https://openalex.org/W2258441002"],"abstract_inverted_index":{"Many":[0],"problems":[1],"in":[2,93,113,128,142,146],"OR":[3],"are":[4,140],"concerned":[5],"with":[6,122,127,161],"the":[7,21,81,84,90,99,103,149],"flow":[8,22,85,101,157],"of":[9,14,23,56,83,89,137],"some":[10,136,162],"\u2018substance\u2019":[11],"or":[12],"\u2018set":[13],"items\u2019":[15],"through":[16,25,30,35,40,43,48,62,102],"a":[17,26,31,36,51,74,154],"network.":[18,91],"For":[19],"example,":[20],"vehicles":[24],"road":[27],"system,":[28],"trains":[29],"railway":[32],"network,":[33,38],"messages":[34],"communication":[37],"fluids":[39],"pipes,":[41],"electricity":[42],"an":[44,69],"electrical":[45],"circuit,":[46],"people":[47],"customs":[49],"at":[50],"large":[52],"airport,":[53],"jobs":[54],"capable":[55],"being":[57,125],"produced":[58],"on":[59,80,98],"different":[60],"machines":[61],"their":[63],"production":[64],"sequence.":[65],"There":[66],"is":[67,107,111,119,158],"usually":[68],"upper":[70],"limit,":[71],"and":[72,105,135,145,170],"sometimes":[73],"non-zero":[75],"lower":[76],"limit":[77],"as":[78],"well,":[79],"magnitude":[82],"along":[86],"each":[87],"arc":[88],"This":[92],"turn":[94],"leads":[95],"to":[96,165],"restrictions":[97],"total":[100],"network":[104],"it":[106],"this":[108],"aspect":[109],"which":[110],"introduced":[112],"section":[114,143,147],"9.1.":[115],"A":[116],"basic":[117],"model":[118],"put":[120],"forward":[121],"various":[123],"extensions":[124],"dealt":[126],"chapter":[129],"10.":[130],"The":[131],"max-flow":[132],"min-cut":[133],"theorem":[134],"its":[138],"consequences":[139],"given":[141],"9.1,":[144],"9.2":[148],"Ford\u2014Fulkerson":[150],"algorithm":[151],"for":[152],"obtaining":[153],"maximal":[155],"static":[156],"presented":[159],"together":[160],"refinements":[163],"due":[164],"Dinic":[166],"(1970),":[167],"Karzanov":[168],"(1974)":[169],"Pohl":[171],"(1977).":[172]},"counts_by_year":[],"updated_date":"2026-10-10T09:11:00.788812","created_date":"2016-07-22T00:00:00"}
