{"id":"https://openalex.org/W2572716357","doi":"https://doi.org/10.3103/s0146411616070191","title":"The problem of finding the maximum multiple flow in the divisible network and its special cases","display_name":"The problem of finding the maximum multiple flow in the divisible network and its special cases","publication_year":2016,"publication_date":"2016-12-01","ids":{"openalex":"https://openalex.org/W2572716357","doi":"https://doi.org/10.3103/s0146411616070191","mag":"2572716357"},"language":"en","primary_location":{"id":"doi:10.3103/s0146411616070191","is_oa":false,"landing_page_url":"https://doi.org/10.3103/s0146411616070191","pdf_url":null,"source":{"id":"https://openalex.org/S17203304","display_name":"Automatic Control and Computer Sciences","issn_l":"0146-4116","issn":["0146-4116","1558-108X"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Automatic Control and Computer Sciences","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/A5019524013","display_name":"\u0410. \u0412. \u0421\u043c\u0438\u0440\u043d\u043e\u0432","orcid":"https://orcid.org/0000-0002-0980-2507"},"institutions":[{"id":"https://openalex.org/I198371094","display_name":"Yaroslavl State University","ror":"https://ror.org/044s2fj67","country_code":"RU","type":"education","lineage":["https://openalex.org/I198371094"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"A. V. Smirnov","raw_affiliation_strings":["Demidov Yaroslavl State University, ul. Sovetskaya 14, Yaroslavl, 150000, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Demidov Yaroslavl State University, ul. Sovetskaya 14, Yaroslavl, 150000, Russia","institution_ids":["https://openalex.org/I198371094"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5019524013"],"corresponding_institution_ids":["https://openalex.org/I198371094"],"apc_list":null,"apc_paid":null,"fwci":1.4669,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.83566327,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"50","issue":"7","first_page":"527","last_page":"535"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13601","display_name":"Urban Transport Systems Analysis","score":0.9641000032424927,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13601","display_name":"Urban Transport Systems Analysis","score":0.9641000032424927,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.921999990940094,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.7011812329292297},{"id":"https://openalex.org/keywords/arc","display_name":"Arc (geometry)","score":0.6174243092536926},{"id":"https://openalex.org/keywords/maximum-flow-problem","display_name":"Maximum flow problem","score":0.5870807766914368},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5556624531745911},{"id":"https://openalex.org/keywords/flow-network","display_name":"Flow network","score":0.5003111362457275},{"id":"https://openalex.org/keywords/multiplicity","display_name":"Multiplicity (mathematics)","score":0.4936174154281616},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.43999406695365906},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39760714769363403},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3695847988128662},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3511795997619629},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.21868500113487244},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.1925455927848816},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07645431160926819}],"concepts":[{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.7011812329292297},{"id":"https://openalex.org/C83415579","wikidata":"https://www.wikidata.org/wiki/Q161973","display_name":"Arc (geometry)","level":2,"score":0.6174243092536926},{"id":"https://openalex.org/C157469704","wikidata":"https://www.wikidata.org/wiki/Q2585642","display_name":"Maximum flow problem","level":2,"score":0.5870807766914368},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5556624531745911},{"id":"https://openalex.org/C114809511","wikidata":"https://www.wikidata.org/wiki/Q1412924","display_name":"Flow network","level":2,"score":0.5003111362457275},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.4936174154281616},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.43999406695365906},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39760714769363403},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3695847988128662},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3511795997619629},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.21868500113487244},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.1925455927848816},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07645431160926819}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3103/s0146411616070191","is_oa":false,"landing_page_url":"https://doi.org/10.3103/s0146411616070191","pdf_url":null,"source":{"id":"https://openalex.org/S17203304","display_name":"Automatic Control and Computer Sciences","issn_l":"0146-4116","issn":["0146-4116","1558-108X"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Automatic Control and Computer Sciences","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W86044744","https://openalex.org/W925666063","https://openalex.org/W1964119857","https://openalex.org/W1986043901","https://openalex.org/W2011039300","https://openalex.org/W2045588107","https://openalex.org/W2053913299","https://openalex.org/W2062754819","https://openalex.org/W2066356146","https://openalex.org/W2069323107","https://openalex.org/W2088158318","https://openalex.org/W2093466946","https://openalex.org/W2401610261","https://openalex.org/W2795674018","https://openalex.org/W3144909185","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2375873432","https://openalex.org/W4206915070","https://openalex.org/W2531764854","https://openalex.org/W3161514703","https://openalex.org/W2141299097","https://openalex.org/W1851375266","https://openalex.org/W2610002854","https://openalex.org/W3141113327","https://openalex.org/W4206407367","https://openalex.org/W3035974271"],"abstract_inverted_index":{"In":[0,152,205],"the":[1,3,7,12,72,90,101,109,112,116,120,125,133,142,155,169,179,208,211,228,233,267,275,290,303,308],"article":[2,110],"problem":[4,117,156,215,278,291],"of":[5,14,24,40,58,71,93,108,115,118,210,227,239,249,255,261,264],"finding":[6,119],"maximum":[8,121,212,276],"multiple":[9,29,34,95,122,213,241],"flow":[10,123,214,277],"in":[11,124,148,160,185,282],"network":[13,51,61,74,79,150,187,226,235,310],"any":[15],"natural":[16],"multiplicity":[17,209,304],"k":[18,41,84,193,220,287],"is":[19,37,75,100,141,178,266,292,315],"studied.":[20],"There":[21],"are":[22,45,54,66,87,111,300],"arcs":[23,30,92],"three":[25],"types:":[26],"ordinary":[27,102],"arcs,":[28,43,242],"and":[31,35,62,96,196],"multi-arcs.":[32],"Each":[33,98],"multi-arc":[36,134,147,171,184,313],"a":[38,59,146,161,183,256,283],"union":[39],"linked":[42,91],"which":[44,86,237],"adjusted":[46,88],"with":[47,132,168,311],"each":[48,94,248,262,297],"other.":[49],"The":[50,56,68,105,129,165,224,294],"constructing":[52],"rules":[53],"described.":[55],"definitions":[57],"divisible":[60,73,78,126,130,166,225,234,309],"some":[63],"associated":[64],"subjects":[65],"stated.":[67],"important":[69],"property":[70],"that":[76,137,174,206,232,259],"every":[77],"can":[80,157,216,243,279],"be":[81,158,217,244,280],"partitioned":[82,245],"into":[83,246],"parts,":[85],"on":[89],"multi-arc.":[97,257],"part":[99],"transportation":[103],"network.":[104,127],"main":[106],"results":[107],"following":[113],"subclasses":[114],"1.":[128],"networks":[131,167],"constraints.":[135,172],"Assume":[136,173,231],"only":[138,175,268],"one":[139,176,253],"vertex":[140,144,177,181],"ending":[143,180],"for":[145,182,296,307],"s":[149,191],"parts.":[151],"this":[153],"case":[154,207],"solved":[159,281],"polynomial":[162,284,298],"time.":[163,285],"2.":[164],"weak":[170,312],"k-1":[186],"parts":[188,198],"(1":[189],"\u2264":[190],"<":[192],"\u2212":[194],"1)":[195],"other":[197],"have":[199],"at":[200],"least":[201],"two":[202],"such":[203],"vertices.":[204],"decreased":[218],"to":[219],"-":[221],"s.":[222],"3.":[223],"parallel":[229],"structure.":[230],"component,":[236],"consists":[238],"all":[240],"subcomponents,":[247],"them":[250],"containing":[251],"exactly":[252],"vertex-beginning":[254],"Suppose":[258],"intersection":[260],"pair":[263],"subcomponents":[265],"vertex-network":[269],"source":[270],"x":[271],"0.":[272],"If":[273,286],"k=2,":[274],"\u2265":[288],"3,":[289],"NP-complete.":[293],"algorithms":[295],"subclass":[299],"suggested.":[301],"Also,":[302],"decreasing":[305],"algorithm":[306],"constraints":[314],"formulated.":[316]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1}],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2025-10-10T00:00:00"}
