{"id":"https://openalex.org/W2121768991","doi":"https://doi.org/10.1002/net.3230180404","title":"Polymatroidal flow network models with multiple sinks","display_name":"Polymatroidal flow network models with multiple sinks","publication_year":1988,"publication_date":"1988-12-01","ids":{"openalex":"https://openalex.org/W2121768991","doi":"https://doi.org/10.1002/net.3230180404","mag":"2121768991"},"language":"en","primary_location":{"id":"doi:10.1002/net.3230180404","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230180404","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks","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/A5090957698","display_name":"Awi Federgruen","orcid":"https://orcid.org/0000-0002-7584-4721"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"A. Federgruen","raw_affiliation_strings":["Graduate School of Business, Columbia University, New York, New York 10027","Graduate School of Business, Columbia University, New York, New York 10027;"],"affiliations":[{"raw_affiliation_string":"Graduate School of Business, Columbia University, New York, New York 10027","institution_ids":["https://openalex.org/I78577930"]},{"raw_affiliation_string":"Graduate School of Business, Columbia University, New York, New York 10027;","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113616807","display_name":"H. Groenevelt","orcid":null},"institutions":[{"id":"https://openalex.org/I5388228","display_name":"University of Rochester","ror":"https://ror.org/022kthw22","country_code":"US","type":"education","lineage":["https://openalex.org/I5388228"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"H. Groenevelt","raw_affiliation_strings":["William E. Simon Graduate School of Business Administration, University of Rochester, Rochester, New York 14627","William E. Simon Graduate School of Business Administration, University of Rochester, Rochester, New York 14627#TAB#"],"affiliations":[{"raw_affiliation_string":"William E. Simon Graduate School of Business Administration, University of Rochester, Rochester, New York 14627","institution_ids":["https://openalex.org/I5388228"]},{"raw_affiliation_string":"William E. Simon Graduate School of Business Administration, University of Rochester, Rochester, New York 14627#TAB#","institution_ids":["https://openalex.org/I5388228"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5090957698"],"corresponding_institution_ids":["https://openalex.org/I78577930"],"apc_list":{"value":3400,"currency":"USD","value_usd":3400},"apc_paid":null,"fwci":1.0708,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.77485158,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"18","issue":"4","first_page":"285","last_page":"302"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9983000159263611,"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":0.9983000159263611,"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":0.9923999905586243,"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/T10991","display_name":"Game Theory and Voting Systems","score":0.9614999890327454,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/flow-network","display_name":"Flow network","score":0.757055401802063},{"id":"https://openalex.org/keywords/maximum-flow-problem","display_name":"Maximum flow problem","score":0.742458164691925},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6601762175559998},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5973890423774719},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5857452750205994},{"id":"https://openalex.org/keywords/minimum-cost-flow-problem","display_name":"Minimum-cost flow problem","score":0.585094690322876},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.54837965965271},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.5010855197906494},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4982895851135254},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4899212718009949},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.459328830242157},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4579244554042816},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4465126395225525},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4140242338180542},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.36913228034973145},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2636321485042572},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.21132206916809082},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.14951196312904358}],"concepts":[{"id":"https://openalex.org/C114809511","wikidata":"https://www.wikidata.org/wiki/Q1412924","display_name":"Flow network","level":2,"score":0.757055401802063},{"id":"https://openalex.org/C157469704","wikidata":"https://www.wikidata.org/wiki/Q2585642","display_name":"Maximum flow problem","level":2,"score":0.742458164691925},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6601762175559998},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5973890423774719},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5857452750205994},{"id":"https://openalex.org/C99545648","wikidata":"https://www.wikidata.org/wiki/Q2897180","display_name":"Minimum-cost flow problem","level":3,"score":0.585094690322876},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.54837965965271},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.5010855197906494},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4982895851135254},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4899212718009949},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.459328830242157},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4579244554042816},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4465126395225525},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4140242338180542},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.36913228034973145},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2636321485042572},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.21132206916809082},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.14951196312904358},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/net.3230180404","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230180404","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks","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":36,"referenced_works":["https://openalex.org/W53882339","https://openalex.org/W191352186","https://openalex.org/W1569458199","https://openalex.org/W1964119857","https://openalex.org/W1978082132","https://openalex.org/W1996754234","https://openalex.org/W2006254094","https://openalex.org/W2010580694","https://openalex.org/W2012329067","https://openalex.org/W2014478542","https://openalex.org/W2019315437","https://openalex.org/W2020801079","https://openalex.org/W2025410044","https://openalex.org/W2043913312","https://openalex.org/W2057927002","https://openalex.org/W2069323107","https://openalex.org/W2070911930","https://openalex.org/W2072492565","https://openalex.org/W2080656989","https://openalex.org/W2081013866","https://openalex.org/W2081185597","https://openalex.org/W2089738123","https://openalex.org/W2096521993","https://openalex.org/W2101957348","https://openalex.org/W2124531440","https://openalex.org/W2125690626","https://openalex.org/W2128805075","https://openalex.org/W2129391890","https://openalex.org/W2141546571","https://openalex.org/W2155921933","https://openalex.org/W2157503827","https://openalex.org/W2170569385","https://openalex.org/W2276056289","https://openalex.org/W4238237534","https://openalex.org/W4238748775","https://openalex.org/W4244424643"],"related_works":["https://openalex.org/W3161514703","https://openalex.org/W3035974271","https://openalex.org/W3141113327","https://openalex.org/W4206915070","https://openalex.org/W2080904092","https://openalex.org/W2531764854","https://openalex.org/W2051329268","https://openalex.org/W1994440468","https://openalex.org/W1970952976","https://openalex.org/W2182648737"],"abstract_inverted_index":{"Abstract":[0],"We":[1,58],"consider":[2],"the":[3,14,24,65,97,109,119,149],"polymatroidal":[4,36,124],"flow":[5,17,92,128,154],"network":[6,129],"model":[7,64],"which":[8],"incorporates":[9],"two":[10],"important":[11,54],"extensions":[12],"of":[13,23,26,31,41,53,67,96,111,123,151],"standard":[15],"maximal":[16],"problem:":[18],"general":[19,63],"concave":[20],"objective":[21,98],"functions":[22],"vector":[25],"supplies":[27],"to":[28,47],"a":[29,48,73,100],"collection":[30],"sinks,":[32],"as":[33,35],"well":[34],"capacity":[37,139],"restrictions":[38,140],"on":[39,133,141],"sets":[40],"arcs":[42,143],"emanating":[43],"from":[44],"or":[45],"pointing":[46],"common":[49,121],"node.":[50],"A":[51],"number":[52,110],"applications":[55],"are":[56],"reviewed.":[57],"show":[59],"that":[60,76,117],"in":[61,157,162],"this":[62],"set":[66],"feasible":[68],"supply":[69],"vectors":[70],"is":[71,108,115],"itself":[72],"polymatroid,":[74],"and":[75,94],"an":[77,126,134,158],"optimal":[78],"solution":[79],"may":[80],"be":[81,131],"determined":[82],"by":[83],"at":[84],"most":[85,120],"2|V":[86],"*":[87,106],"|":[88,107],"\u2014":[89],"1":[90],"maximum":[91,153],"computations":[93],"optimizations":[95],"over":[99],"single":[101],"budget":[102],"constraint,":[103],"where":[104],"|V":[105],"sinks.":[112],"Also,":[113],"it":[114],"shown":[116],"for":[118,148],"types":[122],"structures":[125],"equivalent":[127],"can":[130],"constructed":[132],"expanded":[135],"graph":[136],"but":[137],"with":[138],"individual":[142],"only.":[144],"This":[145],"transformation":[146],"allows":[147],"use":[150],"classical":[152],"procedures":[155],"resulting":[156],"often":[159],"dramatic":[160],"reduction":[161],"complexity.":[163]},"counts_by_year":[{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-03T22:45:19.894376","created_date":"2025-10-10T00:00:00"}
