{"id":"https://openalex.org/W2072713008","doi":"https://doi.org/10.1145/2213977.2213981","title":"Strongly polynomial algorithm for a class of minimum-cost flow problems with separable convex objectives","display_name":"Strongly polynomial algorithm for a class of minimum-cost flow problems with separable convex objectives","publication_year":2012,"publication_date":"2012-05-19","ids":{"openalex":"https://openalex.org/W2072713008","doi":"https://doi.org/10.1145/2213977.2213981","mag":"2072713008"},"language":"en","primary_location":{"id":"doi:10.1145/2213977.2213981","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2213977.2213981","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the forty-fourth annual ACM symposium on Theory of computing","raw_type":"proceedings-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/A5049428164","display_name":"L\u00e1szl\u00f3 A. V\u00e9gh","orcid":"https://orcid.org/0000-0003-1152-200X"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"L\u00e1szl\u00f3 A. V\u00e9gh","raw_affiliation_strings":["Georgia Institute of Technology, Atlanta, GA, USA","Georgia Institute of Technology Atlanta, GA, USA"],"affiliations":[{"raw_affiliation_string":"Georgia Institute of Technology, Atlanta, GA, USA","institution_ids":["https://openalex.org/I130701444"]},{"raw_affiliation_string":"Georgia Institute of Technology Atlanta, GA, USA","institution_ids":["https://openalex.org/I130701444"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5049428164"],"corresponding_institution_ids":["https://openalex.org/I130701444"],"apc_list":null,"apc_paid":null,"fwci":3.7064,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.93341763,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"27","last_page":"40"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9994999766349792,"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":0.9968000054359436,"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/separable-space","display_name":"Separable space","score":0.6499807834625244},{"id":"https://openalex.org/keywords/minimum-cost-flow-problem","display_name":"Minimum-cost flow problem","score":0.6182360649108887},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5988855361938477},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5835357308387756},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.504745602607727},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.4800882935523987},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4762428104877472},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4688226878643036},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4142998158931732},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4092090427875519},{"id":"https://openalex.org/keywords/flow-network","display_name":"Flow network","score":0.10618510842323303},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09602820873260498}],"concepts":[{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.6499807834625244},{"id":"https://openalex.org/C99545648","wikidata":"https://www.wikidata.org/wiki/Q2897180","display_name":"Minimum-cost flow problem","level":3,"score":0.6182360649108887},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5988855361938477},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5835357308387756},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.504745602607727},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.4800882935523987},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4762428104877472},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4688226878643036},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4142998158931732},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4092090427875519},{"id":"https://openalex.org/C114809511","wikidata":"https://www.wikidata.org/wiki/Q1412924","display_name":"Flow network","level":2,"score":0.10618510842323303},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09602820873260498},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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":1,"locations":[{"id":"doi:10.1145/2213977.2213981","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2213977.2213981","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the forty-fourth annual ACM symposium on Theory of computing","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W195739637","https://openalex.org/W1560085727","https://openalex.org/W1967991344","https://openalex.org/W1972029377","https://openalex.org/W1974874470","https://openalex.org/W1977545325","https://openalex.org/W1977895455","https://openalex.org/W1979740015","https://openalex.org/W1980938853","https://openalex.org/W1982522946","https://openalex.org/W1986273263","https://openalex.org/W1989262026","https://openalex.org/W2004578381","https://openalex.org/W2005058686","https://openalex.org/W2007572995","https://openalex.org/W2017427261","https://openalex.org/W2027029507","https://openalex.org/W2039010276","https://openalex.org/W2040481133","https://openalex.org/W2046715803","https://openalex.org/W2051716090","https://openalex.org/W2053060972","https://openalex.org/W2053352956","https://openalex.org/W2061274033","https://openalex.org/W2069596575","https://openalex.org/W2084224084","https://openalex.org/W2097004206","https://openalex.org/W2100440346","https://openalex.org/W2103985627","https://openalex.org/W2113766079","https://openalex.org/W2118008360","https://openalex.org/W2135820054","https://openalex.org/W2149342630","https://openalex.org/W2150154671","https://openalex.org/W2154648819","https://openalex.org/W2156036190","https://openalex.org/W2156347727","https://openalex.org/W2508573783","https://openalex.org/W3138620896","https://openalex.org/W6992951189"],"related_works":["https://openalex.org/W4321064619","https://openalex.org/W2009525028","https://openalex.org/W3011179836","https://openalex.org/W2962925412","https://openalex.org/W2023672523","https://openalex.org/W4246719751","https://openalex.org/W2483165346","https://openalex.org/W2053599029","https://openalex.org/W3044475370","https://openalex.org/W2156347727"],"abstract_inverted_index":{"A":[0],"well-studied":[1],"nonlinear":[2],"extension":[3],"of":[4,25,49,55],"the":[5,12,26,94],"minimum-cost":[6,102],"flow":[7],"problem":[8],"is":[9,29,58,126],"to":[10],"minimize":[11],"objective":[13],"\u2211ij\u2208E":[14],"Cij(fij)":[15],"over":[16],"feasible":[17],"flows":[18,103],"f,":[19],"where":[20],"on":[21],"every":[22],"arc":[23],"ij":[24],"network,":[27],"Cij":[28],"a":[30,35,46],"convex":[31,73],"function.":[32],"We":[33,91],"give":[34,93],"strongly":[36,96],"polynomial":[37,97],"algorithm":[38],"for":[39,45,99,105,130,138,151],"finding":[40],"an":[41,60],"exact":[42],"optimal":[43,61],"solution":[44,62],"broad":[47],"class":[48,57],"such":[50],"problems.":[51],"The":[52,123],"key":[53],"characteristic":[54],"this":[56],"that":[59],"can":[63],"be":[64],"computed":[65],"exactly":[66],"provided":[67],"its":[68],"support.":[69],"This":[70],"includes":[71],"separable":[72,100],"quadratic":[74,101,131],"objectives":[75],"and":[76,86,104,119,144],"also":[77],"certain":[78],"market":[79,83,107],"equilibria":[80],"problems:":[81],"Fisher's":[82,106,139],"with":[84,87,108,141],"linear":[85,142],"spending":[88,109,152],"constraint":[89,110,153],"utilities.":[90,154],"thereby":[92],"first":[95],"algorithms":[98],"utilities,":[111],"settling":[112],"open":[113],"questions":[114],"posed":[115],"e.g.":[116],"in":[117,120],"[15]":[118],"[35],":[121],"respectively.":[122],"running":[124],"time":[125],"O(m4":[127],"log":[128,134,136,147,149],"m)":[129,150],"costs,":[132],"O(n4+n2(m+n":[133],"n)":[135,137,148],"markets":[140],"utilities":[143],"O(mn3":[145],"+m2(m+n":[146]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
