{"id":"https://openalex.org/W2506178252","doi":"https://doi.org/10.1051/ro/2015052","title":"An efficient cutting plane algorithm for the minimum weighted elementary directed cycle problem in planar digraphs","display_name":"An efficient cutting plane algorithm for the minimum weighted elementary directed cycle problem in planar digraphs","publication_year":2015,"publication_date":"2015-11-13","ids":{"openalex":"https://openalex.org/W2506178252","doi":"https://doi.org/10.1051/ro/2015052","mag":"2506178252"},"language":"en","primary_location":{"id":"doi:10.1051/ro/2015052","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ro/2015052","pdf_url":null,"source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748","https://openalex.org/P4310319982"],"host_organization_lineage_names":["EDP Sciences","Science Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-01360381","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057656219","display_name":"Mamane Souley Ibrahim","orcid":null},"institutions":[{"id":"https://openalex.org/I130359222","display_name":"Universit\u00e9 Abdou Moumouni","ror":"https://ror.org/05tj8pb04","country_code":"NE","type":"education","lineage":["https://openalex.org/I130359222"]}],"countries":["NE"],"is_corresponding":false,"raw_author_name":"Mamane Souley Ibrahim","raw_affiliation_strings":["Universit\u00e9 A. Moumouni, Facult\u00e9 des Sciences, BP 10.622, Niamey, Niger"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 A. Moumouni, Facult\u00e9 des Sciences, BP 10.622, Niamey, Niger","institution_ids":["https://openalex.org/I130359222"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091887230","display_name":"Nelson Maculan","orcid":"https://orcid.org/0000-0002-3897-3356"},"institutions":[{"id":"https://openalex.org/I122140584","display_name":"Universidade Federal do Rio de Janeiro","ror":"https://ror.org/03490as77","country_code":"BR","type":"education","lineage":["https://openalex.org/I122140584"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Nelson Maculan","raw_affiliation_strings":["Federal University of Rio de Janeiro, Rio de Janeiro, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Federal University of Rio de Janeiro, Rio de Janeiro, Brazil","institution_ids":["https://openalex.org/I122140584"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014135514","display_name":"Hac\u00e8ne Ouzia","orcid":"https://orcid.org/0000-0002-3707-6741"},"institutions":[{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]},{"id":"https://openalex.org/I4210159731","display_name":"LIP6","ror":"https://ror.org/05krcen59","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I39804081","https://openalex.org/I4210159245","https://openalex.org/I4210159731"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Hac\u00e8ne Ouzia","raw_affiliation_strings":["Sorbonne Universit\u00e9s, UPMC University Paris 06, LIP6 UMR 7606, 4 place Jussieu, 75005 Paris\u00a0"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sorbonne Universit\u00e9s, UPMC University Paris 06, LIP6 UMR 7606, 4 place Jussieu, 75005 Paris\u00a0","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I4210158291","https://openalex.org/I4210159731"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6674,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.75854258,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"50","issue":"3","first_page":"665","last_page":"675"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","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/T10374","display_name":"Advanced Graph Theory Research","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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9962000250816345,"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/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9941999912261963,"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/digraph","display_name":"Digraph","score":0.7888393402099609},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7481549978256226},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.7288416028022766},{"id":"https://openalex.org/keywords/cutting-plane-method","display_name":"Cutting-plane method","score":0.6511349678039551},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.6279193162918091},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.5760101079940796},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5101523995399475},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.49128812551498413},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4880942106246948},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.47081881761550903},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4552946388721466},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4546743333339691},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3938298225402832},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39168107509613037},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.2921302914619446},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14603868126869202},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09945142269134521},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.07649165391921997}],"concepts":[{"id":"https://openalex.org/C2779145032","wikidata":"https://www.wikidata.org/wiki/Q191494","display_name":"Digraph","level":2,"score":0.7888393402099609},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7481549978256226},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.7288416028022766},{"id":"https://openalex.org/C109839438","wikidata":"https://www.wikidata.org/wiki/Q1762039","display_name":"Cutting-plane method","level":3,"score":0.6511349678039551},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.6279193162918091},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5760101079940796},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5101523995399475},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.49128812551498413},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4880942106246948},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.47081881761550903},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4552946388721466},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4546743333339691},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3938298225402832},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39168107509613037},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.2921302914619446},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14603868126869202},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09945142269134521},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.07649165391921997},{"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/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1051/ro/2015052","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ro/2015052","pdf_url":null,"source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868","2804-7303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748","https://openalex.org/P4310319982"],"host_organization_lineage_names":["EDP Sciences","Science Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-01360381v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01360381","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"RAIRO - Operations Research, 2016, 50 (3), pp.665-675. &#x27E8;10.1051/ro/2015052&#x27E9;","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:numdam.org:RO_2016__50_3_665_0","is_oa":false,"landing_page_url":"https://www.numdam.org/articles/10.1051/ro/2015052/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402264","display_name":"French digital mathematics library (Numdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I70900168","host_organization_name":"Universit\u00e9 Savoie Mont Blanc","host_organization_lineage":["https://openalex.org/I70900168"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-01360381v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01360381","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"RAIRO - Operations Research, 2016, 50 (3), pp.665-675. &#x27E8;10.1051/ro/2015052&#x27E9;","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1969240384","https://openalex.org/W1979740015","https://openalex.org/W1991858502","https://openalex.org/W2009614765","https://openalex.org/W2020990638","https://openalex.org/W2025590553","https://openalex.org/W2045859197","https://openalex.org/W2060673920","https://openalex.org/W2064135070","https://openalex.org/W2086498273","https://openalex.org/W2091682467","https://openalex.org/W2095583085","https://openalex.org/W2116211076","https://openalex.org/W2131353183","https://openalex.org/W2131676402","https://openalex.org/W2506178252","https://openalex.org/W2569646339","https://openalex.org/W4230235511"],"related_works":["https://openalex.org/W2038088825","https://openalex.org/W1975203667","https://openalex.org/W2370328482","https://openalex.org/W4287882779","https://openalex.org/W2046896701","https://openalex.org/W2265849288","https://openalex.org/W2140169421","https://openalex.org/W1996632063","https://openalex.org/W3105997665","https://openalex.org/W2126677049"],"abstract_inverted_index":{"In":[0,104],"this":[1],"paper,":[2],"we":[3,58,83,145],"study":[4],"the":[5,18,90,97,123,138,158,163],"efficiency":[6,91],"(both":[7],"theoretically":[8],"and":[9,43],"computationally)":[10],"of":[11,14,56,65,81,92,96,101,122,137,155],"a":[12,53,78,85,93,117],"class":[13],"valid":[15,36,41,63,99,109],"inequalities":[16,37,42,64,100],"for":[17,153],"minimum":[19],"weighted":[20],"elementary":[21,32,166],"directed":[22,33,167],"cycle":[23,40,62,98],"problem":[24],"(MWEDCP)":[25],"in":[26,68,74,147],"planar":[27,69,134],"digraphs":[28],"with":[29],"negative":[30],"weight":[31],"cycles.":[34],"These":[35],"are":[38,44,128],"called":[39,49],"parametrized":[45],"by":[46],"an":[47],"integer":[48,119,165],"inequality\u2019s":[50],"order.":[51],"From":[52,77],"theoretical":[54],"point":[55,80],"view,":[57,82],"prove":[59],"that":[60],"separating":[61],"order":[66,102],"1":[67],"digraph":[70,135],"can":[71],"be":[72],"done":[73],"polynomial":[75],"time.":[76],"computational":[79,126],"present":[84],"cutting":[86],"plane":[87],"algorithm":[88,112],"featuring":[89],"lifted":[94,108],"form":[95],"1.":[103],"addition":[105],"to":[106],"these":[107],"inequalities,":[110],"our":[111,156],"is":[113],"also":[114],"based":[115],"on":[116,131],"mixed":[118],"linear":[120],"formulation":[121],"MWEDCP.":[124,139],"The":[125],"results":[127],"carried":[129],"out":[130],"randomly":[132],"generated":[133],"instances":[136,143,157],"For":[140],"all":[141],"29":[142],"considered,":[144],"obtain":[146],"average":[148],"26.47%":[149],"gap":[150],"improvement.":[151],"Moreover,":[152],"some":[154],"strengthening":[159],"process":[160],"directly":[161],"displays":[162],"optimal":[164],"cycle.":[168]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-08-15T07:11:24.734988","created_date":"2025-10-10T00:00:00"}
