{"id":"https://openalex.org/W4376136443","doi":"https://doi.org/10.1051/ro/2023062","title":"A parallel lagrangian heuristic for the fractional chromatic number of a graph","display_name":"A parallel lagrangian heuristic for the fractional chromatic number of a graph","publication_year":2023,"publication_date":"2023-05-11","ids":{"openalex":"https://openalex.org/W4376136443","doi":"https://doi.org/10.1051/ro/2023062"},"language":"en","primary_location":{"id":"doi:10.1051/ro/2023062","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1051/ro/2023062","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2023/04/ro230158.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":"hybrid","oa_url":"https://www.rairo-ro.org/articles/ro/pdf/2023/04/ro230158.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040750301","display_name":"Paulo Henrique Mac\u00eado de Ara\u00fajo","orcid":"https://orcid.org/0000-0002-9824-3929"},"institutions":[{"id":"https://openalex.org/I243754102","display_name":"Universidade Federal do Cear\u00e1","ror":"https://ror.org/03srtnf24","country_code":"BR","type":"education","lineage":["https://openalex.org/I243754102"]},{"id":"https://openalex.org/I4210163697","display_name":"Centro Universit\u00e1rio Cat\u00f3lica de Quixad\u00e1","ror":"https://ror.org/053kjm920","country_code":"BR","type":"education","lineage":["https://openalex.org/I4210163697"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Paulo Henrique Mac\u00eado de Ara\u00fajo","raw_affiliation_strings":["Federal University of Cear\u00e1, Quixad\u00e1, Brazil"],"raw_orcid":"https://orcid.org/0000-0002-9824-3929","affiliations":[{"raw_affiliation_string":"Federal University of Cear\u00e1, Quixad\u00e1, Brazil","institution_ids":["https://openalex.org/I243754102","https://openalex.org/I4210163697"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086673620","display_name":"Ricardo C. Corr\u00eaa","orcid":"https://orcid.org/0000-0001-5618-9541"},"institutions":[{"id":"https://openalex.org/I161460629","display_name":"Universidade Federal Rural do Rio de Janeiro","ror":"https://ror.org/00xwgyp12","country_code":"BR","type":"education","lineage":["https://openalex.org/I161460629"]},{"id":"https://openalex.org/I4210099050","display_name":"Universidade Igua\u00e7u","ror":"https://ror.org/0152e2z91","country_code":"BR","type":"education","lineage":["https://openalex.org/I4210099050"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Ricardo C. Corr\u00eaa","raw_affiliation_strings":["Digital Humanities Program, Federal Rural University of Rio de Janeiro, Nova, Igua\u00e7u, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Digital Humanities Program, Federal Rural University of Rio de Janeiro, Nova, Igua\u00e7u, Brazil","institution_ids":["https://openalex.org/I161460629","https://openalex.org/I4210099050"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001592356","display_name":"Manoel Camp\u00ealo","orcid":"https://orcid.org/0000-0003-2962-2033"},"institutions":[{"id":"https://openalex.org/I243754102","display_name":"Universidade Federal do Cear\u00e1","ror":"https://ror.org/03srtnf24","country_code":"BR","type":"education","lineage":["https://openalex.org/I243754102"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Manoel Camp\u00ealo","raw_affiliation_strings":["Federal University of Cear\u00e1, Fortaleza, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Federal University of Cear\u00e1, Fortaleza, Brazil","institution_ids":["https://openalex.org/I243754102"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0749328,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"57","issue":"4","first_page":"1821","last_page":"1841"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9965000152587891,"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"}},"topics":[{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9965000152587891,"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"}},{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T12401","display_name":"Scheduling and Timetabling Solutions","score":0.9941999912261963,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lagrangian-relaxation","display_name":"Lagrangian relaxation","score":0.8642327189445496},{"id":"https://openalex.org/keywords/lagrangian","display_name":"Lagrangian","score":0.7203417420387268},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.6563212871551514},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.6439841985702515},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.601207435131073},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.567815363407135},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5438807606697083},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.4974553883075714},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4882962703704834},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.41883760690689087},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3623603880405426},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3184824585914612},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29014381766319275}],"concepts":[{"id":"https://openalex.org/C91765299","wikidata":"https://www.wikidata.org/wiki/Q3424292","display_name":"Lagrangian relaxation","level":2,"score":0.8642327189445496},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.7203417420387268},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.6563212871551514},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.6439841985702515},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.601207435131073},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.567815363407135},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5438807606697083},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.4974553883075714},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4882962703704834},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.41883760690689087},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3623603880405426},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3184824585914612},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29014381766319275},{"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/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1051/ro/2023062","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1051/ro/2023062","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2023/04/ro230158.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1051/ro/2023062","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1051/ro/2023062","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2023/04/ro230158.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G175681305","display_name":null,"funder_award_id":"309315/ 2019-0","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G2351794437","display_name":null,"funder_award_id":"PS1 - 0186-00155.01.00/21","funder_id":"https://openalex.org/F4320323202","funder_display_name":"Funda\u00e7\u00e3o Cearense de Apoio ao Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G3553312304","display_name":null,"funder_award_id":"PNE - 0112-00061.01.00","funder_id":"https://openalex.org/F4320323202","funder_display_name":"Funda\u00e7\u00e3o Cearense de Apoio ao Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G6970008471","display_name":null,"funder_award_id":"422912/2021-2","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"}],"funders":[{"id":"https://openalex.org/F4320321091","display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","ror":"https://ror.org/00x0ma614"},{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"},{"id":"https://openalex.org/F4320323202","display_name":"Funda\u00e7\u00e3o Cearense de Apoio ao Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/007pgtp80"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4376136443.pdf","grobid_xml":"https://content.openalex.org/works/W4376136443.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1506342804","https://openalex.org/W1980677244","https://openalex.org/W1985136662","https://openalex.org/W2013946649","https://openalex.org/W2023200270","https://openalex.org/W2032876227","https://openalex.org/W2034111852","https://openalex.org/W2053867237","https://openalex.org/W2054651287","https://openalex.org/W2055511722","https://openalex.org/W2059453880","https://openalex.org/W2065578109","https://openalex.org/W2068262026","https://openalex.org/W2095691392","https://openalex.org/W2099813847","https://openalex.org/W2156651388","https://openalex.org/W2157693956","https://openalex.org/W2167036627","https://openalex.org/W2170803232","https://openalex.org/W2407753303","https://openalex.org/W2965740165","https://openalex.org/W3007186320","https://openalex.org/W3170760983","https://openalex.org/W3215181870"],"related_works":["https://openalex.org/W3149469165","https://openalex.org/W4313484281","https://openalex.org/W181997498","https://openalex.org/W1984467068","https://openalex.org/W2027845496","https://openalex.org/W3126007678","https://openalex.org/W2170308554","https://openalex.org/W2616198151","https://openalex.org/W1925942709","https://openalex.org/W2047683846"],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2,26,30,38],"new":[3],"integer":[4],"programming":[5],"formulation":[6,14,35],"for":[7,42],"the":[8,43,53],"Fractional":[9],"Chromatic":[10],"Number":[11],"Problem.":[12],"The":[13],"is":[15],"based":[16],"on":[17],"representatives":[18],"of":[19,33],"stable":[20],"sets.":[21],"In":[22],"addition,":[23],"we":[24],"present":[25],"Lagrangian":[27,31],"heuristic":[28],"from":[29],"relaxation":[32],"this":[34],"to":[36,49],"obtain":[37],"good":[39],"feasible":[40],"solution":[41],"problem.":[44],"Computational":[45],"experiments":[46],"are":[47],"presented":[48],"evaluate":[50],"and":[51,55],"compare":[52],"upper":[54],"lower":[56],"bounds":[57],"provided":[58],"by":[59],"our":[60],"approach.":[61]},"counts_by_year":[],"updated_date":"2026-08-18T07:49:30.821534","created_date":"2025-10-10T00:00:00"}
