{"id":"https://openalex.org/W2157164380","doi":"https://doi.org/10.1051/ro:2007024","title":"Clique partitioning of interval graphs with submodular costs on the cliques","display_name":"Clique partitioning of interval graphs with submodular costs on the cliques","publication_year":2007,"publication_date":"2007-07-01","ids":{"openalex":"https://openalex.org/W2157164380","doi":"https://doi.org/10.1051/ro:2007024","mag":"2157164380"},"language":"en","primary_location":{"id":"doi:10.1051/ro:2007024","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ro:2007024","pdf_url":null,"source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868"],"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"],"host_organization_lineage_names":["EDP Sciences"],"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://ir.cwi.nl/pub/11971/11971D.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065602628","display_name":"Dion Gijswijt","orcid":"https://orcid.org/0000-0003-0734-4511"},"institutions":[{"id":"https://openalex.org/I106118109","display_name":"E\u00f6tv\u00f6s Lor\u00e1nd University","ror":"https://ror.org/01jsq2704","country_code":"HU","type":"education","lineage":["https://openalex.org/I106118109"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"Dion Gijswijt","raw_affiliation_strings":["Dep. of Operations Research, EGRES, E\u00f6tv\u00f6s Lorand University, P\u00e1zm\u00e1ny Peter Setany. 1/C, 1117 Budapest, Hungary; dion.gijswijt@gmail.com","Dep. of Operations Research, EGRES, E\u00f6tv\u00f6s Lorand University, P\u00e1zm\u00e1ny Peter Setany. 1/C, 1117 Budapest, Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dep. of Operations Research, EGRES, E\u00f6tv\u00f6s Lorand University, P\u00e1zm\u00e1ny Peter Setany. 1/C, 1117 Budapest, Hungary; dion.gijswijt@gmail.com","institution_ids":["https://openalex.org/I106118109"]},{"raw_affiliation_string":"Dep. of Operations Research, EGRES, E\u00f6tv\u00f6s Lorand University, P\u00e1zm\u00e1ny Peter Setany. 1/C, 1117 Budapest, Hungary","institution_ids":["https://openalex.org/I106118109"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038309602","display_name":"Vincent Jost","orcid":"https://orcid.org/0000-0002-6595-5030"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210136308","display_name":"Translational Innovation in Medicine and Complexity","ror":"https://ror.org/03985kf35","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210095849","https://openalex.org/I4210104684","https://openalex.org/I4210136308","https://openalex.org/I4210159245","https://openalex.org/I899635006","https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Vincent Jost","raw_affiliation_strings":["CNRS, laboratoire Leibniz-IMAG, 46 avenue F\u00e9lix Viallet, 38031 Grenoble Cedex, France; vincent.jost@imag.fr","CNRS, laboratoire Leibniz-IMAG, 46 avenue F\u00e9lix Viallet, 38031 Grenoble Cedex, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CNRS, laboratoire Leibniz-IMAG, 46 avenue F\u00e9lix Viallet, 38031 Grenoble Cedex, France; vincent.jost@imag.fr","institution_ids":["https://openalex.org/I4210136308","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"CNRS, laboratoire Leibniz-IMAG, 46 avenue F\u00e9lix Viallet, 38031 Grenoble Cedex, France","institution_ids":["https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013482862","display_name":"Maurice Queyranne","orcid":"https://orcid.org/0000-0001-7043-788X"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210136308","display_name":"Translational Innovation in Medicine and Complexity","ror":"https://ror.org/03985kf35","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210095849","https://openalex.org/I4210104684","https://openalex.org/I4210136308","https://openalex.org/I4210159245","https://openalex.org/I899635006","https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Maurice Queyranne","raw_affiliation_strings":["CNRS, laboratoire Leibniz-IMAG, 46 avenue F\u00e9lix Viallet, 38031 Grenoble Cedex, France; vincent.jost@imag.fr","CNRS, laboratoire Leibniz-IMAG, 46 avenue F\u00e9lix Viallet, 38031 Grenoble Cedex, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CNRS, laboratoire Leibniz-IMAG, 46 avenue F\u00e9lix Viallet, 38031 Grenoble Cedex, France; vincent.jost@imag.fr","institution_ids":["https://openalex.org/I4210136308","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"CNRS, laboratoire Leibniz-IMAG, 46 avenue F\u00e9lix Viallet, 38031 Grenoble Cedex, France","institution_ids":["https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.7345,"has_fulltext":true,"cited_by_count":38,"citation_normalized_percentile":{"value":0.97098599,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"41","issue":"3","first_page":"275","last_page":"287"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9944999814033508,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9847999811172485,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7894360423088074},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7288904190063477},{"id":"https://openalex.org/keywords/submodular-set-function","display_name":"Submodular set function","score":0.6209881901741028},{"id":"https://openalex.org/keywords/interval-graph","display_name":"Interval graph","score":0.5901145339012146},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5671232342720032},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.5451849699020386},{"id":"https://openalex.org/keywords/split-graph","display_name":"Split graph","score":0.4618280231952667},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.4432709217071533},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.4124460518360138},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3518141508102417},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.16129636764526367}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7894360423088074},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7288904190063477},{"id":"https://openalex.org/C178621042","wikidata":"https://www.wikidata.org/wiki/Q7631710","display_name":"Submodular set function","level":2,"score":0.6209881901741028},{"id":"https://openalex.org/C67810366","wikidata":"https://www.wikidata.org/wiki/Q835942","display_name":"Interval graph","level":5,"score":0.5901145339012146},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5671232342720032},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.5451849699020386},{"id":"https://openalex.org/C8554925","wikidata":"https://www.wikidata.org/wiki/Q3893853","display_name":"Split graph","level":5,"score":0.4618280231952667},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.4432709217071533},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.4124460518360138},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3518141508102417},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.16129636764526367}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1051/ro:2007024","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ro:2007024","pdf_url":null,"source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868"],"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"],"host_organization_lineage_names":["EDP Sciences"],"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:dare.uva.nl:openaire_cris_publications/18ee66c9-12db-478f-9148-50c6068c601c","is_oa":false,"landing_page_url":"https://handle.uba.uva.nl/personal/pure/en/publications/clique-partitioning-of-interval-graphs-with-submodular-costs-on-the-cliques(18ee66c9-12db-478f-9148-50c6068c601c).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Gijswijt, D C, Jost, V & Queyranne, M 2007, 'Clique partitioning of interval graphs with submodular costs on the cliques.', RAIRO : Operations Research, vol. 41, no. 3, pp. 275-288. https://doi.org/10.1051/ro:2007024","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:cwi.nl:11971","is_oa":true,"landing_page_url":"https://ir.cwi.nl/pub/11971","pdf_url":"https://ir.cwi.nl/pub/11971/11971D.pdf","source":{"id":"https://openalex.org/S7407055335","display_name":"Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"RAIRO Operations Research vol. 41 no. 3, pp. 275-287","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.225.8491","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.225.8491","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://oai.cwi.nl/oai/asset/11971/11971A.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00360875v1","is_oa":false,"landing_page_url":"https://hal.science/hal-00360875","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"RAIRO - Operations Research, 2007, 41, pp.275-287","raw_type":"Journal articles"},{"id":"pmh:oai:numdam.org:RO_2007__41_3_275_0","is_oa":false,"landing_page_url":"https://www.numdam.org/articles/10.1051/ro:2007024/","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"},{"id":"pmh:uvapub:oai:dare.uva.nl:publications/18ee66c9-12db-478f-9148-50c6068c601c","is_oa":false,"landing_page_url":"https://dare.uva.nl/personal/pure/en/publications/clique-partitioning-of-interval-graphs-with-submodular-costs-on-the-cliques(18ee66c9-12db-478f-9148-50c6068c601c).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"RAIRO - Operations Research, 41(3), 275 - 288. EDP Sciences","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:cwi.nl:11971","is_oa":true,"landing_page_url":"https://ir.cwi.nl/pub/11971","pdf_url":"https://ir.cwi.nl/pub/11971/11971D.pdf","source":{"id":"https://openalex.org/S7407055335","display_name":"Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"RAIRO Operations Research vol. 41 no. 3, pp. 275-287","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W2157164380.pdf"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W191844704","https://openalex.org/W377799345","https://openalex.org/W1480448117","https://openalex.org/W1484958883","https://openalex.org/W1498089635","https://openalex.org/W1499543701","https://openalex.org/W1604158939","https://openalex.org/W1986115514","https://openalex.org/W2008297846","https://openalex.org/W2029120932","https://openalex.org/W2032299513","https://openalex.org/W2062221600","https://openalex.org/W2093744170","https://openalex.org/W2119336214","https://openalex.org/W2143474538","https://openalex.org/W2154135432","https://openalex.org/W2988480584","https://openalex.org/W3022173737"],"related_works":["https://openalex.org/W2251679127","https://openalex.org/W1534996675","https://openalex.org/W2153789027","https://openalex.org/W1987143101","https://openalex.org/W2006955534","https://openalex.org/W1555816812","https://openalex.org/W1493037708","https://openalex.org/W1986676437","https://openalex.org/W2289382446","https://openalex.org/W1994156213"],"abstract_inverted_index":{"Given":[0],"a":[1,7,20,33,49,67,79,134,157,168,181],"graph":[2,62,170],"G":[3,58,163,187],"=":[4],"(V,E)":[5],"and":[6,63,99,147,171,192],"\u201ccost":[8],"function\u201d":[9],"(provided":[10],"by":[11],"an":[12,60,127,189],"oracle),":[13],"the":[14,30,36,39,42,45,55,86,103,109,148,165],"problem":[15,88],"[PCliqW]":[16,131,161,185],"consists":[17],"in":[18,44,89],"finding":[19],"partition":[21,34],"into":[22],"cliques":[23,43],"of":[24,26,32,38,41,69,85,119,167],"V(G)":[25],"minimum":[27],"cost.":[28],"Here,":[29],"cost":[31],"is":[35,59,108,122,164,173,188,194],"sum":[37],"costs":[40],"partition.":[46],"We":[47,124],"provide":[48,156,180],"polynomial":[50],"time":[51],"dynamic":[52],"program":[53],"for":[54,82,113,130,144,160,184],"case":[56],"where":[57],"interval":[61,190],"f":[64,172,193],"belongs":[65],"to":[66,138,155,179],"subclass":[68],"submodular":[70],"set":[71],"functions,":[72],"which":[73,132],"we":[74],"call":[75],"\u201cvalue-polymatroidal\u201d.":[76],"This":[77,152],"provides":[78],"common":[80,135],"solution":[81],"various":[83],"generalizations":[84],"coloring":[87,98],"co-interval":[90,114],"graphs":[91,146,191],"such":[92,142],"as":[93,143],"max-coloring,":[94],"\u201cGreene-Kleitman's":[95],"dual\u201d,":[96],"probabilist":[97],"chromatic":[100],"entropy.":[101],"In":[102,116],"last":[104],"two":[105],"cases,":[106],"this":[107,176],"first":[110],"polytime":[111],"algorithm":[112],"graphs.":[115],"contrast,":[117],"NP-hardness":[118],"related":[120],"problems":[121],"discussed.":[123],"also":[125],"describe":[126],"ILP":[128],"formulation":[129],"gives":[133],"polyhedral":[136],"framework":[137],"express":[139],"min-max":[140,158,182],"relations":[141],"perfect":[145],"polymatroid":[149],"intersection":[150],"theorem.":[151],"approach":[153,177],"allows":[154],"formula":[159],"if":[162,186],"line-graph":[166],"bipartite":[169],"submodular.":[174],"However,":[175],"fails":[178],"relation":[183],"value-polymatroidal.":[195]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}