{"id":"https://openalex.org/W2018262123","doi":"https://doi.org/10.1109/cec.2010.5585920","title":"Meta-heuristic search and square erickson matrices","display_name":"Meta-heuristic search and square erickson matrices","publication_year":2010,"publication_date":"2010-07-01","ids":{"openalex":"https://openalex.org/W2018262123","doi":"https://doi.org/10.1109/cec.2010.5585920","mag":"2018262123"},"language":"en","primary_location":{"id":"doi:10.1109/cec.2010.5585920","doi":"https://doi.org/10.1109/cec.2010.5585920","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cec.2010.5585920","pdf_url":null,"source":{"id":"https://openalex.org/S4363605353","display_name":"IEEE Congress on Evolutionary Computation (CEC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Congress on Evolutionary Computation","raw_type":"proceedings-article"},"volume":null,"type":"conference-paper","is_traditional":true,"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/A5045208034","display_name":"Denis Robilliard","orcid":"https://orcid.org/0000-0003-1836-6679","observed_orcids":["https://orcid.org/0000-0003-1836-6679"]},"institutions":[{"id":"https://openalex.org/I4387154658","display_name":"Laboratoire d\u2019Informatique Signal et Image de la C\u00f4te d\u2019Opale","ror":"https://ror.org/00tm1qp20","country_code":"FR","type":"facility","lineage":["https://openalex.org/I2802487185","https://openalex.org/I4387154658"]},{"id":"https://openalex.org/I59807433","display_name":"Universit\u00e9 Lille Nord de France","ror":"https://ror.org/03btvgn05","country_code":"FR","type":"education","lineage":["https://openalex.org/I2279609970","https://openalex.org/I59807433"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Denis Robilliard","raw_affiliation_strings":["Laboratoire d'Informatique, Signal et Images de la C\u00f4te d'Opale, Maison de la Recherche Blaise Pascal, Universidad Lille Nord de France, Calais, France","Univ Lille Nord de France, Laboratoire d'Informatique, Signal et Images de la C\u00f4te d'Opale, Maison de la Recherche Blaise Pascal, 50 rue Ferdinand Buisson - BP 719, 62228 CALAIS Cedex, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire d'Informatique, Signal et Images de la C\u00f4te d'Opale, Maison de la Recherche Blaise Pascal, Universidad Lille Nord de France, Calais, France","institution_ids":["https://openalex.org/I4387154658","https://openalex.org/I59807433"]},{"raw_affiliation_string":"Univ Lille Nord de France, Laboratoire d'Informatique, Signal et Images de la C\u00f4te d'Opale, Maison de la Recherche Blaise Pascal, 50 rue Ferdinand Buisson - BP 719, 62228 CALAIS Cedex, France","institution_ids":["https://openalex.org/I4387154658","https://openalex.org/I59807433"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082660969","display_name":"Amine M. Boumaza","orcid":"https://orcid.org/0009-0001-0453-0864","observed_orcids":["https://orcid.org/0009-0001-0453-0864"]},"institutions":[{"id":"https://openalex.org/I4387154658","display_name":"Laboratoire d\u2019Informatique Signal et Image de la C\u00f4te d\u2019Opale","ror":"https://ror.org/00tm1qp20","country_code":"FR","type":"facility","lineage":["https://openalex.org/I2802487185","https://openalex.org/I4387154658"]},{"id":"https://openalex.org/I59807433","display_name":"Universit\u00e9 Lille Nord de France","ror":"https://ror.org/03btvgn05","country_code":"FR","type":"education","lineage":["https://openalex.org/I2279609970","https://openalex.org/I59807433"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Amine Boumaza","raw_affiliation_strings":["Laboratoire d'Informatique, Signal et Images de la C\u00f4te d'Opale, Maison de la Recherche Blaise Pascal, Universidad Lille Nord de France, Calais, France","Univ Lille Nord de France, Laboratoire d'Informatique, Signal et Images de la C\u00f4te d'Opale, Maison de la Recherche Blaise Pascal, 50 rue Ferdinand Buisson - BP 719, 62228 CALAIS Cedex, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire d'Informatique, Signal et Images de la C\u00f4te d'Opale, Maison de la Recherche Blaise Pascal, Universidad Lille Nord de France, Calais, France","institution_ids":["https://openalex.org/I4387154658","https://openalex.org/I59807433"]},{"raw_affiliation_string":"Univ Lille Nord de France, Laboratoire d'Informatique, Signal et Images de la C\u00f4te d'Opale, Maison de la Recherche Blaise Pascal, 50 rue Ferdinand Buisson - BP 719, 62228 CALAIS Cedex, France","institution_ids":["https://openalex.org/I4387154658","https://openalex.org/I59807433"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048171249","display_name":"Virginie Marion-Poty","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4387154658","display_name":"Laboratoire d\u2019Informatique Signal et Image de la C\u00f4te d\u2019Opale","ror":"https://ror.org/00tm1qp20","country_code":"FR","type":"facility","lineage":["https://openalex.org/I2802487185","https://openalex.org/I4387154658"]},{"id":"https://openalex.org/I59807433","display_name":"Universit\u00e9 Lille Nord de France","ror":"https://ror.org/03btvgn05","country_code":"FR","type":"education","lineage":["https://openalex.org/I2279609970","https://openalex.org/I59807433"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Virginie Marion-Poty","raw_affiliation_strings":["Laboratoire d'Informatique, Signal et Images de la C\u00f4te d'Opale, Maison de la Recherche Blaise Pascal, Universidad Lille Nord de France, Calais, France","Univ Lille Nord de France, Laboratoire d'Informatique, Signal et Images de la C\u00f4te d'Opale, Maison de la Recherche Blaise Pascal, 50 rue Ferdinand Buisson - BP 719, 62228 CALAIS Cedex, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire d'Informatique, Signal et Images de la C\u00f4te d'Opale, Maison de la Recherche Blaise Pascal, Universidad Lille Nord de France, Calais, France","institution_ids":["https://openalex.org/I4387154658","https://openalex.org/I59807433"]},{"raw_affiliation_string":"Univ Lille Nord de France, Laboratoire d'Informatique, Signal et Images de la C\u00f4te d'Opale, Maison de la Recherche Blaise Pascal, 50 rue Ferdinand Buisson - BP 719, 62228 CALAIS Cedex, France","institution_ids":["https://openalex.org/I4387154658","https://openalex.org/I59807433"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8422,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.67651403,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":87,"max":92},"biblio":{"volume":"5","issue":null,"first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9785000085830688,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9785000085830688,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.009200000204145908,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.002899999963119626,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/ramsey-theory","display_name":"Ramsey theory","score":0.8429999947547913},{"id":"https://openalex.org/keywords/van-der-waerden-theorem","display_name":"van der Waerden theorem","score":0.847000002861023},{"id":"https://openalex.org/keywords/metaheuristic-search","display_name":"metaheuristic search","score":0.7850000262260437},{"id":"https://openalex.org/keywords/lower-bounds","display_name":"lower bounds","score":0.8500000238418579},{"id":"https://openalex.org/keywords/combinatorial-number-theory","display_name":"combinatorial number theory","score":0.5870000123977661}],"concepts":[{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.544983983039856},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.5113667845726013},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.460812509059906},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3704502582550049},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3207830786705017},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3073533773422241},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06103876233100891}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cec.2010.5585920","doi":"https://doi.org/10.1109/cec.2010.5585920","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cec.2010.5585920","pdf_url":null,"source":{"id":"https://openalex.org/S4363605353","display_name":"IEEE Congress on Evolutionary Computation (CEC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Congress on Evolutionary Computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W18216792","https://openalex.org/W1562606923","https://openalex.org/W1575155528","https://openalex.org/W1576660662","https://openalex.org/W1639032689","https://openalex.org/W1839839470","https://openalex.org/W2056897909","https://openalex.org/W2097571405","https://openalex.org/W2099861483","https://openalex.org/W2106371135","https://openalex.org/W2117396900","https://openalex.org/W2167913911","https://openalex.org/W2171964388","https://openalex.org/W2323697554","https://openalex.org/W2331734388","https://openalex.org/W2484510618","https://openalex.org/W3023540311","https://openalex.org/W4392750738","https://openalex.org/W6634249717","https://openalex.org/W6675709134","https://openalex.org/W6702391514"],"related_works":["https://openalex.org/W2020044057","https://openalex.org/W2331734388","https://openalex.org/W7096675964","https://openalex.org/W7095725989","https://openalex.org/W4407310651","https://openalex.org/W7100898425","https://openalex.org/W6903694995","https://openalex.org/W4297923722","https://openalex.org/W2115811550","https://openalex.org/W4407248590"],"abstract_inverted_index":{"A":[0],"Ramsey":[1],"theory":[2],"problem,":[3,92],"that":[4,34,78,98,179],"can":[5],"be":[6],"seen":[7],"as":[8],"a":[9,57,87,103,161,171],"2":[10],"dimensional":[11],"extension":[12],"of":[13,39,49,56,90,102,109,113,134,148,156,175],"the":[14,30,36,54,63,95,100,114,157],"Van":[15],"der":[16],"Waerden":[17],"theorem,":[18],"was":[19,66],"posed":[20],"by":[21,69],"Martin":[22],"J.":[23],"Erickson":[24],"in":[25,73],"his":[26],"book":[27],"[1]:":[28],"\u201cfind":[29],"minimum":[31,96],"n":[32,79,97,180],"such":[33,170],"if":[35],"lattice":[37],"points":[38,48],"[n]":[40,42,110,112,135],"\u00d7":[41,106,111,123,136,153],"are":[43],"two-colored,":[44],"there":[45],"exist":[46],"four":[47],"one":[50],"color":[51],"lying":[52],"on":[53,141,164],"vertices":[55],"square":[58,173],"with":[59],"sides":[60],"parallel":[61],"to":[62,145],"axes\u201d.":[64],"This":[65],"solved":[67],"recently":[68],"Bacher":[70],"and":[71],"Eliahou":[72],"2009":[74],"[2],":[75],"who":[76],"showed":[77],"=":[80],"15.":[81],"In":[82,166],"this":[83,91,142],"paper":[84],"we":[85,168],"tackle":[86],"derived":[88],"version":[89],"searching":[93],"for":[94,131],"forces":[99],"existence":[101],"monochromatic":[104,151],"[3]":[105,107,152,154],"subgrid":[108,155],"form":[115],"{i,":[116],"i":[117,120],"+":[118,121,126,129],"t,":[119,127],"2t}":[122,130],"{j,":[124],"j":[125,128],"any":[132],"2-coloring":[133],"[n].":[137],"We":[138],"use":[139],"meta-heuristics":[140],"open":[143],"problem":[144],"find":[146],"instances":[147],"2-colorations":[149],"without":[150],"above":[158],"form,":[159],"setting":[160],"lower":[162],"bound":[163],"n.":[165],"particular":[167],"found":[169],"binary":[172],"grid":[174],"size":[176],"662,":[177],"implying":[178],">":[181],"662.":[182]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-10-27T15:51:10.671819","created_date":"2016-06-24T00:00:00"}