{"id":"https://openalex.org/W7161140958","doi":"https://doi.org/10.1016/j.cor.2026.107535","title":"A parallel branch-and-bound-and-check algorithm for nesting","display_name":"A parallel branch-and-bound-and-check algorithm for nesting","publication_year":2026,"publication_date":"2026-05-15","ids":{"openalex":"https://openalex.org/W7161140958","doi":"https://doi.org/10.1016/j.cor.2026.107535"},"language":"en","primary_location":{"id":"doi:10.1016/j.cor.2026.107535","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.cor.2026.107535","pdf_url":null,"source":{"id":"https://openalex.org/S173256270","display_name":"Computers & Operations Research","issn_l":"0305-0548","issn":["0305-0548","1873-765X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computers & Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/j.cor.2026.107535","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136186220","display_name":"Juan J. Lastra-D\u00edaz","orcid":"https://orcid.org/0000-0003-2522-4222"},"institutions":[{"id":"https://openalex.org/I121748325","display_name":"Universidad Complutense de Madrid","ror":"https://ror.org/02p0gd045","country_code":"ES","type":"education","lineage":["https://openalex.org/I121748325"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Juan J. Lastra-D\u00edaz","raw_affiliation_strings":["Department of Statistics and Operational Research, Institute of Interdisciplinary Mathematics, UCM Research Group HUMLOG, Complutense University of Madrid, Spain"],"raw_orcid":"https://orcid.org/0000-0003-2522-4222","affiliations":[{"raw_affiliation_string":"Department of Statistics and Operational Research, Institute of Interdisciplinary Mathematics, UCM Research Group HUMLOG, Complutense University of Madrid, Spain","institution_ids":["https://openalex.org/I121748325"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5136106462","display_name":"M. Teresa Ortu\u00f1o","orcid":"https://orcid.org/0000-0002-5568-9496"},"institutions":[{"id":"https://openalex.org/I121748325","display_name":"Universidad Complutense de Madrid","ror":"https://ror.org/02p0gd045","country_code":"ES","type":"education","lineage":["https://openalex.org/I121748325"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"M. Teresa Ortu\u00f1o","raw_affiliation_strings":["Department of Statistics and Operational Research, Institute of Interdisciplinary Mathematics, UCM Research Group HUMLOG, Complutense University of Madrid, Spain"],"raw_orcid":"https://orcid.org/0000-0002-5568-9496","affiliations":[{"raw_affiliation_string":"Department of Statistics and Operational Research, Institute of Interdisciplinary Mathematics, UCM Research Group HUMLOG, Complutense University of Madrid, Spain","institution_ids":["https://openalex.org/I121748325"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5136186220"],"corresponding_institution_ids":["https://openalex.org/I121748325"],"apc_list":{"value":3210,"currency":"USD","value_usd":3210},"apc_paid":{"value":3210,"currency":"USD","value_usd":3210},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.69366482,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"194","issue":null,"first_page":"107535","last_page":"107535"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.28999999165534973,"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"}},"topics":[{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.28999999165534973,"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.13169999420642853,"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/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.05730000138282776,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/nesting","display_name":"Nesting (process)","score":0.7774999737739563},{"id":"https://openalex.org/keywords/parallel-algorithm","display_name":"Parallel algorithm","score":0.2773999869823456},{"id":"https://openalex.org/keywords/algorithm-design","display_name":"Algorithm design","score":0.22709999978542328}],"concepts":[{"id":"https://openalex.org/C2776937656","wikidata":"https://www.wikidata.org/wiki/Q2229669","display_name":"Nesting (process)","level":2,"score":0.7774999737739563},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.559499979019165},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5203999876976013},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4002000093460083},{"id":"https://openalex.org/C120373497","wikidata":"https://www.wikidata.org/wiki/Q1087987","display_name":"Parallel algorithm","level":2,"score":0.2773999869823456},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2728999853134155},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.26330000162124634},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2630999982357025},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2578999996185303},{"id":"https://openalex.org/C106516650","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm design","level":2,"score":0.22709999978542328}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.cor.2026.107535","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.cor.2026.107535","pdf_url":null,"source":{"id":"https://openalex.org/S173256270","display_name":"Computers & Operations Research","issn_l":"0305-0548","issn":["0305-0548","1873-765X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computers & Operations Research","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1016/j.cor.2026.107535","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.cor.2026.107535","pdf_url":null,"source":{"id":"https://openalex.org/S173256270","display_name":"Computers & Operations Research","issn_l":"0305-0548","issn":["0305-0548","1873-765X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computers & Operations Research","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":88,"referenced_works":["https://openalex.org/W137767366","https://openalex.org/W1614166303","https://openalex.org/W1930241987","https://openalex.org/W1968206323","https://openalex.org/W1973736134","https://openalex.org/W1977402971","https://openalex.org/W1977813285","https://openalex.org/W1979415050","https://openalex.org/W1988545910","https://openalex.org/W1990267895","https://openalex.org/W1993091251","https://openalex.org/W1998094432","https://openalex.org/W2004489140","https://openalex.org/W2006934540","https://openalex.org/W2007611837","https://openalex.org/W2010017787","https://openalex.org/W2013451793","https://openalex.org/W2018273065","https://openalex.org/W2021335272","https://openalex.org/W2022930575","https://openalex.org/W2027852719","https://openalex.org/W2028245985","https://openalex.org/W2029242918","https://openalex.org/W2036267200","https://openalex.org/W2040277549","https://openalex.org/W2054327146","https://openalex.org/W2058618345","https://openalex.org/W2058662585","https://openalex.org/W2059035667","https://openalex.org/W2059909742","https://openalex.org/W2066554880","https://openalex.org/W2068852367","https://openalex.org/W2070487652","https://openalex.org/W2072897920","https://openalex.org/W2082594743","https://openalex.org/W2083565476","https://openalex.org/W2085774108","https://openalex.org/W2090607424","https://openalex.org/W2090665905","https://openalex.org/W2090669908","https://openalex.org/W2105175235","https://openalex.org/W2106783129","https://openalex.org/W2111661250","https://openalex.org/W2116476963","https://openalex.org/W2123516473","https://openalex.org/W2126819110","https://openalex.org/W2131408469","https://openalex.org/W2134092250","https://openalex.org/W2136150677","https://openalex.org/W2139559439","https://openalex.org/W2149454052","https://openalex.org/W2151720296","https://openalex.org/W2153774705","https://openalex.org/W2164496340","https://openalex.org/W2165715946","https://openalex.org/W2171471009","https://openalex.org/W2294646594","https://openalex.org/W2324827308","https://openalex.org/W2554681195","https://openalex.org/W2589791707","https://openalex.org/W2590527033","https://openalex.org/W2598519374","https://openalex.org/W2754611409","https://openalex.org/W2760337973","https://openalex.org/W2765507185","https://openalex.org/W2807641723","https://openalex.org/W2944379335","https://openalex.org/W2950338282","https://openalex.org/W2971677828","https://openalex.org/W3014672470","https://openalex.org/W3035984753","https://openalex.org/W3036882732","https://openalex.org/W3121105430","https://openalex.org/W3126605228","https://openalex.org/W3157282176","https://openalex.org/W3208902804","https://openalex.org/W4210885149","https://openalex.org/W4211218975","https://openalex.org/W4237834555","https://openalex.org/W4281931618","https://openalex.org/W4317243109","https://openalex.org/W4321503104","https://openalex.org/W4353070770","https://openalex.org/W4378839621","https://openalex.org/W4385652325","https://openalex.org/W4387099028","https://openalex.org/W4390627141","https://openalex.org/W4401243177"],"related_works":[],"abstract_inverted_index":{"The":[0,48],"irregular":[1],"strip":[2,22],"packing":[3],"problem,":[4],"also":[5,201],"known":[6],"as":[7,209],"nesting,":[8],"involves":[9],"computing":[10],"a":[11,15,20,70,95,113,135,156,203,210],"non-overlapping":[12,77],"placement":[13],"of":[14,17,23,42,57,64,76,84,94,127,246],"set":[16,130],"polygons":[18,66],"onto":[19],"rectangular":[21],"fixed":[24],"width":[25],"and":[26,86,120,193,226,239],"minimum":[27],"length.":[28],"Recent":[29],"performance":[30],"gains":[31],"in":[32],"Mixed-Integer":[33],"Linear":[34],"Programming":[35],"(MILP)":[36],"solvers":[37],"have":[38],"encouraged":[39,91],"the":[40,54,58,62,65,74,82,92,101,107,128,161,165,179,183,197,220,244],"proposal":[41,93],"exact":[43,149,173],"optimization":[44],"models":[45],"for":[46],"nesting.":[47],"Dotted-Board":[49],"(DB)":[50],"MILP":[51],"model":[52,163,181],"solves":[53],"discrete":[55],"version":[56],"problem":[59],"by":[60,104],"constraining":[61],"positions":[63],"to":[67,117,159,177,195,224,237],"lie":[68],"on":[69],"fixed-point":[71],"grid.":[72],"However,":[73,110],"number":[75,83],"constraints":[78,108],"grows":[79],"quadratically":[80],"with":[81],"dots":[85],"polygon":[87],"types,":[88],"which":[89],"has":[90],"Clique":[96],"Covering":[97],"reformulation":[98],"(DB-CC),":[99],"setting":[100],"current":[102,125],"state-of-the-art":[103],"significantly":[105,218],"reducing":[106],"required.":[109],"DB-CC":[111,225],"requires":[112],"significant":[114],"preprocessing":[115,153,229],"time":[116,222],"compute":[118],"edge":[119],"vertex":[121],"clique":[122],"coverings.":[123],"Moreover,":[124],"knowledge":[126],"stable":[129],"polytope":[131],"suggests":[132],"that":[133,145,215],"achieving":[134],"tighter":[136],"formulation":[137],"is":[138,144],"unlikely.":[139],"Thus,":[140],"our":[141,216,240],"main":[142],"hypothesis":[143],"an":[146,172],"ad":[147,188],"hoc":[148,189],"algorithm":[150,176,208,217,242],"requiring":[151],"no":[152],"might":[154],"be":[155],"better":[157],"option":[158],"solve":[160,178],"DB":[162,180],"than":[164],"costly":[166],"Branch-and-Cut":[167],"approach.":[168],"This":[169],"work":[170],"proposes":[171],"parallel":[174],"branch-and-bound-and-check":[175],"from":[182],"inverse":[184],"conflict":[185],"graph,":[186],"using":[187],"data":[190],"structures,":[191],"bounding,":[192],"forward-checking":[194],"prune":[196],"search":[198],"space.":[199],"We":[200],"introduce":[202],"new":[204],"Lower":[205],"Bound":[206],"(LB)":[207],"by-product.":[211],"Our":[212],"experiments":[213],"show":[214],"reduces":[219],"resolution":[221],"compared":[223],"eliminates":[227],"its":[228],"step.":[230],"Seventeen":[231],"open":[232],"instances":[233],"are":[234],"solved":[235],"up":[236],"optimality,":[238],"LB":[241],"proves":[243],"optimality":[245],"fifty-one":[247],"instances.":[248]},"counts_by_year":[],"updated_date":"2026-06-21T06:12:48.119943","created_date":"2026-05-15T00:00:00"}