{"id":"https://openalex.org/W2129423814","doi":"https://doi.org/10.1142/s0218195900000280","title":"EXACT SOLUTIONS OF RECTANGULAR PARTITIONS VIA INTEGER PROGRAMMING","display_name":"EXACT SOLUTIONS OF RECTANGULAR PARTITIONS VIA INTEGER PROGRAMMING","publication_year":2000,"publication_date":"2000-10-01","ids":{"openalex":"https://openalex.org/W2129423814","doi":"https://doi.org/10.1142/s0218195900000280","mag":"2129423814"},"language":"en","primary_location":{"id":"doi:10.1142/s0218195900000280","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195900000280","pdf_url":null,"source":{"id":"https://openalex.org/S25827807","display_name":"International Journal of Computational Geometry & Applications","issn_l":"0218-1959","issn":["0218-1959","1793-6357"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Geometry &amp; Applications","raw_type":"journal-article"},"type":"article","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/A5031920560","display_name":"Cl\u00e1udio N. Meneses","orcid":"https://orcid.org/0000-0002-7668-9727"},"institutions":[{"id":"https://openalex.org/I181391015","display_name":"Universidade Estadual de Campinas (UNICAMP)","ror":"https://ror.org/04wffgt70","country_code":"BR","type":"education","lineage":["https://openalex.org/I181391015"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"CL\u00c1UDIO N. DE MENESES","raw_affiliation_strings":["Universidade Estadual de Campinas, Instituto de Computa\u00e7\u00e3o, Campinas/SP, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidade Estadual de Campinas, Instituto de Computa\u00e7\u00e3o, Campinas/SP, Brazil","institution_ids":["https://openalex.org/I181391015"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005416520","display_name":"Cid C. de Souza","orcid":"https://orcid.org/0000-0002-5945-0845"},"institutions":[{"id":"https://openalex.org/I181391015","display_name":"Universidade Estadual de Campinas (UNICAMP)","ror":"https://ror.org/04wffgt70","country_code":"BR","type":"education","lineage":["https://openalex.org/I181391015"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"CID C. DE SOUZA","raw_affiliation_strings":["Universidade Estadual de Campinas, Instituto de Computa\u00e7\u00e3o, C.P. 6176, 13083-970, Campinas/SP, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidade Estadual de Campinas, Instituto de Computa\u00e7\u00e3o, C.P. 6176, 13083-970, Campinas/SP, Brazil","institution_ids":["https://openalex.org/I181391015"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3796,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.83034948,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"10","issue":"05","first_page":"477","last_page":"522"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T12176","display_name":"Optimization and Packing Problems","score":0.9873999953269958,"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/T10551","display_name":"Scheduling and Optimization Algorithms","score":0.9717000126838684,"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/mathematics","display_name":"Mathematics","score":0.8225619196891785},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.8112825155258179},{"id":"https://openalex.org/keywords/rectangle","display_name":"Rectangle","score":0.7655527591705322},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.5936851501464844},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5827363729476929},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4895370900630951},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4841652512550354},{"id":"https://openalex.org/keywords/partition-problem","display_name":"Partition problem","score":0.4214797616004944},{"id":"https://openalex.org/keywords/cutting-plane-method","display_name":"Cutting-plane method","score":0.4107479751110077},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36058205366134644},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3389520049095154},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.20092186331748962},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10623824596405029},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0938551127910614}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8225619196891785},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.8112825155258179},{"id":"https://openalex.org/C2781302577","wikidata":"https://www.wikidata.org/wiki/Q209","display_name":"Rectangle","level":2,"score":0.7655527591705322},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.5936851501464844},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5827363729476929},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4895370900630951},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4841652512550354},{"id":"https://openalex.org/C35995877","wikidata":"https://www.wikidata.org/wiki/Q1065968","display_name":"Partition problem","level":3,"score":0.4214797616004944},{"id":"https://openalex.org/C109839438","wikidata":"https://www.wikidata.org/wiki/Q1762039","display_name":"Cutting-plane method","level":3,"score":0.4107479751110077},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36058205366134644},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3389520049095154},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20092186331748962},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10623824596405029},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0938551127910614},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218195900000280","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195900000280","pdf_url":null,"source":{"id":"https://openalex.org/S25827807","display_name":"International Journal of Computational Geometry & Applications","issn_l":"0218-1959","issn":["0218-1959","1793-6357"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Geometry &amp; Applications","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.39.7951","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.39.7951","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://goa.pos.dcc.unicamp.br/otimo/pubtexts/rt98-35.ps.gz","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1975550656","https://openalex.org/W2007813600","https://openalex.org/W2032846908","https://openalex.org/W2100264647"],"related_works":["https://openalex.org/W2048233275","https://openalex.org/W2110818895","https://openalex.org/W2045076853","https://openalex.org/W1973064890","https://openalex.org/W2002159391","https://openalex.org/W2065369945","https://openalex.org/W2038141985","https://openalex.org/W1991394924","https://openalex.org/W3126345618","https://openalex.org/W2039438774"],"abstract_inverted_index":{"Given":[0],"a":[1,8,54,79,124,191],"rectangle":[2,47],"R":[3,24],"in":[4,14,39,98,183,189],"the":[5,18,21,43,49,59,62,65,69,112,131,149,152,168,171,184],"plane":[6],"and":[7,95,121,129,142,151],"finite":[9],"set":[10],"P":[11,35,40],"of":[12,20,23,45,48,53,61,64,71,133,170,181,186,194],"points":[13,188],"its":[15,72],"interior,":[16],"consider":[17],"partitions":[19],"surface":[22],"into":[25],"smaller":[26],"rectangles.":[27,73],"A":[28],"partition":[29,55,81],"is":[30,56,76,198],"feasible":[31,80],"with":[32,82,159,174],"respect":[33],"to":[34,77,91,107,127],"if":[36],"each":[37],"point":[38],"lie":[41],"on":[42],"boundary":[44,70],"some":[46],"partition.":[50],"The":[51,74,164],"length":[52],"computed":[57],"as":[58],"sum":[60],"lengths":[63],"line":[66],"segments":[67],"defining":[68],"goal":[75],"find":[78],"minimum":[83],"length.":[84],"This":[85],"problem,":[86],"denoted":[87],"by":[88,178],"RGP,":[89],"belongs":[90],"[Formula:":[92],"see":[93],"text]-hard":[94],"has":[96],"application":[97],"VLSI":[99],"design.":[100],"In":[101],"this":[102],"paper":[103],"we":[104,145],"investigate":[105],"how":[106],"obtain":[108],"exact":[109],"solutions":[110],"for":[111,140,148],"RGP.":[113],"We":[114],"introduce":[115],"two":[116],"different":[117],"Integer":[118],"Programming":[119],"formulations":[120],"carry":[122],"out":[123],"theoretical":[125],"study":[126],"evaluate":[128],"compare":[130],"strength":[132],"their":[134],"bounds.":[135],"Computational":[136],"experiments":[137],"are":[138,161],"reported":[139],"Branch-and-Cut":[141],"Branch-and-Price":[143],"algorithms":[144,176],"have":[146],"implemented":[147],"first":[150],"second":[153],"formulation,":[154],"respectively.":[155],"Randomly":[156],"generated":[157],"instances":[158,172],"|P|\u2264200":[160],"solved":[162,173],"exactly.":[163],"tests":[165],"indicate":[166],"that":[167],"size":[169],"our":[175],"decrease":[177],"an":[179],"order":[180],"magnitude":[182],"absence":[185],"corectilinear":[187],"P,":[190],"special":[192],"case":[193],"RGP":[195],"whose":[196],"complexity":[197],"still":[199],"open.":[200]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
