{"id":"https://openalex.org/W2132818870","doi":"https://doi.org/10.1145/1498698.1564504","title":"Experiments on exact crossing minimization using column generation","display_name":"Experiments on exact crossing minimization using column generation","publication_year":2009,"publication_date":"2009-12-01","ids":{"openalex":"https://openalex.org/W2132818870","doi":"https://doi.org/10.1145/1498698.1564504","mag":"2132818870"},"language":"en","primary_location":{"id":"doi:10.1145/1498698.1564504","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1498698.1564504","pdf_url":null,"source":{"id":"https://openalex.org/S201104086","display_name":"ACM Journal of Experimental Algorithmics","issn_l":"1084-6654","issn":["1084-6654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Journal of Experimental Algorithmics","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/A5044475263","display_name":"Markus Chimani","orcid":"https://orcid.org/0000-0002-4681-5550"},"institutions":[{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Markus Chimani","raw_affiliation_strings":["TU Dortmund, Germany","TU Dortmund, Germany#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"TU Dortmund, Germany","institution_ids":["https://openalex.org/I200332995"]},{"raw_affiliation_string":"TU Dortmund, Germany#TAB#","institution_ids":["https://openalex.org/I200332995"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108096194","display_name":"Carsten Gutwenger","orcid":null},"institutions":[{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Carsten Gutwenger","raw_affiliation_strings":["TU Dortmund, Germany","TU Dortmund, Germany#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"TU Dortmund, Germany","institution_ids":["https://openalex.org/I200332995"]},{"raw_affiliation_string":"TU Dortmund, Germany#TAB#","institution_ids":["https://openalex.org/I200332995"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012801992","display_name":"Petra Mutzel","orcid":"https://orcid.org/0000-0001-7621-971X"},"institutions":[{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Petra Mutzel","raw_affiliation_strings":["TU Dortmund, Germany","TU Dortmund, Germany#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"TU Dortmund, Germany","institution_ids":["https://openalex.org/I200332995"]},{"raw_affiliation_string":"TU Dortmund, Germany#TAB#","institution_ids":["https://openalex.org/I200332995"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I200332995"],"apc_list":null,"apc_paid":null,"fwci":2.5362,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.90200573,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"14","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T11106","display_name":"Data Management and Algorithms","score":0.9923999905586243,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10799","display_name":"Data Visualization and Analytics","score":0.9909999966621399,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/crossing-number","display_name":"Crossing number (knot theory)","score":0.669602632522583},{"id":"https://openalex.org/keywords/column-generation","display_name":"Column generation","score":0.6355160474777222},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.6214410662651062},{"id":"https://openalex.org/keywords/column","display_name":"Column (typography)","score":0.5757203102111816},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.5269842147827148},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49879980087280273},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.45969358086586},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4227175712585449},{"id":"https://openalex.org/keywords/level-crossing","display_name":"Level crossing","score":0.4177754819393158},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.4147886633872986},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39085453748703003},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38841140270233154},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35841405391693115},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.32636159658432007},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11084184050559998},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.08200353384017944}],"concepts":[{"id":"https://openalex.org/C2777724877","wikidata":"https://www.wikidata.org/wiki/Q2548661","display_name":"Crossing number (knot theory)","level":3,"score":0.669602632522583},{"id":"https://openalex.org/C168956720","wikidata":"https://www.wikidata.org/wiki/Q3123181","display_name":"Column generation","level":2,"score":0.6355160474777222},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.6214410662651062},{"id":"https://openalex.org/C2780551164","wikidata":"https://www.wikidata.org/wiki/Q2306599","display_name":"Column (typography)","level":3,"score":0.5757203102111816},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.5269842147827148},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49879980087280273},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.45969358086586},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4227175712585449},{"id":"https://openalex.org/C1975866","wikidata":"https://www.wikidata.org/wiki/Q171448","display_name":"Level crossing","level":2,"score":0.4177754819393158},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.4147886633872986},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39085453748703003},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38841140270233154},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35841405391693115},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32636159658432007},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11084184050559998},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.08200353384017944},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1498698.1564504","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1498698.1564504","pdf_url":null,"source":{"id":"https://openalex.org/S201104086","display_name":"ACM Journal of Experimental Algorithmics","issn_l":"1084-6654","issn":["1084-6654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Journal of Experimental Algorithmics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W15502516","https://openalex.org/W272982077","https://openalex.org/W1490332542","https://openalex.org/W1521554751","https://openalex.org/W1523103567","https://openalex.org/W1528512098","https://openalex.org/W1535967299","https://openalex.org/W1589012584","https://openalex.org/W1598585423","https://openalex.org/W1603713238","https://openalex.org/W1908738628","https://openalex.org/W1968592790","https://openalex.org/W1974970215","https://openalex.org/W1976060438","https://openalex.org/W2005080287","https://openalex.org/W2011039300","https://openalex.org/W2024366499","https://openalex.org/W2035471954","https://openalex.org/W2037121654","https://openalex.org/W2038195012","https://openalex.org/W2052400534","https://openalex.org/W2069321029","https://openalex.org/W2101447138","https://openalex.org/W2105560970","https://openalex.org/W2123054688","https://openalex.org/W2149348205","https://openalex.org/W2161714963","https://openalex.org/W3136685299","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2247897807","https://openalex.org/W1501216548","https://openalex.org/W4287994559","https://openalex.org/W2145082692","https://openalex.org/W2006081158","https://openalex.org/W2031089199","https://openalex.org/W3023007420","https://openalex.org/W2030780938","https://openalex.org/W2165908618","https://openalex.org/W2805001731"],"abstract_inverted_index":{"The":[0,108],"crossing":[1,30,73,136],"number":[2,10,31,47,137],"of":[3,11,17,48,51,111,147],"a":[4],"graph":[5],"G":[6,18],"is":[7,86,114],"the":[8,20,23,29,45,60,65,84,93,115,119,130,134,141,145,148],"smallest":[9],"edge":[12],"crossings":[13],"in":[14,36,59],"any":[15],"drawing":[16],"into":[19],"plane.":[21],"Recently,":[22],"first":[24,85],"branch-and-cut":[25],"approach":[26,121],"for":[27],"solving":[28],"problem":[32],"has":[33],"been":[34],"presented":[35],"Buchheim":[37],"et":[38],"al.":[39],"[2005].":[40],"Its":[41],"major":[42],"drawback":[43],"was":[44],"huge":[46],"variables":[49,103],"out":[50],"which":[52,102],"only":[53],"very":[54],"few":[55],"were":[56],"actually":[57],"used":[58],"optimal":[61],"solution.":[62],"This":[63],"restricted":[64],"algorithm":[66],"to":[67,98,105],"rather":[68],"small":[69],"graphs":[70],"with":[71,144],"low":[72],"number.":[74],"In":[75,126],"this":[76,112],"article,":[77],"we":[78,128],"discuss":[79],"two":[80,124],"column":[81],"generation":[82],"schemes;":[83],"based":[87],"on":[88],"traditional":[89],"algebraic":[90],"pricing,":[91],"and":[92,101,122],"second":[94],"uses":[95],"combinatorial":[96],"arguments":[97],"decide":[99],"whether":[100],"need":[104],"be":[106],"added.":[107],"main":[109],"focus":[110],"article":[113],"experimental":[116],"comparison":[117],"between":[118],"original":[120],"these":[123],"schemes.":[125],"addition,":[127],"evaluate":[129],"quality":[131],"achieved":[132],"by":[133,139],"best-known":[135],"heuristic":[138],"comparing":[140],"new":[142],"results":[143,146],"heuristic.":[149]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}