{"id":"https://openalex.org/W2782195163","doi":"https://doi.org/10.1145/3325861","title":"Geometric Heuristics for Rectilinear Crossing Minimization","display_name":"Geometric Heuristics for Rectilinear Crossing Minimization","publication_year":2019,"publication_date":"2019-07-19","ids":{"openalex":"https://openalex.org/W2782195163","doi":"https://doi.org/10.1145/3325861","mag":"2782195163"},"language":"en","primary_location":{"id":"doi:10.1145/3325861","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3325861","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/A5014484000","display_name":"Marcel Radermacher","orcid":"https://orcid.org/0000-0002-7661-0767"},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Marcel Radermacher","raw_affiliation_strings":["Karlsruhe Institute of Technology, Karlsruhe, Germany"],"affiliations":[{"raw_affiliation_string":"Karlsruhe Institute of Technology, Karlsruhe, Germany","institution_ids":["https://openalex.org/I102335020"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003564228","display_name":"Klara Reichard","orcid":null},"institutions":[{"id":"https://openalex.org/I186354981","display_name":"University of Passau","ror":"https://ror.org/05ydjnb78","country_code":"DE","type":"education","lineage":["https://openalex.org/I186354981"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Klara Reichard","raw_affiliation_strings":["Universit\u00e4t Passau, Passau, Germany"],"affiliations":[{"raw_affiliation_string":"Universit\u00e4t Passau, Passau, Germany","institution_ids":["https://openalex.org/I186354981"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036986694","display_name":"Ignaz Rutter","orcid":"https://orcid.org/0000-0002-3794-4406"},"institutions":[{"id":"https://openalex.org/I186354981","display_name":"University of Passau","ror":"https://ror.org/05ydjnb78","country_code":"DE","type":"education","lineage":["https://openalex.org/I186354981"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ignaz Rutter","raw_affiliation_strings":["Universit\u00e4t Passau, Passau, Germany"],"affiliations":[{"raw_affiliation_string":"Universit\u00e4t Passau, Passau, Germany","institution_ids":["https://openalex.org/I186354981"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045460793","display_name":"Dorothea Wagner","orcid":"https://orcid.org/0000-0002-9141-7076"},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Dorothea Wagner","raw_affiliation_strings":["Karlsruhe Institute of Technology, Karlsruhe, Germany"],"affiliations":[{"raw_affiliation_string":"Karlsruhe Institute of Technology, Karlsruhe, Germany","institution_ids":["https://openalex.org/I102335020"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5014484000"],"corresponding_institution_ids":["https://openalex.org/I102335020"],"apc_list":null,"apc_paid":null,"fwci":0.5829,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.67932218,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"24","issue":null,"first_page":"1","last_page":"21"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9991999864578247,"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":0.9991999864578247,"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/T10799","display_name":"Data Visualization and Analytics","score":0.9983000159263611,"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"}},{"id":"https://openalex.org/T11106","display_name":"Data Management and Algorithms","score":0.9962999820709229,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/heuristics","display_name":"Heuristics","score":0.7968099117279053},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.6479296088218689},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5697540044784546},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5613099336624146},{"id":"https://openalex.org/keywords/crossing-number","display_name":"Crossing number (knot theory)","score":0.5313718318939209},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5299433469772339},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.512575089931488},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.468037873506546},{"id":"https://openalex.org/keywords/line-segment","display_name":"Line segment","score":0.435404896736145},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.42533552646636963},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.41483357548713684},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3573642671108246},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3564532399177551},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2757124900817871},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.1854911744594574}],"concepts":[{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.7968099117279053},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.6479296088218689},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5697540044784546},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5613099336624146},{"id":"https://openalex.org/C2777724877","wikidata":"https://www.wikidata.org/wiki/Q2548661","display_name":"Crossing number (knot theory)","level":3,"score":0.5313718318939209},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5299433469772339},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.512575089931488},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.468037873506546},{"id":"https://openalex.org/C182124507","wikidata":"https://www.wikidata.org/wiki/Q166154","display_name":"Line segment","level":2,"score":0.435404896736145},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.42533552646636963},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.41483357548713684},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3573642671108246},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3564532399177551},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2757124900817871},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.1854911744594574},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3325861","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3325861","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":[{"id":"https://openalex.org/G172406378","display_name":null,"funder_award_id":"RU 1903/3-1, WA 654/21-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W67348729","https://openalex.org/W149069588","https://openalex.org/W176071698","https://openalex.org/W634834491","https://openalex.org/W1479963486","https://openalex.org/W1503013560","https://openalex.org/W1504716054","https://openalex.org/W1564330171","https://openalex.org/W1874694348","https://openalex.org/W1975370820","https://openalex.org/W1981172165","https://openalex.org/W1987959163","https://openalex.org/W2004181701","https://openalex.org/W2009543464","https://openalex.org/W2011039300","https://openalex.org/W2012931553","https://openalex.org/W2021053884","https://openalex.org/W2023655578","https://openalex.org/W2060205664","https://openalex.org/W2060538865","https://openalex.org/W2069321029","https://openalex.org/W2075220720","https://openalex.org/W2131662609","https://openalex.org/W2167482691","https://openalex.org/W2397834228","https://openalex.org/W2403720295","https://openalex.org/W2408539216","https://openalex.org/W2441637932","https://openalex.org/W2569314284","https://openalex.org/W2797072400","https://openalex.org/W2963030908","https://openalex.org/W2963794747","https://openalex.org/W2964267621","https://openalex.org/W2971168062","https://openalex.org/W3136685299","https://openalex.org/W4300127662","https://openalex.org/W6602687376"],"related_works":["https://openalex.org/W2121875028","https://openalex.org/W2135709899","https://openalex.org/W2079123808","https://openalex.org/W30750922","https://openalex.org/W1719252778","https://openalex.org/W4300715025","https://openalex.org/W1977633508","https://openalex.org/W2374778222","https://openalex.org/W4323924016","https://openalex.org/W2782195163"],"abstract_inverted_index":{"In":[0,142],"this":[1],"article,":[2],"we":[3,12,102,146,180],"consider":[4],"the":[5,63,83,96,122,125,132,139,162,183,186,195,202],"rectilinear":[6,64,75],"crossing":[7,76],"minimization":[8,35],"problem":[9],",":[10,24],"i.e.,":[11],"seek":[13],"a":[14,19,28,47,88,173,221],"straight-line":[15,152,207],"drawing":[16,98],"\u0393":[17],"of":[18,31,40,49,86,124,134,138,176,185,188,190,204,225],"graph":[20],"G":[21,165],"=(":[22],"V":[23],"E":[25],")":[26,110],"with":[27,154,194,220],"small":[29],"number":[30,133,187,203],"edge":[32,196],"crossings.":[33],"Crossing":[34],"is":[36,46,121,213],"an":[37,104,143],"active":[38],"field":[39],"research":[41],"[1,":[42],"10].":[43],"While":[44],"there":[45],"lot":[48],"work":[50],"on":[51,82,172],"heuristics":[52,73],"for":[53,74,100],"topological":[54,191],"drawings,":[55],"these":[56],"techniques":[57],"are":[58,80,131,218],"typically":[59],"not":[60],"transferable":[61],"to":[62,91],"(i.e.,":[65],"straight-line)":[66],"setting.":[67],"We":[68],"introduce":[69],"and":[70,127,129,136,201],"evaluate":[71],"three":[72],"minimization.":[77],"The":[78],"approaches":[79],"based":[81],"primitive":[84],"operation":[85],"moving":[87],"single":[89],"vertex":[90,126],"its":[92],"crossing-minimal":[93],"position":[94],"in":[95,161,206],"current":[97],"\u0393,":[99],"which":[101],"give":[103],"O":[105,163],"((":[106],"kn":[107,114],"+":[108,115],"m":[109,116,130],"2":[111],"log":[112],"(":[113],"))-time":[117],"algorithm,":[118],"where":[119],"k":[120],"degree":[123],"n":[128],"vertices":[135],"edges":[137],"graph,":[140],"respectively.":[141],"experimental":[144],"evaluation,":[145],"demonstrate":[147],"that":[148,182],"our":[149,211],"algorithms":[150,159],"compute":[151],"drawings":[153,192,208],"fewer":[155],"crossings":[156,189,205],"than":[157],"energy-based":[158],"implemented":[160],"pen":[164],"raph":[166],"D":[167],"rawing":[168],"F":[169],"ramework":[170],"[11]":[171],"varied":[174],"set":[175],"benchmark":[177],"instances.":[178],"Additionally,":[179],"show":[181],"difference":[184],"computed":[193,209],"insertion":[197],"approach":[198],"[10,":[199],"13]":[200],"by":[210],"heuristic":[212],"relatively":[214],"small.":[215],"All":[216],"experiments":[217],"evaluated":[219],"statistical":[222],"significance":[223],"level":[224],"\u03b1":[226],"=":[227],"0.05.":[228]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
