{"id":"https://openalex.org/W4367680781","doi":"https://doi.org/10.1080/10556788.2023.2205646","title":"Crossing edge minimization in radial outerplanar layered graphs using segment paths","display_name":"Crossing edge minimization in radial outerplanar layered graphs using segment paths","publication_year":2023,"publication_date":"2023-05-02","ids":{"openalex":"https://openalex.org/W4367680781","doi":"https://doi.org/10.1080/10556788.2023.2205646"},"language":"en","primary_location":{"id":"doi:10.1080/10556788.2023.2205646","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1080/10556788.2023.2205646","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","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/A5068583263","display_name":"Francisco Madera-Ram\u00edrez","orcid":"https://orcid.org/0000-0002-4495-2017"},"institutions":[{"id":"https://openalex.org/I23878562","display_name":"Autonomous University of Yucat\u00e1n","ror":"https://ror.org/032p1n739","country_code":"MX","type":"education","lineage":["https://openalex.org/I23878562"]}],"countries":["MX"],"is_corresponding":true,"raw_author_name":"Francisco Madera-Ram\u00edrez","raw_affiliation_strings":["Universidad Aut\u00f3noma de Yucat\u00e1n-Facultad de Matem\u00e1ticas, M\u00e9rida, Mexico"],"raw_orcid":"https://orcid.org/0000-0002-4495-2017","affiliations":[{"raw_affiliation_string":"Universidad Aut\u00f3noma de Yucat\u00e1n-Facultad de Matem\u00e1ticas, M\u00e9rida, Mexico","institution_ids":["https://openalex.org/I23878562"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025309299","display_name":"Joel Antonio Trejo-S\u00e1nchez","orcid":"https://orcid.org/0000-0001-9326-7713"},"institutions":[{"id":"https://openalex.org/I124618812","display_name":"Mathematics Research Center","ror":"https://ror.org/02nhmp827","country_code":"MX","type":"facility","lineage":["https://openalex.org/I124618812"]},{"id":"https://openalex.org/I4210163111","display_name":"Secretar\u00eda de Ciencia, Humanidades, Tecnolog\u00eda e Innovaci\u00f3n","ror":"https://ror.org/059ex5q34","country_code":"MX","type":"government","lineage":["https://openalex.org/I4210163111"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Joel Antonio Trejo-S\u00e1nchez","raw_affiliation_strings":["CONACYT-Centro de Investigaci\u00f3n en Matem\u00e1ticas, M\u00e9rida, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CONACYT-Centro de Investigaci\u00f3n en Matem\u00e1ticas, M\u00e9rida, Mexico","institution_ids":["https://openalex.org/I124618812","https://openalex.org/I4210163111"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035388670","display_name":"Jos\u00e9 Luis L\u00f3pez Mart\u00ednez","orcid":"https://orcid.org/0000-0002-2489-7559"},"institutions":[{"id":"https://openalex.org/I23878562","display_name":"Autonomous University of Yucat\u00e1n","ror":"https://ror.org/032p1n739","country_code":"MX","type":"education","lineage":["https://openalex.org/I23878562"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Jos\u00e9 L\u00f3pez-Mart\u00ednez","raw_affiliation_strings":["Universidad Aut\u00f3noma de Yucat\u00e1n-Facultad de Matem\u00e1ticas, M\u00e9rida, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidad Aut\u00f3noma de Yucat\u00e1n-Facultad de Matem\u00e1ticas, M\u00e9rida, Mexico","institution_ids":["https://openalex.org/I23878562"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015160042","display_name":"Jorge R\u00edos-Mart\u00ednez","orcid":"https://orcid.org/0000-0003-4208-0515"},"institutions":[{"id":"https://openalex.org/I23878562","display_name":"Autonomous University of Yucat\u00e1n","ror":"https://ror.org/032p1n739","country_code":"MX","type":"education","lineage":["https://openalex.org/I23878562"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Jorge R\u00edos-Mart\u00ednez","raw_affiliation_strings":["Universidad Aut\u00f3noma de Yucat\u00e1n-Facultad de Matem\u00e1ticas, M\u00e9rida, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidad Aut\u00f3noma de Yucat\u00e1n-Facultad de Matem\u00e1ticas, M\u00e9rida, Mexico","institution_ids":["https://openalex.org/I23878562"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5068583263"],"corresponding_institution_ids":["https://openalex.org/I23878562"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.03441593,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"38","issue":"6","first_page":"1142","last_page":"1162"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10799","display_name":"Data Visualization and Analytics","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T10799","display_name":"Data Visualization and Analytics","score":0.9991999864578247,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9990000128746033,"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/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9850000143051147,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/concentric","display_name":"Concentric","score":0.5857976078987122},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.579710841178894},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5738957524299622},{"id":"https://openalex.org/keywords/rotation","display_name":"Rotation (mathematics)","score":0.5724793672561646},{"id":"https://openalex.org/keywords/graph-drawing","display_name":"Graph drawing","score":0.5622178316116333},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.5450151562690735},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49450013041496277},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.4897013008594513},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4230022132396698},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.41747069358825684},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.4131092429161072},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.37829646468162537},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36507728695869446},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.33446842432022095},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.18827149271965027},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15771278738975525}],"concepts":[{"id":"https://openalex.org/C90296322","wikidata":"https://www.wikidata.org/wiki/Q619776","display_name":"Concentric","level":2,"score":0.5857976078987122},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.579710841178894},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5738957524299622},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.5724793672561646},{"id":"https://openalex.org/C112953755","wikidata":"https://www.wikidata.org/wiki/Q739462","display_name":"Graph drawing","level":3,"score":0.5622178316116333},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5450151562690735},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49450013041496277},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.4897013008594513},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4230022132396698},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.41747069358825684},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.4131092429161072},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.37829646468162537},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36507728695869446},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.33446842432022095},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.18827149271965027},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15771278738975525},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10556788.2023.2205646","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1080/10556788.2023.2205646","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.49000000953674316,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W174566906","https://openalex.org/W1521554751","https://openalex.org/W1535274625","https://openalex.org/W1585105437","https://openalex.org/W1594340659","https://openalex.org/W1642013906","https://openalex.org/W1913975410","https://openalex.org/W1972151695","https://openalex.org/W1999287341","https://openalex.org/W2005331431","https://openalex.org/W2005349020","https://openalex.org/W2032684479","https://openalex.org/W2032958186","https://openalex.org/W2034335672","https://openalex.org/W2047417978","https://openalex.org/W2060538865","https://openalex.org/W2071353749","https://openalex.org/W2079589956","https://openalex.org/W2126536832","https://openalex.org/W2146928413","https://openalex.org/W2156760067","https://openalex.org/W2397623442","https://openalex.org/W2400748517","https://openalex.org/W2403720295","https://openalex.org/W2406931340","https://openalex.org/W2499989309","https://openalex.org/W2626587102","https://openalex.org/W2753334663","https://openalex.org/W2932081406","https://openalex.org/W2963761062","https://openalex.org/W3215529594","https://openalex.org/W4220824342","https://openalex.org/W4230728195","https://openalex.org/W4246219036","https://openalex.org/W4249379071","https://openalex.org/W4297810159"],"related_works":["https://openalex.org/W2032745795","https://openalex.org/W4241659117","https://openalex.org/W2042569643","https://openalex.org/W4252230788","https://openalex.org/W4235256213","https://openalex.org/W2254998354","https://openalex.org/W2061842045","https://openalex.org/W2048369647","https://openalex.org/W1535456929","https://openalex.org/W2186444269"],"abstract_inverted_index":{"Crossing":[0],"minimization":[1],"is":[2,67,133],"a":[3,18,61,126,141],"natural":[4],"problem":[5],"in":[6,14,35,47,69,161,176],"graph":[7],"drawing,":[8],"which":[9],"consists":[10,53],"of":[11,21,45,54,64,94,108,129,164],"drawing":[12],"it":[13],"the":[15,24,32,42,58,70,90,109,113,118,122,136],"plane":[16],"with":[17,82,166],"minimum":[19],"number":[20,128],"crossings":[22,173],"on":[23],"edges.":[25],"We":[26],"present":[27],"an":[28],"algorithm":[29,40,86,110,156],"to":[30,134,139],"minimize":[31,135],"crossing":[33,137,148],"edges":[34,73,138],"radial":[36],"layered":[37],"graphs.":[38],"The":[39,131,155],"determines":[41],"optimal":[43],"location":[44],"nodes":[46,95],"their":[48],"corresponding":[49],"circle":[50],"layer":[51],"and":[52,96,100,151,169,179],"two":[55],"phases.":[56],"In":[57],"first":[59],"phase,":[60,72],"counterclockwise":[62],"rotation":[63,99],"concentric":[65],"circles":[66],"performed;":[68],"next":[71],"are":[74,104,174],"converted":[75],"into":[76],"segment":[77,152],"paths.":[78,130],"Unlike":[79],"other":[80],"algorithms":[81],"circular":[83],"drawings,":[84],"our":[85],"does":[87],"not":[88],"require":[89],"insertion":[91],"or":[92],"removal":[93],"edges;":[97],"only":[98],"path":[101,153],"construction":[102],"operations":[103],"utilized.":[105],"Two":[106],"versions":[107],"were":[111],"created;":[112],"exhaustive":[114],"version":[115,124],"tests":[116,125],"all":[117],"possible":[119],"paths,":[120],"while":[121],"random":[123],"few":[127],"goal":[132],"obtain":[140],"clear":[142],"visualization":[143],"using":[144],"three":[145],"criteria:":[146],"rotation,":[147],"edge":[149],"detection":[150],"construction.":[154],"has":[157],"been":[158],"successfully":[159],"implemented":[160],"30":[162],"instances":[163],"graphs":[165],"20,":[167],"35":[168],"50":[170],"layers,":[171],"where":[172],"minimized":[175],"86\u201393%,":[177],"93\u201396%":[178],"95\u201397%,":[180],"respectively.":[181]},"counts_by_year":[],"updated_date":"2025-12-24T23:09:58.560324","created_date":"2025-10-10T00:00:00"}