{"id":"https://openalex.org/W4297462892","doi":"https://doi.org/10.1109/tvcg.2022.3209371","title":"Taurus: Towards a Unified Force Representation and Universal Solver for Graph Layout","display_name":"Taurus: Towards a Unified Force Representation and Universal Solver for Graph Layout","publication_year":2022,"publication_date":"2022-09-27","ids":{"openalex":"https://openalex.org/W4297462892","doi":"https://doi.org/10.1109/tvcg.2022.3209371","pmid":"https://pubmed.ncbi.nlm.nih.gov/36166546"},"language":"en","primary_location":{"id":"doi:10.1109/tvcg.2022.3209371","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvcg.2022.3209371","pdf_url":null,"source":{"id":"https://openalex.org/S84775595","display_name":"IEEE Transactions on Visualization and Computer Graphics","issn_l":"1077-2626","issn":["1077-2626","1941-0506","2160-9306"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Visualization and Computer Graphics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://ink.library.smu.edu.sg/sis_research/7795","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084870136","display_name":"Mingliang Xue","orcid":"https://orcid.org/0000-0001-8842-1667"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Mingliang Xue","raw_affiliation_strings":["Department of Computer Science, Shandong University, China"],"raw_orcid":"https://orcid.org/0000-0001-8842-1667","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Shandong University, China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Zhi Wang","orcid":"https://orcid.org/0000-0003-0059-6580"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhi Wang","raw_affiliation_strings":["Department of Computer Science, Shandong University, China"],"raw_orcid":"https://orcid.org/0000-0003-0059-6580","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Shandong University, China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056898219","display_name":"Fahai Zhong","orcid":"https://orcid.org/0000-0002-0971-0821"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fahai Zhong","raw_affiliation_strings":["Department of Computer Science, Shandong University, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Shandong University, China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100424394","display_name":"Yong Wang","orcid":"https://orcid.org/0000-0002-0092-0793"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]},{"id":"https://openalex.org/I79891267","display_name":"Singapore Management University","ror":"https://ror.org/050qmg959","country_code":"SG","type":"education","lineage":["https://openalex.org/I79891267"]}],"countries":["CN","SG"],"is_corresponding":false,"raw_author_name":"Yong Wang","raw_affiliation_strings":["Department of Computer Science, Shandong University, China","School of Computing and Information Systems, Singapore Management University, Singapore"],"raw_orcid":"https://orcid.org/0000-0002-0092-0793","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Shandong University, China","institution_ids":["https://openalex.org/I154099455"]},{"raw_affiliation_string":"School of Computing and Information Systems, Singapore Management University, Singapore","institution_ids":["https://openalex.org/I79891267"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081346568","display_name":"Mingliang Xu","orcid":"https://orcid.org/0000-0002-6885-3451"},"institutions":[{"id":"https://openalex.org/I38877650","display_name":"Zhengzhou University","ror":"https://ror.org/04ypx8c21","country_code":"CN","type":"education","lineage":["https://openalex.org/I38877650"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mingliang Xu","raw_affiliation_strings":["Zhengzhou University, Zhengzhou, China"],"raw_orcid":"https://orcid.org/0000-0002-6885-3451","affiliations":[{"raw_affiliation_string":"Zhengzhou University, Zhengzhou, China","institution_ids":["https://openalex.org/I38877650"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036489223","display_name":"Oliver Deu\u00dfen","orcid":"https://orcid.org/0000-0001-5803-2185"},"institutions":[{"id":"https://openalex.org/I189712700","display_name":"University of Konstanz","ror":"https://ror.org/0546hnb39","country_code":"DE","type":"education","lineage":["https://openalex.org/I189712700"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Oliver Deussen","raw_affiliation_strings":["Computer and Information Science, University of Konstanz, Konstanz, Germany"],"raw_orcid":"https://orcid.org/0000-0001-5803-2185","affiliations":[{"raw_affiliation_string":"Computer and Information Science, University of Konstanz, Konstanz, Germany","institution_ids":["https://openalex.org/I189712700"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068526974","display_name":"Yunhai Wang","orcid":"https://orcid.org/0000-0003-0059-6580"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]},{"id":"https://openalex.org/I79891267","display_name":"Singapore Management University","ror":"https://ror.org/050qmg959","country_code":"SG","type":"education","lineage":["https://openalex.org/I79891267"]}],"countries":["CN","SG"],"is_corresponding":false,"raw_author_name":"Yunhai Wang","raw_affiliation_strings":["Department of Computer Science, Shandong University, China","School of Computing and Information Systems, Singapore Management University, Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Shandong University, China","institution_ids":["https://openalex.org/I154099455"]},{"raw_affiliation_string":"School of Computing and Information Systems, Singapore Management University, Singapore","institution_ids":["https://openalex.org/I79891267"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5084870136"],"corresponding_institution_ids":["https://openalex.org/I154099455"],"apc_list":null,"apc_paid":null,"fwci":0.7143,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.70773503,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"29","issue":"1","first_page":"886","last_page":"895"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10799","display_name":"Data Visualization and Analytics","score":1.0,"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":1.0,"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.9907000064849854,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12292","display_name":"Graph Theory and Algorithms","score":0.9894999861717224,"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/graph-layout","display_name":"Graph Layout","score":0.8654721975326538},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.8056594133377075},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.581813633441925},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.5598804354667664},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.49749043583869934},{"id":"https://openalex.org/keywords/graph-drawing","display_name":"Graph drawing","score":0.46900415420532227},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.46853747963905334}],"concepts":[{"id":"https://openalex.org/C2911174283","wikidata":"https://www.wikidata.org/wiki/Q739462","display_name":"Graph Layout","level":4,"score":0.8654721975326538},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.8056594133377075},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.581813633441925},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5598804354667664},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.49749043583869934},{"id":"https://openalex.org/C112953755","wikidata":"https://www.wikidata.org/wiki/Q739462","display_name":"Graph drawing","level":3,"score":0.46900415420532227},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.46853747963905334},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tvcg.2022.3209371","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvcg.2022.3209371","pdf_url":null,"source":{"id":"https://openalex.org/S84775595","display_name":"IEEE Transactions on Visualization and Computer Graphics","issn_l":"1077-2626","issn":["1077-2626","1941-0506","2160-9306"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Visualization and Computer Graphics","raw_type":"journal-article"},{"id":"pmid:36166546","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/36166546","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on visualization and computer graphics","raw_type":null},{"id":"pmh:oai:ink.library.smu.edu.sg:sis_research-8798","is_oa":true,"landing_page_url":"https://ink.library.smu.edu.sg/sis_research/7795","pdf_url":null,"source":{"id":"https://openalex.org/S4306401925","display_name":"Singapore Management University Institutional Knowledge (InK) (Singapore Management University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79891267","host_organization_name":"Singapore Management University","host_organization_lineage":["https://openalex.org/I79891267"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://doi.org/10.1109/TVCG.2022.3209371","raw_type":"Journal Article"}],"best_oa_location":{"id":"pmh:oai:ink.library.smu.edu.sg:sis_research-8798","is_oa":true,"landing_page_url":"https://ink.library.smu.edu.sg/sis_research/7795","pdf_url":null,"source":{"id":"https://openalex.org/S4306401925","display_name":"Singapore Management University Institutional Knowledge (InK) (Singapore Management University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79891267","host_organization_name":"Singapore Management University","host_organization_lineage":["https://openalex.org/I79891267"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://doi.org/10.1109/TVCG.2022.3209371","raw_type":"Journal Article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1283425618","display_name":null,"funder_award_id":"2018AAA0101100","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G1569404422","display_name":null,"funder_award_id":"62141217","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3146585569","display_name":null,"funder_award_id":"2,51654672 - TRR 161","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8783846746","display_name":null,"funder_award_id":"62132017","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W38619841","https://openalex.org/W634834491","https://openalex.org/W1504716054","https://openalex.org/W1564330171","https://openalex.org/W1842847600","https://openalex.org/W1931404780","https://openalex.org/W1982532805","https://openalex.org/W1993069528","https://openalex.org/W2001914359","https://openalex.org/W2028695285","https://openalex.org/W2049335983","https://openalex.org/W2068306188","https://openalex.org/W2075220720","https://openalex.org/W2119998616","https://openalex.org/W2132774043","https://openalex.org/W2135415614","https://openalex.org/W2144394238","https://openalex.org/W2152422369","https://openalex.org/W2156358318","https://openalex.org/W2164381372","https://openalex.org/W2167482691","https://openalex.org/W2187089797","https://openalex.org/W2294347342","https://openalex.org/W2397834228","https://openalex.org/W2408539216","https://openalex.org/W2507855339","https://openalex.org/W2732947513","https://openalex.org/W2753739056","https://openalex.org/W2797920702","https://openalex.org/W2919115771","https://openalex.org/W2955313235","https://openalex.org/W3022981850","https://openalex.org/W3108305122","https://openalex.org/W3167882161","https://openalex.org/W4200634330","https://openalex.org/W4206275846","https://openalex.org/W4214877290","https://openalex.org/W4220954304","https://openalex.org/W4253891982","https://openalex.org/W4394304100","https://openalex.org/W6601609194","https://openalex.org/W6731270529","https://openalex.org/W6777060225"],"related_works":["https://openalex.org/W2031908202","https://openalex.org/W2766563406","https://openalex.org/W3160329999","https://openalex.org/W2026729066","https://openalex.org/W2895526338","https://openalex.org/W2010800245","https://openalex.org/W2003783600","https://openalex.org/W4297904617","https://openalex.org/W2367461170","https://openalex.org/W1555430809"],"abstract_inverted_index":{"Over":[0],"the":[1,36,78,87,135],"past":[2],"few":[3],"decades,":[4],"a":[5,26,48,58,97,116,142,149],"large":[6,150],"number":[7,151],"of":[8,60,67,82,89,137,145,152,166],"graph":[9,168,173,181],"layout":[10,107,131,169,182],"techniques":[11,33,56,147],"have":[12],"been":[13],"proposed":[14],"for":[15,30,129,171],"visualizing":[16],"graphs":[17,108],"from":[18],"various":[19],"domains.":[20],"In":[21,112],"this":[22],"paper,":[23],"we":[24,95,114,140],"present":[25],"general":[27],"framework,":[28,139],"Taurus,":[29],"unifying":[31],"popular":[32],"such":[34],"as":[35,57,175,177],"spring-electrical":[37],"model,":[38,40],"stress":[39,100],"and":[41,69,80,154],"maxent-stress":[42],"model.":[43],"It":[44],"is":[45,104],"based":[46],"on":[47,93,148],"unified":[49],"force":[50],"representation,":[51],"which":[52,162],"formulates":[53],"most":[54],"existing":[55,83,146],"combination":[59],"quotient-based":[61],"forces":[62],"that":[63,103,124],"combine":[64],"power":[65,136],"functions":[66],"graph-theoretical":[68],"Euclidean":[70],"distances.":[71],"This":[72],"representation":[73],"enables":[74],"us":[75],"to":[76,106],"compare":[77],"strengths":[79],"weaknesses":[81],"techniques,":[84],"while":[85],"facilitating":[86],"development":[88],"new":[90,98],"methods.":[91],"Based":[92],"this,":[94],"propose":[96],"balanced":[99],"model":[101],"(BSM)":[102],"able":[105],"in":[109],"superior":[110],"quality.":[111],"addition,":[113],"introduce":[115],"universal":[117],"augmented":[118],"stochastic":[119],"gradient":[120],"descent":[121],"(SGD)":[122],"optimizer":[123],"efficiently":[125],"finds":[126],"proper":[127],"solutions":[128],"all":[130],"techniques.":[132,183],"To":[133],"demonstrate":[134],"our":[138],"conduct":[141],"comprehensive":[143],"evaluation":[144],"synthetic":[153],"real":[155],"graphs.":[156],"We":[157],"release":[158],"an":[159],"open-source":[160],"package,":[161],"facilitates":[163],"easy":[164],"comparison":[165],"different":[167],"methods":[170],"any":[172],"input":[174],"well":[176],"effectively":[178],"creating":[179],"customized":[180]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1}],"updated_date":"2026-01-28T23:14:49.684275","created_date":"2025-10-10T00:00:00"}