{"id":"https://openalex.org/W2753739056","doi":"https://doi.org/10.1109/tvcg.2017.2745919","title":"Revisiting Stress Majorization as a Unified Framework for Interactive Constrained Graph Visualization","display_name":"Revisiting Stress Majorization as a Unified Framework for Interactive Constrained Graph Visualization","publication_year":2017,"publication_date":"2017-08-28","ids":{"openalex":"https://openalex.org/W2753739056","doi":"https://doi.org/10.1109/tvcg.2017.2745919","mag":"2753739056","pmid":"https://pubmed.ncbi.nlm.nih.gov/28866589"},"language":"en","primary_location":{"id":"doi:10.1109/tvcg.2017.2745919","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvcg.2017.2745919","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","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"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yunhai Wang","raw_affiliation_strings":["Shandong University"],"affiliations":[{"raw_affiliation_string":"Shandong University","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100388805","display_name":"Yanyan Wang","orcid":"https://orcid.org/0009-0000-5116-7001"},"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":"Yanyan Wang","raw_affiliation_strings":["Shandong University"],"affiliations":[{"raw_affiliation_string":"Shandong University","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028439227","display_name":"Yinqi Sun","orcid":"https://orcid.org/0009-0000-3783-5472"},"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":"Yinqi Sun","raw_affiliation_strings":["Shandong University"],"affiliations":[{"raw_affiliation_string":"Shandong University","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009912040","display_name":"Lifeng Zhu","orcid":"https://orcid.org/0000-0002-9999-4513"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lifeng Zhu","raw_affiliation_strings":["Southeast University"],"affiliations":[{"raw_affiliation_string":"Southeast University","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049188592","display_name":"Kecheng Lu","orcid":"https://orcid.org/0000-0001-5990-3296"},"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":"Kecheng Lu","raw_affiliation_strings":["Shandong University"],"affiliations":[{"raw_affiliation_string":"Shandong University","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054382056","display_name":"Chi\u2010Wing Fu","orcid":"https://orcid.org/0000-0002-5238-593X"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chi-Wing Fu","raw_affiliation_strings":["VRHIT SIAT, Chinese University of Hong Kong"],"affiliations":[{"raw_affiliation_string":"VRHIT SIAT, Chinese University of Hong Kong","institution_ids":["https://openalex.org/I177725633"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037110552","display_name":"Michael Sedlmair","orcid":"https://orcid.org/0000-0001-7048-9292"},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Michael Sedlmair","raw_affiliation_strings":["University of Vienna, Austria"],"affiliations":[{"raw_affiliation_string":"University of Vienna, Austria","institution_ids":["https://openalex.org/I129774422"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036489223","display_name":"Oliver Deu\u00dfen","orcid":"https://orcid.org/0000-0001-5803-2185"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Oliver Deussen","raw_affiliation_strings":["Konstanz University, VCC SIAT, China"],"affiliations":[{"raw_affiliation_string":"Konstanz University, VCC SIAT, China","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010714340","display_name":"Baoquan Chen","orcid":"https://orcid.org/0000-0003-4702-036X"},"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":"Baoquan Chen","raw_affiliation_strings":["Shandong University"],"affiliations":[{"raw_affiliation_string":"Shandong University","institution_ids":["https://openalex.org/I154099455"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":9,"corresponding_author_ids":["https://openalex.org/A5068526974"],"corresponding_institution_ids":["https://openalex.org/I154099455"],"apc_list":null,"apc_paid":null,"fwci":2.1845,"has_fulltext":false,"cited_by_count":62,"citation_normalized_percentile":{"value":0.93029646,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"24","issue":"1","first_page":"489","last_page":"499"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10799","display_name":"Data Visualization and Analytics","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9890999794006348,"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/T12292","display_name":"Graph Theory and Algorithms","score":0.9854000210762024,"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/computer-science","display_name":"Computer science","score":0.7195805311203003},{"id":"https://openalex.org/keywords/graph-layout","display_name":"Graph Layout","score":0.6564597487449646},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.6375807523727417},{"id":"https://openalex.org/keywords/graph-drawing","display_name":"Graph drawing","score":0.62379390001297},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5997470617294312},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5747894048690796},{"id":"https://openalex.org/keywords/visualization","display_name":"Visualization","score":0.5555482506752014},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.5060126185417175},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5047956705093384},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.48200908303260803},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.47639957070350647},{"id":"https://openalex.org/keywords/majorization","display_name":"Majorization","score":0.46251025795936584},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4185091555118561},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3665434718132019},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.18795225024223328},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.16876715421676636},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1298041045665741}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7195805311203003},{"id":"https://openalex.org/C2911174283","wikidata":"https://www.wikidata.org/wiki/Q739462","display_name":"Graph Layout","level":4,"score":0.6564597487449646},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6375807523727417},{"id":"https://openalex.org/C112953755","wikidata":"https://www.wikidata.org/wiki/Q739462","display_name":"Graph drawing","level":3,"score":0.62379390001297},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5997470617294312},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5747894048690796},{"id":"https://openalex.org/C36464697","wikidata":"https://www.wikidata.org/wiki/Q451553","display_name":"Visualization","level":2,"score":0.5555482506752014},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.5060126185417175},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5047956705093384},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.48200908303260803},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.47639957070350647},{"id":"https://openalex.org/C2777818330","wikidata":"https://www.wikidata.org/wiki/Q1994695","display_name":"Majorization","level":2,"score":0.46251025795936584},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4185091555118561},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3665434718132019},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.18795225024223328},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.16876715421676636},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1298041045665741},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tvcg.2017.2745919","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvcg.2017.2745919","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:28866589","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/28866589","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}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G45661303","display_name":null,"funder_award_id":"U1501255","funder_id":"https://openalex.org/F4320336213","funder_display_name":"National Natural Science Foundation of China-Guangdong Joint Fund"},{"id":"https://openalex.org/G5568398972","display_name":null,"funder_award_id":"2016ZRE27617","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"}],"funders":[{"id":"https://openalex.org/F4320324174","display_name":"Natural Science Foundation of Shandong Province","ror":null},{"id":"https://openalex.org/F4320336213","display_name":"National Natural Science Foundation of China-Guangdong Joint Fund","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":61,"referenced_works":["https://openalex.org/W634834491","https://openalex.org/W1479963486","https://openalex.org/W1486079222","https://openalex.org/W1487444668","https://openalex.org/W1490445522","https://openalex.org/W1493030655","https://openalex.org/W1564536329","https://openalex.org/W1586092564","https://openalex.org/W1586461361","https://openalex.org/W1889256802","https://openalex.org/W1984244946","https://openalex.org/W1997952588","https://openalex.org/W1998703808","https://openalex.org/W1999134477","https://openalex.org/W1999287341","https://openalex.org/W2015342663","https://openalex.org/W2026506423","https://openalex.org/W2033257135","https://openalex.org/W2035080386","https://openalex.org/W2049335983","https://openalex.org/W2049981393","https://openalex.org/W2071353749","https://openalex.org/W2075220720","https://openalex.org/W2096054537","https://openalex.org/W2100108891","https://openalex.org/W2100112610","https://openalex.org/W2104706725","https://openalex.org/W2116856566","https://openalex.org/W2123322679","https://openalex.org/W2126003552","https://openalex.org/W2126536832","https://openalex.org/W2138959470","https://openalex.org/W2140063299","https://openalex.org/W2146055051","https://openalex.org/W2151636374","https://openalex.org/W2152825437","https://openalex.org/W2155142785","https://openalex.org/W2156458358","https://openalex.org/W2158378644","https://openalex.org/W2158453355","https://openalex.org/W2162553820","https://openalex.org/W2163449287","https://openalex.org/W2164381372","https://openalex.org/W2167482691","https://openalex.org/W2184417913","https://openalex.org/W2205695184","https://openalex.org/W2256067809","https://openalex.org/W2295139528","https://openalex.org/W2469279958","https://openalex.org/W2479500547","https://openalex.org/W3022981850","https://openalex.org/W4253665446","https://openalex.org/W4301621763","https://openalex.org/W6628707120","https://openalex.org/W6633642838","https://openalex.org/W6634839552","https://openalex.org/W6639627849","https://openalex.org/W6678782800","https://openalex.org/W6682441149","https://openalex.org/W6687858105","https://openalex.org/W6777060225"],"related_works":["https://openalex.org/W2010800245","https://openalex.org/W2917246213","https://openalex.org/W1912392752","https://openalex.org/W1912645081","https://openalex.org/W2377311228","https://openalex.org/W2583175499","https://openalex.org/W181985080","https://openalex.org/W4288051214","https://openalex.org/W2090914728","https://openalex.org/W3089914529"],"abstract_inverted_index":{"We":[0],"present":[1],"an":[2,97,128],"improved":[3],"stress":[4,29,86],"majorization":[5],"method":[6],"that":[7],"incorporates":[8],"various":[9],"constraints,":[10,69],"including":[11],"directional":[12],"constraints":[13,33,84],"without":[14],"the":[15,28,36,45,78,118],"necessity":[16],"of":[17,42,121],"solving":[18],"a":[19,52,114],"constraint":[20],"optimization":[21],"problem.":[22],"This":[23,50,88],"is":[24,51],"achieved":[25],"by":[26],"reformulating":[27],"function":[30],"to":[31,93],"impose":[32],"on":[34,44],"both":[35,56],"edge":[37,46],"vectors":[38],"and":[39,58,81,106],"lengths":[40,47],"instead":[41],"just":[43],"(node":[48],"distances).":[49],"unified":[53],"framework":[54],"for":[55,110],"constrained":[57],"unconstrained":[59],"graph":[60],"visualizations,":[61],"where":[62],"we":[63,116],"can":[64],"model":[65],"most":[66],"existing":[67],"layout":[68],"as":[70,72,77],"well":[71],"develop":[73],"new":[74],"ones":[75],"such":[76],"star":[79],"shapes":[80],"cluster":[82],"separation":[83],"within":[85],"majorization.":[87],"improvement":[89],"also":[90],"allows":[91],"us":[92],"parallelize":[94],"computation":[95],"with":[96,124],"efficient":[98],"GPU":[99],"conjugant":[100],"gradient":[101],"solver,":[102],"which":[103,130],"yields":[104],"fast":[105],"stable":[107],"solutions,":[108],"even":[109],"large":[111,122],"graphs.":[112],"As":[113],"result,":[115],"allow":[117],"constraint-based":[119],"exploration":[120],"graphs":[123],"10K":[125],"nodes":[126],"-":[127],"approach":[129],"previous":[131],"methods":[132],"cannot":[133],"support.":[134]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}