{"id":"https://openalex.org/W1504159395","doi":"https://doi.org/10.1109/ciss.2012.6310764","title":"Convex Graph Invariants","display_name":"Convex Graph Invariants","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W1504159395","doi":"https://doi.org/10.1109/ciss.2012.6310764","mag":"1504159395"},"language":"en","primary_location":{"id":"doi:10.1109/ciss.2012.6310764","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ciss.2012.6310764","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 46th Annual Conference on Information Sciences and Systems (CISS)","raw_type":"proceedings-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1012.0623","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5105003932","display_name":"Venkat Chandrasekaran","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Venkat Chandrasekaran","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031935416","display_name":"Pablo A. Parrilo","orcid":"https://orcid.org/0000-0003-1132-8477"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pablo A. Parrilo","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5107833743","display_name":"Alan S. Willsky","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alan S. Willsky","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5105003932"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02997874,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2","issue":"3","first_page":"1","last_page":"541"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9729999899864197,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9729999899864197,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10211","display_name":"Computational Drug Discovery Methods","score":0.9725000262260437,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9513000249862671,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/mathematics","display_name":"Mathematics","score":0.7371433973312378},{"id":"https://openalex.org/keywords/adjacency-matrix","display_name":"Adjacency matrix","score":0.5287038087844849},{"id":"https://openalex.org/keywords/graph-property","display_name":"Graph property","score":0.5103101134300232},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5074636340141296},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.4345402717590332},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4015454649925232},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.34623104333877563},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3017466962337494}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7371433973312378},{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.5287038087844849},{"id":"https://openalex.org/C64339825","wikidata":"https://www.wikidata.org/wiki/Q722659","display_name":"Graph property","level":5,"score":0.5103101134300232},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5074636340141296},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.4345402717590332},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4015454649925232},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.34623104333877563},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3017466962337494}],"mesh":[],"locations_count":10,"locations":[{"id":"doi:10.1109/ciss.2012.6310764","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ciss.2012.6310764","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 46th Annual Conference on Information Sciences and Systems (CISS)","raw_type":"proceedings-article"},{"id":"doi:10.1137/100816900","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100816900","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Review","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1012.0623","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1012.0623","pdf_url":"https://arxiv.org/pdf/1012.0623","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:authors.library.caltech.edu:36295","is_oa":true,"landing_page_url":"https://authors.library.caltech.edu/36295/","pdf_url":"https://resolver.caltech.edu/CaltechAUTHORS:20130110-100237034","source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.190.2602","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.190.2602","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://ssg.mit.edu/%7Evenkatc/cpw_cgi_preprint10.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.300.1299","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.300.1299","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://ssg.mit.edu/~willsky/publ_pdfs/212_pub_SIAMonline.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.352.6212","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.352.6212","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://users.cms.caltech.edu/~venkatc/cpw_cgi_sirev12.pdf","raw_type":"text"},{"id":"pmh:oai:dspace.mit.edu:1721.1/75012","is_oa":true,"landing_page_url":"http://hdl.handle.net/1721.1/75012","pdf_url":null,"source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM","raw_type":"http://purl.org/eprint/type/JournalArticle"},{"id":"doi:10.48550/arxiv.1012.0623","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1012.0623","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"mag:1504159395","is_oa":false,"landing_page_url":"http://dspace.mit.edu/handle/1721.1/75012","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1012.0623","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1012.0623","pdf_url":"https://arxiv.org/pdf/1012.0623","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1523888516","display_name":null,"funder_award_id":"FA9550-","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G414638342","display_name":null,"funder_award_id":"W911NF-06-1-0076","funder_id":"https://openalex.org/F4320333591","funder_display_name":"Multidisciplinary University Research Initiative"},{"id":"https://openalex.org/G5809100787","display_name":null,"funder_award_id":"FA9550","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G5968161667","display_name":null,"funder_award_id":"W911NF-06-1-0076","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G7452299184","display_name":null,"funder_award_id":"W911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G8009762827","display_name":"FRG: Collaborative Research: Semidefinite optimization and convex algebraic geometry","funder_award_id":"0757207","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8998121839","display_name":null,"funder_award_id":"911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320333591","display_name":"Multidisciplinary University Research Initiative","ror":null},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1595903022","https://openalex.org/W1647779468","https://openalex.org/W1970630090","https://openalex.org/W1985123706","https://openalex.org/W1986591158","https://openalex.org/W2002722727","https://openalex.org/W2018047324","https://openalex.org/W2027470314","https://openalex.org/W2029213856","https://openalex.org/W2038098381","https://openalex.org/W2045391460","https://openalex.org/W2078289947","https://openalex.org/W2088062845","https://openalex.org/W2109427113","https://openalex.org/W2116616571","https://openalex.org/W2116673134","https://openalex.org/W2120146316","https://openalex.org/W2134711723","https://openalex.org/W2188609405","https://openalex.org/W2296148711","https://openalex.org/W3125965187","https://openalex.org/W4230109265"],"related_works":["https://openalex.org/W2022330001","https://openalex.org/W1591975452","https://openalex.org/W2971477758","https://openalex.org/W2950539638","https://openalex.org/W2581369832","https://openalex.org/W344717706","https://openalex.org/W3182351221","https://openalex.org/W2183689255","https://openalex.org/W3143049041","https://openalex.org/W2000304287","https://openalex.org/W3175737004","https://openalex.org/W2786472204","https://openalex.org/W2077287201","https://openalex.org/W1475836543","https://openalex.org/W1651250096","https://openalex.org/W2431948738","https://openalex.org/W1608566908","https://openalex.org/W1973860121","https://openalex.org/W1994637765","https://openalex.org/W2183721992"],"abstract_inverted_index":{"The":[0],"structural":[1,93,198],"properties":[2],"of":[3,10,15,24,43,47,54,76,107,118,125,146,175,178,193],"graphs":[4,16,180,194],"are":[5,13,36,40],"usually":[6],"characterized":[7],"in":[8,123],"terms":[9,124],"invariants,":[11,34,128,148],"which":[12,35],"functions":[14,42,53,82],"that":[17,39,90],"do":[18],"not":[19],"depend":[20],"on":[21,95],"the":[22,25,44,59,62,74,77,143,173,176,182,191],"labeling":[23],"nodes.":[26],"In":[27],"this":[28],"paper":[29],"we":[30,130,157],"study":[31],"convex":[32,41,88,112,120,137,152,159,165],"graph":[33,37,56,109,121,138,160,169,188],"invariants":[38,71,122,139,161],"adjacency":[45],"matrix":[46],"a":[48,55,100,105,116],"graph.":[49],"Some":[50],"examples":[51],"include":[52],"such":[57,72,171],"as":[58,73,172],"maximum":[60],"degree,":[61],"MAXCUT":[63],"value":[64],"(and":[65],"its":[66],"semidefinite":[67],"relaxation),":[68],"and":[69,97,129,149,153,190],"spectral":[70,147],"sum":[75],"k":[78],"largest":[79],"eigenvalues.":[80],"Such":[81],"can":[83],"be":[84],"used":[85],"to":[86,133,162,168],"construct":[87],"sets":[89],"impose":[91],"various":[92],"constraints":[94],"graphs,":[96],"thus":[98],"provide":[99,163],"unified":[101],"framework":[102],"for":[103],"solving":[104],"number":[106],"interesting":[108,144],"problems":[110,170],"via":[111],"optimization.":[113],"We":[114,141],"give":[115],"representation":[117],"all":[119],"certain":[126,196],"elementary":[127],"describe":[131],"methods":[132],"compute":[134],"or":[135],"approximate":[136],"tractably.":[140],"discuss":[142],"subclass":[145],"also":[150],"compare":[151],"non-convex":[154],"invariants.":[155],"Finally":[156],"use":[158],"efficient":[164],"programming":[166],"solutions":[167],"deconvolution":[174],"composition":[177],"two":[179],"into":[181],"individual":[183],"components,":[184],"hypothesis":[185],"testing":[186],"between":[187],"families,":[189],"generation":[192],"with":[195],"desired":[197],"properties.":[199]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
