{"id":"https://openalex.org/W2132687600","doi":"https://doi.org/10.1137/050637467","title":"A Copositive Programming Approach to Graph Partitioning","display_name":"A Copositive Programming Approach to Graph Partitioning","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2132687600","doi":"https://doi.org/10.1137/050637467","mag":"2132687600"},"language":"en","primary_location":{"id":"doi:10.1137/050637467","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050637467","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"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 Journal on Optimization","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/A5074212676","display_name":"Janez Povh","orcid":"https://orcid.org/0000-0002-9856-1476"},"institutions":[{"id":"https://openalex.org/I134023368","display_name":"Institute for Interdisciplinary Studies of Austrian Universities","ror":"https://ror.org/001zf8v27","country_code":"AT","type":"education","lineage":["https://openalex.org/I134023368","https://openalex.org/I4210166741"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Janez Povh","raw_affiliation_strings":["[Alpen-Adria Universit\u00e4t Klagenfurt]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"[Alpen-Adria Universit\u00e4t Klagenfurt]","institution_ids":["https://openalex.org/I134023368"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036114620","display_name":"Franz Rendl","orcid":"https://orcid.org/0000-0003-1578-9414"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Franz Rendl","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.8546,"has_fulltext":false,"cited_by_count":73,"citation_normalized_percentile":{"value":0.9303628,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"18","issue":"1","first_page":"223","last_page":"241"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9990000128746033,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9977999925613403,"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/semidefinite-programming","display_name":"Semidefinite programming","score":0.8495740294456482},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7309070229530334},{"id":"https://openalex.org/keywords/graph-partition","display_name":"Graph partition","score":0.6231477856636047},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6206921339035034},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5230154395103455},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5120659470558167},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.4882102310657501},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.4720754623413086},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.46741676330566406},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.42308181524276733},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.355851411819458},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35371658205986023},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.18882626295089722}],"concepts":[{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.8495740294456482},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7309070229530334},{"id":"https://openalex.org/C48903430","wikidata":"https://www.wikidata.org/wiki/Q491370","display_name":"Graph partition","level":3,"score":0.6231477856636047},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6206921339035034},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5230154395103455},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5120659470558167},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.4882102310657501},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.4720754623413086},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.46741676330566406},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.42308181524276733},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.355851411819458},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35371658205986023},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.18882626295089722},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/050637467","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050637467","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"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 Journal on Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1606488336","https://openalex.org/W1964488715","https://openalex.org/W1971398013","https://openalex.org/W1984283136","https://openalex.org/W1995658164","https://openalex.org/W2011039300","https://openalex.org/W2013153664","https://openalex.org/W2025902957","https://openalex.org/W2035400420","https://openalex.org/W2044427170","https://openalex.org/W2045756072","https://openalex.org/W2069037000","https://openalex.org/W2076164610","https://openalex.org/W2079135578","https://openalex.org/W2079966248","https://openalex.org/W2120146316","https://openalex.org/W2133404041","https://openalex.org/W2158598102","https://openalex.org/W2534895530","https://openalex.org/W3152126650","https://openalex.org/W4235419234","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1502458949","https://openalex.org/W2323830966","https://openalex.org/W2362838148","https://openalex.org/W1983756092","https://openalex.org/W188032563","https://openalex.org/W2359279826","https://openalex.org/W2085581092","https://openalex.org/W2361901126","https://openalex.org/W2951676025","https://openalex.org/W2101911765"],"abstract_inverted_index":{"We":[0,52,82],"consider":[1],"3\u2010partitioning":[2],"the":[3,19,42,65,80,87,129],"vertices":[4],"of":[5,14,22,67,79,110],"a":[6,46,50,61,73,101,107,125],"graph":[7],"into":[8],"sets":[9],"$S_1$,":[10],"$S_2$,":[11],"and":[12,27,114],"$S_3$":[13],"specified":[15],"cardinalities,":[16],"such":[17],"that":[18,54,86,120],"total":[20],"weight":[21],"all":[23],"edges":[24],"joining":[25],"$S_1$":[26],"$S_2$":[28],"is":[29,33,124],"minimized.":[30],"This":[31],"problem":[32,56],"closely":[34],"related":[35],"to":[36,76],"several":[37],"NP\u2010hard":[38],"problems":[39],"like":[40],"determining":[41],"bandwidth":[43],"or":[44],"finding":[45],"vertex":[47],"separator":[48],"in":[49,72,84],"graph.":[51],"show":[53,83,115],"this":[55,111,121],"can":[57,96],"be":[58,98],"formulated":[59,99],"as":[60,100],"linear":[62],"program":[63,113],"over":[64,128],"cone":[66],"completely":[68],"positive":[69],"matrices,":[70],"leading":[71],"natural":[74],"way":[75],"semidefinite":[77,102,112],"relaxations":[78],"problem.":[81],"particular":[85],"spectral":[88,130],"relaxation":[89],"introduced":[90],"by":[91],"Helmberg":[92],"et":[93],"al.":[94],"(1995)":[95],"equivalently":[97],"program.":[103],"Finally":[104],"we":[105],"propose":[106],"tightened":[108],"version":[109],"on":[116],"some":[117],"small":[118],"instances":[119],"new":[122],"bound":[123],"significant":[126],"improvement":[127],"bound.":[131]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":3}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}