{"id":"https://openalex.org/W2136811867","doi":"https://doi.org/10.1016/s0166-218x(01)00266-9","title":"Strengthened semidefinite relaxations via a second lifting for the Max-Cut problem","display_name":"Strengthened semidefinite relaxations via a second lifting for the Max-Cut problem","publication_year":2002,"publication_date":"2002-06-01","ids":{"openalex":"https://openalex.org/W2136811867","doi":"https://doi.org/10.1016/s0166-218x(01)00266-9","mag":"2136811867"},"language":"en","primary_location":{"id":"doi:10.1016/s0166-218x(01)00266-9","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0166-218x(01)00266-9","pdf_url":null,"source":{"id":"https://openalex.org/S171741597","display_name":"Discrete Applied Mathematics","issn_l":"0166-218X","issn":["0166-218X","1872-6771"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Applied Mathematics","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/A5005540131","display_name":"Miguel F. Anjos","orcid":"https://orcid.org/0000-0002-8258-9116"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Miguel F. Anjos","raw_affiliation_strings":["Department of Combinatorics & Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ont Canada N2L 3G1","Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ont., Canada N2L 3G1#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Combinatorics & Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ont Canada N2L 3G1","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ont., Canada N2L 3G1#TAB#","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061777786","display_name":"Henry Wolkowicz","orcid":"https://orcid.org/0000-0003-1572-3060"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Henry Wolkowicz","raw_affiliation_strings":["Department of Combinatorics & Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ont Canada N2L 3G1","Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ont., Canada N2L 3G1#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Combinatorics & Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ont Canada N2L 3G1","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ont., Canada N2L 3G1#TAB#","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5061777786"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":{"value":2750,"currency":"USD","value_usd":2750},"apc_paid":null,"fwci":4.5493,"has_fulltext":false,"cited_by_count":51,"citation_normalized_percentile":{"value":0.95525153,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"119","issue":"1-2","first_page":"79","last_page":"106"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9994000196456909,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9937999844551086,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9695000052452087,"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":0.818076491355896},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.7756761312484741},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.7661728858947754},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.7544762492179871},{"id":"https://openalex.org/keywords/maximum-cut","display_name":"Maximum cut","score":0.6527028679847717},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.584856390953064},{"id":"https://openalex.org/keywords/lagrangian-relaxation","display_name":"Lagrangian relaxation","score":0.5725715160369873},{"id":"https://openalex.org/keywords/flexibility","display_name":"Flexibility (engineering)","score":0.5699931383132935},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5341203808784485},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.51971435546875},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5131261944770813},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4992337226867676},{"id":"https://openalex.org/keywords/relaxation-technique","display_name":"Relaxation technique","score":0.497010737657547},{"id":"https://openalex.org/keywords/feasible-region","display_name":"Feasible region","score":0.4762706458568573},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4284459054470062},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.4118277132511139},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39774399995803833},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11818188428878784},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1141766607761383}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.818076491355896},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.7756761312484741},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.7661728858947754},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.7544762492179871},{"id":"https://openalex.org/C165526019","wikidata":"https://www.wikidata.org/wiki/Q942557","display_name":"Maximum cut","level":3,"score":0.6527028679847717},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.584856390953064},{"id":"https://openalex.org/C91765299","wikidata":"https://www.wikidata.org/wiki/Q3424292","display_name":"Lagrangian relaxation","level":2,"score":0.5725715160369873},{"id":"https://openalex.org/C2780598303","wikidata":"https://www.wikidata.org/wiki/Q65921492","display_name":"Flexibility (engineering)","level":2,"score":0.5699931383132935},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5341203808784485},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.51971435546875},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5131261944770813},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4992337226867676},{"id":"https://openalex.org/C2780554755","wikidata":"https://www.wikidata.org/wiki/Q955260","display_name":"Relaxation technique","level":3,"score":0.497010737657547},{"id":"https://openalex.org/C177067428","wikidata":"https://www.wikidata.org/wiki/Q17013331","display_name":"Feasible region","level":2,"score":0.4762706458568573},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4284459054470062},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.4118277132511139},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39774399995803833},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11818188428878784},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1141766607761383},{"id":"https://openalex.org/C204787440","wikidata":"https://www.wikidata.org/wiki/Q188504","display_name":"Alternative medicine","level":2,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"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/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","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},{"id":"https://openalex.org/C142724271","wikidata":"https://www.wikidata.org/wiki/Q7208","display_name":"Pathology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1016/s0166-218x(01)00266-9","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0166-218x(01)00266-9","pdf_url":null,"source":{"id":"https://openalex.org/S171741597","display_name":"Discrete Applied Mathematics","issn_l":"0166-218X","issn":["0166-218X","1872-6771"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:eprints.soton.ac.uk:29672","is_oa":false,"landing_page_url":"https://eprints.soton.ac.uk/29672/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401019","display_name":"ePrints Soton (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"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:publications.polymtl.ca:38318","is_oa":false,"landing_page_url":"https://publications.polymtl.ca/38318/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401013","display_name":"PolyPublie (\u00c9cole Polytechnique de Montr\u00e9al)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45683168","host_organization_name":"Polytechnique Montr\u00e9al","host_organization_lineage":["https://openalex.org/I45683168"],"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 de revue"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":59,"referenced_works":["https://openalex.org/W572922989","https://openalex.org/W1488435683","https://openalex.org/W1488876970","https://openalex.org/W1527552358","https://openalex.org/W1530202807","https://openalex.org/W1582056940","https://openalex.org/W1783633569","https://openalex.org/W1970193303","https://openalex.org/W1975442866","https://openalex.org/W1976962893","https://openalex.org/W1985123706","https://openalex.org/W1985476702","https://openalex.org/W1999613943","https://openalex.org/W1999735208","https://openalex.org/W2003276565","https://openalex.org/W2006704773","https://openalex.org/W2007157764","https://openalex.org/W2011039300","https://openalex.org/W2035400420","https://openalex.org/W2045427092","https://openalex.org/W2049143039","https://openalex.org/W2051306216","https://openalex.org/W2058497129","https://openalex.org/W2060660073","https://openalex.org/W2061607408","https://openalex.org/W2066356146","https://openalex.org/W2066492681","https://openalex.org/W2069313750","https://openalex.org/W2070982319","https://openalex.org/W2076535438","https://openalex.org/W2080905757","https://openalex.org/W2082156532","https://openalex.org/W2085427851","https://openalex.org/W2087226760","https://openalex.org/W2092812429","https://openalex.org/W2093790790","https://openalex.org/W2098499818","https://openalex.org/W2106264302","https://openalex.org/W2118807841","https://openalex.org/W2119007640","https://openalex.org/W2128202699","https://openalex.org/W2158598102","https://openalex.org/W2158907148","https://openalex.org/W2159739530","https://openalex.org/W2169399056","https://openalex.org/W2234551864","https://openalex.org/W2340149117","https://openalex.org/W2792481128","https://openalex.org/W2912475851","https://openalex.org/W2917997019","https://openalex.org/W2970724759","https://openalex.org/W4241080567","https://openalex.org/W4241760093","https://openalex.org/W4285719527","https://openalex.org/W6629579937","https://openalex.org/W6637982578","https://openalex.org/W6644040475","https://openalex.org/W6689927298","https://openalex.org/W6821646526"],"related_works":["https://openalex.org/W2784134589","https://openalex.org/W2132400628","https://openalex.org/W1584951881","https://openalex.org/W579949368","https://openalex.org/W2952554274","https://openalex.org/W3178878483","https://openalex.org/W3000089047","https://openalex.org/W1985283864","https://openalex.org/W3110578096","https://openalex.org/W2136811867"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
