{"id":"https://openalex.org/W288944068","doi":"https://doi.org/10.1145/1250790.1250836","title":"Tight integrality gaps for Lovasz-Schrijver LP relaxations of vertex cover and max cut","display_name":"Tight integrality gaps for Lovasz-Schrijver LP relaxations of vertex cover and max cut","publication_year":2007,"publication_date":"2007-06-11","ids":{"openalex":"https://openalex.org/W288944068","doi":"https://doi.org/10.1145/1250790.1250836","mag":"288944068"},"language":"en","primary_location":{"id":"doi:10.1145/1250790.1250836","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1250790.1250836","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the thirty-ninth annual ACM symposium on Theory of computing","raw_type":"proceedings-article"},"type":"conference-paper","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/A5073672615","display_name":"Grant Schoenebeck","orcid":"https://orcid.org/0000-0001-6878-0670"},"institutions":[{"id":"https://openalex.org/I134446601","display_name":"Berkeley College","ror":"https://ror.org/02xewxa75","country_code":"US","type":"education","lineage":["https://openalex.org/I134446601"]},{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Grant Schoenebeck","raw_affiliation_strings":["UC Berkeley, Berkeley, CA","UC Berkeley, Berkeley, CA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UC Berkeley, Berkeley, CA","institution_ids":["https://openalex.org/I134446601","https://openalex.org/I95457486"]},{"raw_affiliation_string":"UC Berkeley, Berkeley, CA#TAB#","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057752375","display_name":"Luca Trevisan","orcid":"https://orcid.org/0000-0002-6982-8530"},"institutions":[{"id":"https://openalex.org/I134446601","display_name":"Berkeley College","ror":"https://ror.org/02xewxa75","country_code":"US","type":"education","lineage":["https://openalex.org/I134446601"]},{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Luca Trevisan","raw_affiliation_strings":["UC Berkeley, Berkeley, CA","UC Berkeley, Berkeley, CA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UC Berkeley, Berkeley, CA","institution_ids":["https://openalex.org/I134446601","https://openalex.org/I95457486"]},{"raw_affiliation_string":"UC Berkeley, Berkeley, CA#TAB#","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057481716","display_name":"Madhur Tulsiani","orcid":null},"institutions":[{"id":"https://openalex.org/I134446601","display_name":"Berkeley College","ror":"https://ror.org/02xewxa75","country_code":"US","type":"education","lineage":["https://openalex.org/I134446601"]},{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Madhur Tulsiani","raw_affiliation_strings":["UC Berkeley, Berkeley, CA","UC Berkeley, Berkeley, CA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UC Berkeley, Berkeley, CA","institution_ids":["https://openalex.org/I134446601","https://openalex.org/I95457486"]},{"raw_affiliation_string":"UC Berkeley, Berkeley, CA#TAB#","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0178634,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":null,"first_page":"302","last_page":"310"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9901000261306763,"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":0.9901000261306763,"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/T12288","display_name":"Optimization and Search Problems","score":0.9883999824523926,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.9319999814033508,"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/combinatorics","display_name":"Combinatorics","score":0.7900166511535645},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.7349188327789307},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.656416118144989},{"id":"https://openalex.org/keywords/vertex-cover","display_name":"Vertex cover","score":0.6235568523406982},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5814024209976196},{"id":"https://openalex.org/keywords/linear-programming-relaxation","display_name":"Linear programming relaxation","score":0.5600146055221558},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.5463505387306213},{"id":"https://openalex.org/keywords/lift","display_name":"Lift (data mining)","score":0.509980320930481},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.47113388776779175},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.42871496081352234},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40183407068252563},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.31428417563438416},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16859331727027893},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1324934959411621},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.120368093252182}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7900166511535645},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.7349188327789307},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.656416118144989},{"id":"https://openalex.org/C40687702","wikidata":"https://www.wikidata.org/wiki/Q11515519","display_name":"Vertex cover","level":3,"score":0.6235568523406982},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5814024209976196},{"id":"https://openalex.org/C25360446","wikidata":"https://www.wikidata.org/wiki/Q1512771","display_name":"Linear programming relaxation","level":3,"score":0.5600146055221558},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.5463505387306213},{"id":"https://openalex.org/C139002025","wikidata":"https://www.wikidata.org/wiki/Q3001212","display_name":"Lift (data mining)","level":2,"score":0.509980320930481},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.47113388776779175},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.42871496081352234},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40183407068252563},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.31428417563438416},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16859331727027893},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1324934959411621},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.120368093252182},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"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/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","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}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1145/1250790.1250836","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1250790.1250836","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the thirty-ninth annual ACM symposium on Theory of computing","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.115.1339","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.115.1339","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.berkeley.edu/~grant/papers/LSbounds2.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.212.1881","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.212.1881","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://eccc.hpi-web.de/report/2006/132/download/","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.369.6615","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.369.6615","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://ttic.uchicago.edu/~madhurt/Papers/stt-lp.pdf","raw_type":"text"},{"id":"mag:288944068","is_oa":false,"landing_page_url":"http://eccc.hpi-web.de/eccc-reports/2006/TR06-132/index.html","pdf_url":null,"source":{"id":"https://openalex.org/S11189987","display_name":"Electronic colloquium on computational complexity","issn_l":"1433-8092","issn":["1433-8092"],"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":"Electronic colloquium on computational complexity","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1524356573","https://openalex.org/W1587123489","https://openalex.org/W1985123706","https://openalex.org/W2049143039","https://openalex.org/W2104727719","https://openalex.org/W2106264302","https://openalex.org/W2143698439"],"related_works":["https://openalex.org/W2083896132","https://openalex.org/W278947496","https://openalex.org/W2104727719","https://openalex.org/W232814632","https://openalex.org/W2467099678","https://openalex.org/W1723348560","https://openalex.org/W2963620836","https://openalex.org/W2148872782","https://openalex.org/W2276905128","https://openalex.org/W2950087375","https://openalex.org/W1977134485","https://openalex.org/W2034163095","https://openalex.org/W2951093874","https://openalex.org/W2073114700","https://openalex.org/W2962913778","https://openalex.org/W1971195978","https://openalex.org/W2964386895","https://openalex.org/W2200051489","https://openalex.org/W2131906507","https://openalex.org/W1581729816"],"abstract_inverted_index":{"We":[0],"study":[1],"linear":[2,26],"programming":[3,27],"relaxations":[4],"of":[5,14,18],"Vertex":[6],"Cover":[7],"and":[8,20],"Max":[9],"Cutarising":[10],"from":[11,23],"repeated":[12],"applications":[13],"the":[15,24],"\"lift-and-project\"":[16],"method":[17],"Lovasz":[19],"Schrijver":[21],"starting":[22],"standard":[25],"relaxation.":[28]},"counts_by_year":[],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}