{"id":"https://openalex.org/W2077658979","doi":"https://doi.org/10.1145/2746539.2746550","title":"Inapproximability of Combinatorial Problems via Small LPs and SDPs","display_name":"Inapproximability of Combinatorial Problems via Small LPs and SDPs","publication_year":2015,"publication_date":"2015-06-03","ids":{"openalex":"https://openalex.org/W2077658979","doi":"https://doi.org/10.1145/2746539.2746550","mag":"2077658979"},"language":"en","primary_location":{"id":"doi:10.1145/2746539.2746550","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2746539.2746550","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the forty-seventh 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/A5052424155","display_name":"G\u00e1bor Braun","orcid":null},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"G\u00e1bor Braun","raw_affiliation_strings":["Georgia Institute of Technology, Atlanta, GA, USA","Georgia Institute of Technology Atlanta, GA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Georgia Institute of Technology, Atlanta, GA, USA","institution_ids":["https://openalex.org/I130701444"]},{"raw_affiliation_string":"Georgia Institute of Technology Atlanta, GA, USA","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043574831","display_name":"Sebastian Pokutta","orcid":"https://orcid.org/0000-0001-7365-3000"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sebastian Pokutta","raw_affiliation_strings":["Georgia Institute of Technology, Atlanta, GA, USA","Georgia Institute of Technology Atlanta, GA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Georgia Institute of Technology, Atlanta, GA, USA","institution_ids":["https://openalex.org/I130701444"]},{"raw_affiliation_string":"Georgia Institute of Technology Atlanta, GA, USA","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055879319","display_name":"Daniel Zink","orcid":null},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel Zink","raw_affiliation_strings":["Georgia Institute of Technology, Atlanta, GA, USA","Georgia Institute of Technology Atlanta, GA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Georgia Institute of Technology, Atlanta, GA, USA","institution_ids":["https://openalex.org/I130701444"]},{"raw_affiliation_string":"Georgia Institute of Technology Atlanta, GA, USA","institution_ids":["https://openalex.org/I130701444"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I130701444"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"107","last_page":"116"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9984999895095825,"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":0.9918000102043152,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.7349115610122681},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.5735377669334412},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5628641247749329},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.5478624105453491},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5043801069259644},{"id":"https://openalex.org/keywords/vertex-cover","display_name":"Vertex cover","score":0.46991127729415894},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.45760512351989746},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4450478255748749},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4431852400302887},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.41469907760620117},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3873637020587921},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3027235269546509},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.24184048175811768}],"concepts":[{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.7349115610122681},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.5735377669334412},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5628641247749329},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.5478624105453491},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5043801069259644},{"id":"https://openalex.org/C40687702","wikidata":"https://www.wikidata.org/wiki/Q11515519","display_name":"Vertex cover","level":3,"score":0.46991127729415894},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.45760512351989746},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4450478255748749},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4431852400302887},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.41469907760620117},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3873637020587921},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3027235269546509},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.24184048175811768},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2746539.2746550","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2746539.2746550","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the forty-seventh annual ACM symposium on Theory of Computing","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337391","display_name":"Division of Civil, Mechanical and Manufacturing Innovation","ror":"https://ror.org/028yd4c30"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W331442585","https://openalex.org/W777079203","https://openalex.org/W1521148214","https://openalex.org/W1528220564","https://openalex.org/W1539191226","https://openalex.org/W1547496874","https://openalex.org/W1963547452","https://openalex.org/W1967232806","https://openalex.org/W1970439924","https://openalex.org/W1973698443","https://openalex.org/W1985123706","https://openalex.org/W1998919258","https://openalex.org/W1999032440","https://openalex.org/W1999590989","https://openalex.org/W2002025272","https://openalex.org/W2004660767","https://openalex.org/W2031923588","https://openalex.org/W2033871299","https://openalex.org/W2038225707","https://openalex.org/W2038907843","https://openalex.org/W2061987651","https://openalex.org/W2066620631","https://openalex.org/W2068190866","https://openalex.org/W2081254453","https://openalex.org/W2083858754","https://openalex.org/W2087038607","https://openalex.org/W2091039687","https://openalex.org/W2107052785","https://openalex.org/W2119368733","https://openalex.org/W2125534993","https://openalex.org/W2127114399","https://openalex.org/W2138677859","https://openalex.org/W2141815340","https://openalex.org/W2146489710","https://openalex.org/W2150285483","https://openalex.org/W2161719898","https://openalex.org/W2166369652","https://openalex.org/W2488008928","https://openalex.org/W2489729120","https://openalex.org/W2534717833","https://openalex.org/W2569455461","https://openalex.org/W2624693542","https://openalex.org/W2951693280","https://openalex.org/W3123950972","https://openalex.org/W4242184967"],"related_works":["https://openalex.org/W2056597184","https://openalex.org/W1712180277","https://openalex.org/W1608414128","https://openalex.org/W2023546589","https://openalex.org/W2029933769","https://openalex.org/W2551034790","https://openalex.org/W2096382750","https://openalex.org/W2094388041","https://openalex.org/W4250124835","https://openalex.org/W3102280101"],"abstract_inverted_index":{"Motivated":[0],"by":[1],"[12],":[2,146],"we":[3,54,105,126,147,171,184],"provide":[4],"a":[5,36,46,52,56,65,88,103,114,128,149],"framework":[6],"for":[7,39,119,131,166,189],"studying":[8],"the":[9,40,71,97,138,180],"size":[10],"of":[11,21,49,91,99,117,137,152,164,174,182],"linear":[12,30,78,108],"programming":[13,19,81,109],"formulations":[14,20],"as":[15,17,29],"well":[16],"semidefinite":[18,80],"combinatorial":[22],"optimization":[23,41],"problems":[24,121],"without":[25],"encoding":[26,48],"them":[27],"first":[28],"programs.":[31],"This":[32],"is":[33,74,87,135],"done":[34],"via":[35],"factorization":[37],"theorem":[38],"problem":[42],"itself":[43],"(and":[44],"not":[45,124,136],"specific":[47],"such).":[50],"As":[51,102],"result":[53],"define":[55],"consistent":[57],"reduction":[58,85],"mechanism":[59,86],"that":[60,122],"degrades":[61],"approximation":[62],"factors":[63],"in":[64,96,145,158],"controlled":[66],"fashion":[67],"and":[68,79,170],"which,":[69],"at":[70],"same":[72],"time,":[73],"compatible":[75],"with":[76,113],"approximate":[77],"formulations.":[82],"Moreover,":[83],"our":[84,153],"minor":[89],"restriction":[90],"classical":[92],"reductions":[93],"establishing":[94],"inapproximability":[95,110,130,162,173,187],"context":[98],"PCP":[100],"theorems.":[101],"consequence":[104],"establish":[106,172],"strong":[107],"(for":[111],"LPs":[112],"polynomial":[115],"number":[116],"constraints)":[118],"several":[120],"are":[123],"0/1-CSPs:":[125],"obtain":[127,185],"3/2-epsilon":[129],"Vertex":[132],"Cover":[133],"(which":[134],"CSP":[139],"type)":[140],"answering":[141],"an":[142,161],"open":[143],"question":[144],"answer":[148],"weak":[150],"version":[151],"sparse":[154],"graph":[155],"conjecture":[156],"posed":[157],"[6]":[159],"showing":[160],"factor":[163],"1/2+\u03b5":[165],"bounded":[167],"degree":[168],"IndependentSet,":[169],"MaxMULTICUT":[175],"(a":[176],"non-binary":[177],"CSP).":[178],"In":[179],"case":[181],"SDPs,":[183],"relative":[186],"results":[188],"these":[190],"problems.":[191]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":4},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
