{"id":"https://openalex.org/W2019404063","doi":"https://doi.org/10.1145/1806689.1806792","title":"Graph expansion and the unique games conjecture","display_name":"Graph expansion and the unique games conjecture","publication_year":2010,"publication_date":"2010-06-05","ids":{"openalex":"https://openalex.org/W2019404063","doi":"https://doi.org/10.1145/1806689.1806792","mag":"2019404063"},"language":"en","primary_location":{"id":"doi:10.1145/1806689.1806792","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1806689.1806792","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-second 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/A5101701586","display_name":"Prasad Raghavendra","orcid":"https://orcid.org/0009-0009-7851-0653"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Prasad Raghavendra","raw_affiliation_strings":["MSR New England, Cambridge, MA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MSR New England, Cambridge, MA, USA","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089128021","display_name":"David Steurer","orcid":"https://orcid.org/0000-0002-3908-8180"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David Steurer","raw_affiliation_strings":["Princeton University, Princeton, NJ, USA","Princeton University , Princeton, NJ, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Princeton University, Princeton, NJ, USA","institution_ids":["https://openalex.org/I20089843"]},{"raw_affiliation_string":"Princeton University , Princeton, NJ, USA","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":275,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"755","last_page":"764"},"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":0.9994000196456909,"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/T12288","display_name":"Optimization and Search Problems","score":0.993399977684021,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6316295862197876},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.618768036365509},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5889918804168701},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4703125059604645},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3704720139503479}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6316295862197876},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.618768036365509},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5889918804168701},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4703125059604645},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3704720139503479}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1806689.1806792","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1806689.1806792","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-second ACM symposium on Theory of computing","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.5099999904632568,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W186443161","https://openalex.org/W1571037334","https://openalex.org/W1631603072","https://openalex.org/W1985476702","https://openalex.org/W1993111701","https://openalex.org/W2020632401","https://openalex.org/W2051184870","https://openalex.org/W2083858754","https://openalex.org/W2083896132","https://openalex.org/W2087038607","https://openalex.org/W2091885230","https://openalex.org/W2098350988","https://openalex.org/W2102373437","https://openalex.org/W2107881198","https://openalex.org/W2110871651","https://openalex.org/W2120358419","https://openalex.org/W2137118456","https://openalex.org/W2137955570","https://openalex.org/W2141793995","https://openalex.org/W2150148016","https://openalex.org/W2151395725","https://openalex.org/W2154386769","https://openalex.org/W2155188403","https://openalex.org/W2155618818","https://openalex.org/W2162898372","https://openalex.org/W2168669141","https://openalex.org/W2176446742","https://openalex.org/W6604134081"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"The":[0],"edge":[1,28,82,134,158],"expansion":[2,83,126,135,159,185,205],"of":[3,6,18,31,47,64,119,122,136,149,186,206,220],"a":[4,12,24,32,56,62,115,147,170,178],"subset":[5,33],"vertices":[7],"S":[8,34],"\u2286":[9,35],"V":[10,36],"in":[11,160],"graph":[13],"G":[14],"measures":[15],"the":[16,27,45,65,97,103,110,120,150,164,218],"fraction":[17],"edges":[19],"that":[20,60,114,182,191,211],"leave":[21],"S.":[22],"In":[23,92],"d-regular":[25],"graph,":[26],"expansion/conductance":[29],"\u03a6(S)":[30,40],"is":[37,55,61,139,144,163,193,214],"defined":[38],"as":[39],"=":[41,85],"(|E(S,":[42],"V\\S)|)/(d|S|).":[43],"Approximating":[44],"conductance":[46],"small":[48,124,137,187,197,207],"linear":[49],"sized":[50],"sets":[51,138],"(size":[52],"\u03b4":[53],"n)":[54],"natural":[57,171],"optimization":[58,172],"question":[59],"variant":[63],"well-studied":[66],"Sparsest":[67],"Cut":[68],"problem.":[69],"However,":[70],"there":[71],"are":[72],"no":[73],"known":[74],"algorithms":[75,155],"to":[76,89,128,156,174,195],"even":[77],"distinguish":[78],"between":[79,99],"almost":[80],"complete":[81],"(\u03a6(S)":[84],"1-\u03b5),":[86],"and":[87,102],"close":[88],"0":[90],"expansion.":[91,199],"this":[93],"work,":[94],"we":[95,108,189,209],"investigate":[96],"connection":[98],"Graph":[100],"Expansion":[101],"Unique":[104,129,142,175,212],"Games":[105,143,213],"Conjecture.":[106],"Specifically,":[107],"show":[109,113,190,210],"following:":[111],"We":[112],"simple":[116],"decision":[117],"version":[118],"problem":[121,173],"approximating":[123,133],"set":[125,198],"reduces":[127],"Games.":[130,176],"Thus":[131],"if":[132],"hard,":[140],"then":[141],"hard.":[145],"Alternatively,":[146],"refutation":[148],"UGC":[151,181],"will":[152],"yield":[153],"better":[154],"approximate":[157,196],"graphs.":[161],"This":[162],"first":[165],"non-trivial":[166],"\"reverse\"":[167],"reduction":[168],"from":[169],"Under":[177],"slightly":[179],"stronger":[180],"assumes":[183],"mild":[184],"sets,":[188,208],"it":[192],"UG-hard":[194],"On":[200],"instances":[201],"with":[202],"sufficiently":[203],"good":[204],"easy":[215],"by":[216],"extending":[217],"techniques":[219],"[4].":[221]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":23},{"year":2021,"cited_by_count":14},{"year":2020,"cited_by_count":27},{"year":2019,"cited_by_count":38},{"year":2018,"cited_by_count":18},{"year":2017,"cited_by_count":18},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":22},{"year":2014,"cited_by_count":26},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":26}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}