{"id":"https://openalex.org/W3036135716","doi":"https://doi.org/10.1145/3406325.3451099","title":"Playing unique games on certified small-set expanders","display_name":"Playing unique games on certified small-set expanders","publication_year":2021,"publication_date":"2021-06-15","ids":{"openalex":"https://openalex.org/W3036135716","doi":"https://doi.org/10.1145/3406325.3451099","mag":"3036135716"},"language":"en","primary_location":{"id":"doi:10.1145/3406325.3451099","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3406325.3451099","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2006.09969","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039083557","display_name":"Mitali Bafna","orcid":"https://orcid.org/0000-0002-3003-2017"},"institutions":[{"id":"https://openalex.org/I2801851002","display_name":"Harvard University Press","ror":"https://ror.org/006v7bf86","country_code":"US","type":"other","lineage":["https://openalex.org/I136199984","https://openalex.org/I2801851002"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mitali Bafna","raw_affiliation_strings":["Harvard University, USA","Harvard University ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Harvard University, USA","institution_ids":["https://openalex.org/I2801851002"]},{"raw_affiliation_string":"Harvard University ,","institution_ids":["https://openalex.org/I2801851002"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102710346","display_name":"Boaz Barak","orcid":"https://orcid.org/0000-0002-4053-8927"},"institutions":[{"id":"https://openalex.org/I2801851002","display_name":"Harvard University Press","ror":"https://ror.org/006v7bf86","country_code":"US","type":"other","lineage":["https://openalex.org/I136199984","https://openalex.org/I2801851002"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Boaz Barak","raw_affiliation_strings":["Harvard University, USA","Harvard University USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Harvard University, USA","institution_ids":["https://openalex.org/I2801851002"]},{"raw_affiliation_string":"Harvard University USA","institution_ids":["https://openalex.org/I2801851002"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068103506","display_name":"Pravesh K. Kothari","orcid":"https://orcid.org/0000-0002-8689-6770"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pravesh K. Kothari","raw_affiliation_strings":["Carnegie Mellon University, USA","Carnegie Mellon University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, USA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081583404","display_name":"Tselil Schramm","orcid":"https://orcid.org/0000-0002-8494-5778"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tselil Schramm","raw_affiliation_strings":["Stanford University, USA","Stanford University ()"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Stanford University, USA","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Stanford University ()","institution_ids":["https://openalex.org/I97018004"]}]},{"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/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"David Steurer","raw_affiliation_strings":["ETH Zurich, Switzerland","ETH Z\u00fcrich"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ETH Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]},{"raw_affiliation_string":"ETH Z\u00fcrich","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1629","last_page":"1642"},"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":0.9983000159263611,"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":0.7736690640449524},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6665595173835754},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4765394628047943},{"id":"https://openalex.org/keywords/hypercube","display_name":"Hypercube","score":0.44022414088249207},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.41795921325683594},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33884456753730774}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7736690640449524},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6665595173835754},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4765394628047943},{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.44022414088249207},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.41795921325683594},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33884456753730774}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/3406325.3451099","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3406325.3451099","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:2006.09969","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2006.09969","pdf_url":"https://arxiv.org/pdf/2006.09969","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},{"id":"doi:10.48550/arxiv.2006.09969","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2006.09969","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"},{"id":"mag:3036135716","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2006.09969","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2006.09969","pdf_url":"https://arxiv.org/pdf/2006.09969","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3606811033","display_name":"AF: Small: Communication Amid Uncertainty","funder_award_id":"1715187","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4908881666","display_name":"AF: Large: Collaborative Research: Algebraic Proof Systems, Convexity, and Algorithms","funder_award_id":"1565264","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5107914303","display_name":null,"funder_award_id":"CCF 1715187, CCF 1565264, CNS 1618026, CAREER Award 2047933","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8910507742","display_name":"TWC: Small: Complexity Assumptions for Cryptographic Schemes","funder_award_id":"1618026","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8983132490","display_name":null,"funder_award_id":"CCF 1715187","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309622","display_name":"Harvard University","ror":"https://ror.org/03vek6s52"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3036135716.pdf","grobid_xml":"https://content.openalex.org/works/W3036135716.grobid-xml"},"referenced_works_count":62,"referenced_works":["https://openalex.org/W186443161","https://openalex.org/W1511070007","https://openalex.org/W1754192177","https://openalex.org/W1886138972","https://openalex.org/W1891181203","https://openalex.org/W1965562201","https://openalex.org/W1967344706","https://openalex.org/W1999877046","https://openalex.org/W2004879152","https://openalex.org/W2019404063","https://openalex.org/W2028932986","https://openalex.org/W2034534236","https://openalex.org/W2039592987","https://openalex.org/W2072142887","https://openalex.org/W2087038607","https://openalex.org/W2095315734","https://openalex.org/W2103749128","https://openalex.org/W2110180651","https://openalex.org/W2110871651","https://openalex.org/W2115318789","https://openalex.org/W2117220151","https://openalex.org/W2120358419","https://openalex.org/W2133404041","https://openalex.org/W2137118456","https://openalex.org/W2146777332","https://openalex.org/W2148858749","https://openalex.org/W2151395725","https://openalex.org/W2155618818","https://openalex.org/W2161719898","https://openalex.org/W2162746978","https://openalex.org/W2242403914","https://openalex.org/W2277469547","https://openalex.org/W2346393863","https://openalex.org/W2581091247","https://openalex.org/W2619061098","https://openalex.org/W2625656873","https://openalex.org/W2771009994","https://openalex.org/W2773686537","https://openalex.org/W2787022562","https://openalex.org/W2798524658","https://openalex.org/W2805609980","https://openalex.org/W2809286765","https://openalex.org/W2883468257","https://openalex.org/W2949580236","https://openalex.org/W2950706437","https://openalex.org/W2953243699","https://openalex.org/W2962820675","https://openalex.org/W2962907923","https://openalex.org/W2962944954","https://openalex.org/W2964013189","https://openalex.org/W2964758001","https://openalex.org/W2972821478","https://openalex.org/W3022327706","https://openalex.org/W3025893026","https://openalex.org/W3035763474","https://openalex.org/W3098071389","https://openalex.org/W3141099616","https://openalex.org/W4205196152","https://openalex.org/W4233079698","https://openalex.org/W4233411607","https://openalex.org/W6638976330","https://openalex.org/W6752400976"],"related_works":["https://openalex.org/W3208004815","https://openalex.org/W2593693579","https://openalex.org/W2963153697","https://openalex.org/W2590395400","https://openalex.org/W2957416585","https://openalex.org/W2949942456","https://openalex.org/W3160700943","https://openalex.org/W2783218141","https://openalex.org/W3158676953","https://openalex.org/W2546840917","https://openalex.org/W2341911604","https://openalex.org/W3017555096","https://openalex.org/W2123734400","https://openalex.org/W2963608970","https://openalex.org/W2787935570","https://openalex.org/W2808514443","https://openalex.org/W3130046014","https://openalex.org/W820199756","https://openalex.org/W3107874748","https://openalex.org/W2951719725"],"abstract_inverted_index":{"We":[0],"give":[1],"an":[2],"algorithm":[3,30],"for":[4,99,103],"solving":[5],"unique":[6],"games":[7],"(UG)":[8],"instances":[9],"whenever":[10],"low-degree":[11,63],"sum-of-squares":[12,64,84],"proofs":[13],"certify":[14],"good":[15],"bounds":[16],"on":[17],"the":[18,21,40,51,92],"small-set-expansion":[19],"of":[20,53,96],"underlying":[22],"constraint":[23,41],"graph":[24,42],"via":[25,76],"a":[26,45,62,77],"hypercontractive":[27],"inequality.":[28],"Our":[29,66],"is":[31,43,57],"in":[32],"fact":[33],"more":[34],"versatile,":[35],"and":[36],"succeeds":[37],"even":[38],"when":[39],"not":[44],"small-set":[46],"expander":[47],"as":[48,50],"long":[49],"structure":[52],"non-expanding":[54],"small":[55],"sets":[56],"(informally":[58],"speaking)":[59],"\u201ccharacterized\u201d":[60],"by":[61,70],"proof.":[65],"results":[67],"are":[68],"obtained":[69],"rounding":[71],"low-entropy":[72],"solutions":[73],"\u2014":[74,82],"measured":[75],"new":[78],"global":[79],"potential":[80],"function":[81],"to":[83,91],"(SoS)":[85],"semidefinite":[86],"programs.":[87],"This":[88],"technique":[89],"adds":[90],"(currently":[93],"short)":[94],"list":[95],"general":[97],"tools":[98],"analyzing":[100],"SoS":[101],"relaxations":[102],"worst-case":[104],"optimization":[105],"problems.":[106]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}