{"id":"https://openalex.org/W2221384962","doi":"https://doi.org/10.1145/2751322","title":"Hardness of Max-2Lin and Max-3Lin over Integers, Reals, and Large Cyclic Groups","display_name":"Hardness of Max-2Lin and Max-3Lin over Integers, Reals, and Large Cyclic Groups","publication_year":2015,"publication_date":"2015-05-11","ids":{"openalex":"https://openalex.org/W2221384962","doi":"https://doi.org/10.1145/2751322","mag":"2221384962"},"language":"en","primary_location":{"id":"doi:10.1145/2751322","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2751322","pdf_url":null,"source":{"id":"https://openalex.org/S205019203","display_name":"ACM Transactions on Computation Theory","issn_l":"1942-3454","issn":["1942-3454","1942-3462"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Computation Theory","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/A5051167298","display_name":"Ryan O\u2019Donnell","orcid":"https://orcid.org/0009-0005-5609-5795"},"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":"Ryan O\u2019Donnell","raw_affiliation_strings":["Carnegie Mellon University, Pittsburgh, PA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, PA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073986426","display_name":"Yi Wu","orcid":"https://orcid.org/0009-0006-3120-3769"},"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":"Yi Wu","raw_affiliation_strings":["Carnegie Mellon University, West Lafayette, IN"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, West Lafayette, IN","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045927034","display_name":"Yuan Zhou","orcid":"https://orcid.org/0009-0008-1706-6539"},"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":"Yuan Zhou","raw_affiliation_strings":["Carnegie Mellon University, Pittsburgh, PA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, PA","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.10276392,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"7","issue":"2","first_page":"1","last_page":"16"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":1.0,"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":1.0,"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/T10237","display_name":"Cryptography and Data Security","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.9972000122070312,"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":0.8396615982055664},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7489771842956543},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4760065972805023},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.45284026861190796},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37751513719558716}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8396615982055664},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7489771842956543},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4760065972805023},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.45284026861190796},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37751513719558716},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2751322","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2751322","pdf_url":null,"source":{"id":"https://openalex.org/S205019203","display_name":"ACM Transactions on Computation Theory","issn_l":"1942-3454","issn":["1942-3454","1942-3462"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Computation Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3741414206","display_name":null,"funder_award_id":"2008477","funder_id":"https://openalex.org/F4320320950","funder_display_name":"United States-Israel Binational Science Foundation"},{"id":"https://openalex.org/G7119349915","display_name":"CAREER: Optimal Approximability","funder_award_id":"0747250","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/F4320320950","display_name":"United States-Israel Binational Science Foundation","ror":"https://ror.org/00j8z2m73"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W183568742","https://openalex.org/W1967826576","https://openalex.org/W1970259241","https://openalex.org/W1985123706","https://openalex.org/W1991143034","https://openalex.org/W1999032440","https://openalex.org/W2019578639","https://openalex.org/W2026103826","https://openalex.org/W2069971337","https://openalex.org/W2087038607","https://openalex.org/W2120358419","https://openalex.org/W2132302072","https://openalex.org/W2133263321","https://openalex.org/W2148352980"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"In":[0,37,77,105],"1997,":[1],"H\u00e5stad":[2],"showed":[3,40],"NP-hardness":[4,30],"of":[5,31,42,89,111,149],"(1":[6,32,43,119],"\u2212":[7,33,44,120],"\u03f5,":[8,34,45],"1/":[9],"q":[10,14,48,51,53,92,96,146],"+":[11],"\u03b4)-approximating":[12,35,46],"Max-3Lin(Z":[13,91],");":[15],"however,":[16,60],"it":[17,125],"was":[18,67],"not":[19],"until":[20],"2007":[21],"that":[22,82],"Guruswami":[23],"and":[24,94],"Raghavendra":[25],"were":[26],"able":[27],"to":[28,86,131],"show":[29,81,108],"Max-3Lin(Z).":[36],"2004,":[38],"Khot--Kindler--Mossel--O\u2019Donnell":[39],"UG-hardness":[41],"Max-2Lin(Z":[47,95],")":[49,93,97],"for":[50,65,128,142],"=":[52],"(\u03f5,":[54,147],"\u03b4)":[55,148],"a":[56,109,118,133],"sufficiently":[57],"large":[58],"constant;":[59],"achieving":[61],"the":[62,87,90,150],"same":[63],"hardness":[64,101],"Max-2Lin(Z)":[66],"given":[68],"as":[69],"an":[70,129],"open":[71],"problem":[72],"in":[73],"Raghavendra\u2019s":[74],"2009":[75],"thesis.":[76],"this":[78],"work,":[79],"we":[80,107],"fairly":[83],"simple":[84],"modifications":[85],"proofs":[88],"results":[98,102],"yield":[99],"optimal":[100],"over":[103,123,136],"Z.":[104],"fact,":[106],"kind":[110],"\u201cbicriteria\u201d":[112],"hardness:":[113],"Even":[114],"when":[115],"there":[116],"is":[117,126],"\u03f5)-good":[121],"solution":[122,135],"Z,":[124,137],"hard":[127],"algorithm":[130],"find":[132],"\u03b4-good":[134],"R,":[138],"or":[139],"Z":[140],"m":[141,144],"any":[143],"\u2a7e":[145],"algorithm\u2019s":[151],"choosing.":[152]},"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-10-10T00:00:00"}
