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ACM"],"published-print":{"date-parts":[[2016,9]]},"abstract":"<jats:p>\n                    We show optimal (up to a constant factor) NP-hardness for a maximum constraint satisfaction problem with\n                    <jats:italic toggle=\"yes\">k<\/jats:italic>\n                    variables per constraint (Max-\n                    <jats:italic toggle=\"yes\">k<\/jats:italic>\n                    CSP) whenever\n                    <jats:italic toggle=\"yes\">k<\/jats:italic>\n                    is larger than the domain size. This follows from our main result concerning CSPs given by a predicate: A CSP is approximation resistant if its predicate contains a subgroup that is balanced pairwise independent. Our main result is analogous to Austrin and Mossel\u2019s, bypassing their Unique-Games Conjecture assumption whenever the predicate is an abelian subgroup.\n                  <\/jats:p>\n                  <jats:p>Our main ingredient is a new gap-amplification technique inspired by XOR lemmas. Using this technique, we also improve the NP-hardness of approximating Independent-Set on bounded-degree graphs, Almost-Coloring, Label-Cover, and various other problems.<\/jats:p>","DOI":"10.1145\/2873054","type":"journal-article","created":{"date-parts":[[2016,8,15]],"date-time":"2016-08-15T14:17:46Z","timestamp":1471270666000},"page":"1-32","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":39,"title":["Approximation Resistance from Pairwise-Independent Subgroups"],"prefix":"10.1145","volume":"63","author":[{"given":"Siu On","family":"Chan","sequence":"first","affiliation":[{"name":"University of California, Berkeley"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2016,8,12]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01277956"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1006\/jcss.1997.1472"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2010.59"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1109\/SFCS.2005.57"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/2462896.2462897"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.4086\/toc.2011.v007a003"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00037-009-0272-6"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.5555\/2722129.2722130"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2009.23"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/2213977.2214006"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/1806689.1806701"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539796302531"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.4086\/toc.2012.v008a012"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/1536414.1536437"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1137\/070712109"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.5555\/2481602.2481613"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1137\/110832240"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1145\/1541885.1541893"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00037-008-0250-4"},{"key":"e_1_2_1_20_1","volume-title":"Composition of low-error 2-query PCPs using decodable PCPs. 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