### Approximation Resistance from Pairwise-Independent SubgroupsApproximation Resistance from Pairwise-Independent Subgroups

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 Author Chan, Siu On Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©2016 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword Inapproximability ♦ Integrality gaps ♦ Maximum constraint satisfaction problems ♦ Probabilistically checkable proofs Abstract We show optimal (up to a constant factor) NP-hardness for a maximum constraint satisfaction problem with $\textit{k}$ variables per constraint $(Max-\textit{k}CSP)$ whenever $\textit{k}$ 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’s, bypassing their Unique-Games Conjecture assumption whenever the predicate is an abelian subgroup. 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. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 2016-08-12 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 63 Issue Number 3 Page Count 32 Starting Page 1 Ending Page 32

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Source: ACM Digital Library