Affiliation:
1. University of California, Berkeley
Abstract
We show optimal (up to a constant factor) NP-hardness for a maximum constraint satisfaction problem with
k
variables per constraint (Max-
k
CSP) whenever
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.
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Cited by
34 articles.
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