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Paper detail

Approximation Algorithm for Non-Boolean MAX k-CSP

In this paper, we present a randomized polynomial-time approximation algorithm for k-CSPd. In k-CSPd, we are given a set of predicates of arity k over an alphabet of size d. Our goal is to find an assignment that maximizes the number of satisfied constraints. Our algorithm has approximation factor Omega(kd/d^k) (when k > Ω(log d)). This bound is asymptotically optimal assuming the Unique Games Conjecture. The best previously known algorithm has approximation factor Omega(k log d/d^k). We also give an approximation algorithm for the boolean MAX k-CSP2 problem with a slightly improved approximation guarantee.

preprint2012arXivOpen access
Konstantin MakarychevYury Makarychev
Data Structures and Algorithms
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Konstantin MakarychevYury Makarychev

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