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arXiv · 1206.3603

Approximation Algorithm for Non-Boolean MAX k-CSP

Konstantin Makarychev·Yury Makarychev
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Abstract

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.

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BibTeXRIS

Konstantin Makarychev, Yury Makarychev. 2012-06-15. Approximation Algorithm for Non-Boolean MAX k-CSP. https://arxiv.org/abs/1206.3603

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