Volume 10 (2014) Article 13 pp. 341-358
APPROX-RANDOM 2012 Special Issue

Approximation Algorithm for Non-Boolean Max-$k$-CSP

by Konstantin Makarychev and Yury Makarychev

Received: October 31, 2012
Revised: May 12, 2014
Published: October 10, 2014

In this paper we present a randomized polynomial-time approximation algorithm for Max-$k$-CSP_d. In Max-$k$-CSP_d 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 $k \geq \Omega(\log d)$). The best previously known algorithm has approximation factor $\Omega({k\log d}/{d^k})$. Our bound is asymptotically optimal when $d = \Omega(d)$.

We also give an approximation algorithm for the Boolean Max-$k$-CSP₂ problem with a slightly improved approximation guarantee.

DOI: 10.4086/toc.2014.v010a013

© 2014 Konstantin Makarychev and Yury Makarychev
Licensed under a Creative Commons Attribution License (CC-BY)