Volume 10 (2014) Article 13 pp. 341-358
APPROX-RANDOM 2012 Special Issue
Approximation Algorithm for Non-Boolean Max-$k$-CSP
Revised: May 12, 2014
Published: October 10, 2014
In this paper we present a randomized polynomial-time approximation algorithm for Max-$k$-CSPd. In Max-$k$-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 $k \geq \Omega(\log d)$). 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.