Approximation Algorithm for Non-boolean MAX k-CSP

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 Ω(kd/d) (when k ≥ Ω(log d)). This bound is asymptotically optimal assuming the Unique Games Conjecture. The best previously known algorithm has approximation factor Ω(k log d/d). We also give an approximation algorithm for the boolean MAX k-CSP2 problem with a slightly improved approximation guarantee.