Theory of Computing ------------------- Title : Approximation Algorithm for Non-Boolean Max-$k$-CSP Authors : Konstantin Makarychev and Yury Makarychev Volume : 10 Number : 13 Pages : 341-358 URL : https://theoryofcomputing.org/articles/v010a013 Abstract -------- 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-CSP_2 problem with a slightly improved approximation guarantee.