Improved algorithms for sparse MAX-SAT and MAX-k-CSP

Abstract

We give improved deterministic algorithms solving sparse instances of MAX-SAT and MAX-k-CSP. For instances with n variables and cn clauses (constraints), we give algorithms running in time poly(n)· 2n(1−μ) for (Formula presented.) and polynomial space solving MAX-SAT and MAX-k-SAT, (Formula presented.) and exponential space solving MAX-SAT and MAX-k-SAT, (Formula presented.) and polynomial space solving MAX-k-CSP, (Formula presented.) and exponential space solving MAX-k-CSP. The previous MAX-SAT algorithms have savings (Formula presented.) for running in polynomial space [15] and (Formula presented.) for exponential space [5]. We also give an algorithm with improved savings for satisfiability of depth-2 threshold circuits with cn wires.