Improved Algorithms for Sparse MAX-SAT and MAX-k-CSP

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 – μ = Ω( 1 c ) and polynomial space solving MAX-SAT and MAX-kSAT, – μ = Ω( 1 √ c ) and exponential space solving MAX-SAT and MAX-kSAT, – μ = Ω( 1 ck2 ) and polynomial space solving MAX-k-CSP, – μ = Ω( 1 √ ck3 ) and exponential space solving MAX-k-CSP. The previous MAX-SAT algorithms have savings μ = Ω( 1 c2 log2 c ) for running in polynomial space [15] and μ = Ω( 1 c log c ) for exponential space [5]. We also give an algorithm with improved savings for satisfiability of depth-2 threshold circuits with cn wires.