Pdmi Preprint — 14/1998 Approximation Algorithms for Max Sat: a Better Performance Ratio at the Cost of a Longer Running Time

We describe approximation algorithms for (unweighted) MAX SAT with performance ratios arbitrarily close to 1 (in particular, when performance ratios exceed the limit of polynomialtime approximation). Namely, we show how to construct an (α + ε)-approximation algorithm A from a given polynomial-time α-approximation algorithm A0. The algorithm A runs in time of the order φ −1 K , where φ is the golden ratio (≈ 1.618) and K is the number of clauses in the input formula. Thus we estimate the cost of improving a performance ratio. Similar constructions for MAX 2SAT and MAX 3SAT are described too. We apply our constructions to some known polynomial-time algorithms taken as A0 and give upper bounds on the running time of the respective algorithms A.