MAX SAT approximation beyond the limits of polynomial-time approximation Original Research Article

We describe approximation algorithms for (unweighted) MAX SAT with performance ratios arbitrarily close to 1, in particular, when performance ratios exceed the limits of polynomial-time approximation. Namely, given a polynomial-time α-approximation algorithm View the MathML source, we construct an (α+ε)-approximation algorithm View the MathML source. The algorithm View the MathML source runs in time of the order cεk, where k is the number of clauses in the input formula and c is a constant depending on α. Thus we estimate the cost of improving a performance ratio. Similar constructions for MAX 2SAT and MAX 3SAT are also described. Taking known algorithms as View the MathML source (for example, the Karloff–Zwick algorithm for MAX 3SAT), we obtain particular upper bounds on the running time of View the MathML source.