MAX SAT approximation beyond the limits of polynomial-time approximation

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Abstract

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 A0, we construct an (α+ε)-approximation algorithm A. The algorithm A 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 A0 (for example, the Karloff–Zwick algorithm for MAX 3SAT), we obtain particular upper bounds on the running time of A.

MSC

03B05
03B25
68W25

Keywords

Approximation algorithms
Maximum satisfiability problem

Cited by (0)

1

On leave from Steklov Institute of Mathematics. Supported in part by grants from EPSRC and INTAS.

2

Supported in part by grants from INTAS and RFBR. Web: http://logic.pdmi.ras.ru/∼hirsch/.

3

Supported in part by grants from INTAS and RFBR.