An approximation algorithm for MAX-2-SAT with cardinality constraint

Abstract

We present a randomized polynomial-time approximation algorithm for the MAX-2-SAT problem in the presence of an extra cardinality constraint which lias an asymptotic worst-case ratio of 0.75. This improves upon the previously best approximation ratio 0.6603 which was achieved by Bläser and Manthey [BM]. Our approach is to use a solution obtained from a linear program which we first modify greedily and to which we then apply randomized rounding. The greedy phase guarantees that the errors introduced by the randomized rounding are not too large, an approach that might be interesting for other applications as well. © Springer-Verlag 2003.