Bounding Linear Programs by Constraint Propagation: Application to Max-SAT

Abstract

The Virtual Arc Consistency (VAC) algorithm by Cooper et al. is a soft local consistency technique that computes, in linear space, a bound on the basic LP relaxation of the Weighted CSP (WCSP). We generalize this technique by replacing arc consistency with a (problem-dependent) constraint propagation in a system of linear inequalities over the reals. When propagation detects infeasibility, the infeasibility certificate (a solution to the alternative system in Farkas’ lemma) provides a dual improving direction. We illustrate this approach on the LP relaxation of Weighted Max-SAT. We show in experiments that the obtained bounds are often not far from global LP optima and we prove that they are exact for known tractable subclasses of Weighted Max-SAT.