Approximating Weighted Max-SAT Problems by Compensating for Relaxations

We introduce a new approach to approximating weighted Max-SAT problems that is based on simplifying a given instance, and then tightening the approximation. First, we relax its structure until it is tractable for exact algorithms. Second, we compensate for the relaxation by introducing auxiliary weights. More specifically, we relax equivalence constraints from a given Max-SAT problem, which we compensate for by recovering a weaker notion of equivalence. We provide a simple algorithm for finding these approximations, that is based on iterating over relaxed constraints, compensating for them one-by-one. We show that the resulting Max-SAT instances have certain interesting properties, both theoretical and empirical.

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