Treffer: Core-Guided Linear Programming-Based Maximum Satisfiability

International audience ; The core-guided algorithm OLL is the basis of some of the most successful algorithms for MaxSAT in recent evaluations. It works by iteratively finding cores of the formula and transforming it so that it exhibits a higher lower bound. It has recently been shown to implicitly discover cores of the original formula, as well as a compact representation of its reasoning within a linear program. In this paper, we use and extend these results to design a practical MaxSAT solver. We show an explicit linear program which matches and usually exceeds the bound computed by OLL. We show that OLL can be restated as an algorithm that explicitly computes a feasible dual solution of this linear program. This restated algorithm naturally works with an arbitrary dual solution. It can in fact be used to improve any LP representation of the MaxSAT instance. This presents a large increase of the potential design space for such algorithms. We describe some potential improvements from this insight and show that an implementation outperforms the state of the art algorithms on the set of instances from the latest MaxSAT evaluation.