Solving weighted CSP by maintaining arc consistency

Recently, a general definition of arc consistency (AC) for soft constraint frameworks has been proposed by T. Schiex [Proc. CP-2000, Singapore, 2000, pp. 411–424]. In this paper we specialize this definition to weighted CSP and introduce two O(ed3) enforcing algorithms. Then, we refine the definition and introduce a stronger form of arc consistency (AC*) along with two O(n^2d^2+ed^3) algorithms. As in the CSP case, an important application of AC is to combine it with search. We empirically demonstrate that a branch and bound algorithm that maintains either AC or AC* is a state-of-the-art general solver for weighted CSP. Our experiments cover binary Max-CSP and Max-SAT problems.