Une étude des supports résiduels pour la consistance d'arc

In an Arc Consistency (AC) algorithm, a residual support, or residue, is a support that has been stored during an execution of the procedure which determines if a value is supported by a constraint. The point is that a residue is not guaranteed to represent a lower bound of the smallest current support of a value. In this paper, we study the theoretical impact of exploiting residues with respect to the basic algorithm AC3. First, we prove that AC3r(m) (i.e. AC3 exploiting residues) is optimal for low and high constraint tightness. Second, we show that MAC2001 presents, with respect to MAC3r(m), an overhead in O(μed) per branch of the binary tree built by MAC, where μ denotes the number of refutations of the branch, e the number of constraints and d the greatest domain size. One consequence is that, MAC3r(m) admits a better worst-case time complexity than MAC2001 for a branch involving μ refutations when either μ > d or μ > d and the tightness of any constraint is either low or high. Our experimental results clearly show that exploiting residues allows enhancing MAC and SAC algorithms embedding coarsegrained AC algorithms.