A generic arc-consistency algorithm and its specializations

Consistency techniques have been studied extensively in the past as a way oftackling constraint satisfaction problems (CSP). In particular, various arc-consistency algorithms have been proposed, originating from Waltz's ltering algorithm [27] and culminating in the optimal algorithm AC-4 of Mohr and Henderson [16]. AC-4 runs in O(ed 2)intheworst case, where e is the number of arcs (or constraints) and d is the size of the largest domain. Being applicable to the whole class of (binary) CSP, these algorithms do not take into account the semantics of constraints. In this paper, we present a new generic arc-consistency algorithm AC-5. This algorithm is parametrized on two speci ed procedures and can be instantiated to reduce to AC-3 and AC-4. More important, AC-5 can be instantiated to produce an O(ed) algorithm for a number of important classes of constraints: functional, anti-functional, monotonic and their generalization to (functional, anti-functional, and monotonic) piecewise constraints. We also show thatAC-5 has an important application in constraint logic programming over nite domains [24]. The kernel of the constraint solver for such a programming language is an arc-consistency algorithm for a set of basic constraints. We prove that AC-5, in conjunction with node consistency, provides a decision procedure for these constraints running in time O(ed)