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A generic arc-consistency algorithm and its specializations. (English) Zbl 0763.68059
Summary: Consistency techniques have been studied extensively in the past as a way of tackling constraint satisfaction problems (CSP). In particular, various arc-consistency algorithms have been proposed, originating from Waltz’s filtering algorithm [D. Waltz, Generating semantic descriptions from drawings of scenes with shadows, Tech. Rept. AI271, MIT, Cambridge, MA (1972)] and culminating in the optimal algorithm AC-4 of R. Mohr and T. C. Henderson [Arc and path consistency revisited, Artif. Intell. 28, 225-233 (1986)]. AC-4 runs in $$O(ed^ 2)$$ in the worst 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.
We present a new generic arc-consistency algorithm AC-5. This algorithm is parametrized on two specified procedures and can be instantiated to reduce to AC-3 and AC-4. More important, AC-5 can be instantiated to produce and $$O(ed)$$ 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 that AC-5 has an important application in constraint logic programming over finite domains. 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 $$O(ed)$$.

##### MSC:
 68T20 Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.)
CHIP
Full Text:
##### References:
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