Lazy Arc Consistency

Thomas Schiex, Jean-Charles Régin, Christine Gaspin, Gérard Verfaillie

Arc consistency filtering is widely used in the framework of binary constraint satisfaction problems: with a low complexity, inconsistency may be detected,and domains are filtered. In this paper, we show that when detecting inconsistency is the objective, a systematic domain filtering is useless and a lazy approach is more adequate. Whereas usual arc consistency algorithms produce the maximum arc consistent sub-domain, when it exists, we propose a method, called LACY, which only looks for any arc consistent sub-domain. The algorithm is then extended to provide the additional service of locating one variable with a minimum domain cardinality in the maximum arc consistent sub-domain, without necessarily computing all domain sizes. Finally, we compare traditional AC enforcing and lazy AC enforcing using several benchmark problems, both randomly generated CSP and real life problems.

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