A labelling arc consistency method for functional constraints
Numerous arc consistency algorithms have been developed for filtering constraint satisfaction problems (CSP). But, few of them considered the semantic of the constraints. Arc consistency algorithms work with a queue containing element to reconsider. Then, some constraints may be checked many times. Recently, Liu has proposed an improved specific version AC5+ of the AC5 algorithm. AC5+ deals with a subclass of functional constraints, called “Increasing Functional Constraints (IFC)”. It allows some IFC constraints of a CSP to be checked only once, when achieving arc consistency. In this paper, we propose a labelling arc consistency method (LAC) for filtering CSPs containing functional constraints. LAC uses two concepts:arc consistency and label-arc consistency. It allows all functional constraints to be checked only once, and some general constraints to be checked at most twice. Although, the complexity of LAC is still in O(ed) for functional constraints, where e is the number of constraints and d the size of the largest domain, the technique used in LAC leads to improve the performances and the effectiveness of classical arc consistency algorithms for CSPs containing functional constraints. The empirical results presented show the substantial gain brought by the LAC method.
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- Bessière C., “Arc-consistency and arc-consistency again”, Research Note in Artificial Intelligence, Vol. 65, 1 pp. 179–190.Google Scholar
- Bessière C., Freuder E.C., and Régin J-C, “Using Inference to Reduce Arc Consistency Computation”, IJCAI95, Montreal, pp592–598.Google Scholar
- David P., “When functional and bijective constraints make a CSP polynomial”, IJCAI93, Chambery, France, pp. 224–229.Google Scholar
- Dincbas M. and al., “Solving large combinatorial problems in logic programming”, Journal of Logic Programming, 8, pp. 75–93, 1990.Google Scholar
- Hubbe P. and Freuder H., “An efficient Cross-Product Representation of the Constraint Satisfaction Problem Search Space”, In proc. of AAAI, 1992, P. 421–427.Google Scholar
- Liu B., “Increasing Functional Constraints Need to Be Checked Only Once”, IJCAI95, Montreal, pp 586–591.Google Scholar
- Mohr R. and Henderson T.C., “Arc and path consistency revisited”, Artificial Intelligence, 28–2, 1986, pp. 225–233.Google Scholar
- Mohr R. and Masini G., “Running efficiently arc consistency”, Springer, Berlin, 1988, pp. 217–231.Google Scholar
- Montanari U., “Networks of constraints: Fundamental properties and applications to picture processing”, Inform. Sci., vol. 7 n∘2, 1974, p. 95–132.Google Scholar
- Van Hentenryck P., “Constraint satisfaction in Logic Programming”, MIT press, Cambridge, MA, 1989.Google Scholar
- Van Hentenryck P., Devilles Y. and Teng C-M., A generic arc consistency algorithm and its specifications. Artificial Intelligence, 27, pp. 291–322, 1992.Google Scholar