A labelling arc consistency method for functional constraints

Abstract

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.