Incrementally Solving Functional Constraints

Abstract

Binary functional constraints represent an important constraint class in Constraint Satisfaction Problems (CSPs). They have been studied in different contexts [for example (van Hentenryck et al. 1992; Kirousis 1993; van Beek and Dechter 1995; David 1995; Zhang et al. 1999)]. Functional constraints are also a primitive in Constraint Programming (CP) systems. In a CP system (Jaffar and Maher 1994), constraints are incrementally added to and removed from its constraint store which can be modeled as a CSP. The success of CP systems illustrates the need to have efficient incremental CSP algorithms. Existing work on functional constraints deals mainly with static CSPs where all constraints are known a priori. We show that an incremental CSP with pure functional constraints can be solved in almost the same time complexity as a static one. To solve more constraints (not only pure functional constraints) in a mixed CSP with both functional and non-functional constraints, we propose an algorithm with complexity comparable to the cost of enforcing arc consistency.