Solving over-constrained CSP using weighted OBDDs

Abstract

In Artificial Intelligence, for practical applications, we often have to manage over-constrained systems of constraints. So, a model based on the formalism of finite Constraint Satisfaction Problems (CSPs) [14] has been proposed with Dynamic CSPs (DCSPs) to handle this kind of problems [10][11]. Some classical techniques defined in the field of CSPs are usable in DCSPs, but the management of over-constrained system with DCSPs induces new problems. The purpose of this paper is to introduce an efficient way to solve DCSPs based on a logical approach. We use Ordered Binary Decision Diagrams (OBDDs) [3] and propose a particular coding for dynamicity. We show that our approach allows to solve some major questions in the field of DCSP, particularly consistency maintenance. This kind of problems is naturally expressed as a problem of optimal path computing in weighted graphs. Moreover, we shall see that the problem of finding optimal solutions can be solved easily and efficiently by our approach. One important problem in OBDD is the amount of memory required to represent the OBDD. In the worst case, this amount is in O(2^N) where N is the number of propositional variables for static CSPs. We prove here that, if the number of dynamic constraints is m and if n is the number of variables in the problem, the size of OBDD is bounded by O(m×2ⁿ). First experimental results attest the interest of the approach.