Improvement of CSP resolution algorithms using partial orders on domain values

Abstract

In [Fre91], Freuder defined the notion of interchangeability of values in a CSP, whose purpose is to reduce the size of the problem without losing any solution. He also defined related and weaker notions, such as substitutability. This paper explores this latter notion : firstly the partial pre-orders on domain values induced by the substitutability relation are emphasized ; then these pre-orders are used to improve standard algorithms of resolution such as backtracking or forward-checking, for the task of computing a single solution : the size of the problem is reduced by filtering techniques that preserve the satisfiability. Keywords Constraint Satisfaction Problems, Partial Pre-Orders. 1 Introduction Constraint Satisfaction Problems (CSPs) represent an interesting way of modelization for many Artificial Intelligence and optimization problems. Unfortunately, the resolution of such problems is generally NP-complete. So, in order to facilitate the resolution task, a lot of techniques..