A Probabilistic Model to Count Solutions on the alldifferent Constraint

Abstract : This article presents two probabilistic models for the alldifferent constraint. We are interested in studying the combinatorial structure of the alldifferent constraint. More specifically, we are interested in the existence of solutions for an instance of alldifferent and to count them. Such informations can be used in search heuristics. From this probabilistic approach, we show how to compute some estimators of the number of solutions and we use them in a search heuristics inspired by Counting-Based Search heuristics.