Consistency and propagation with multiset constraints: A formal viewpoint

Abstract

We study from a formal perspective the consistency and propagation of constraints involving multiset variables. That is, variables whose values are multisets. These help us model problems more naturally and can, for example, prevent introducing unnecessary symmetry into a model. We identify a number of different representations for multiset variables and compare them. We then propose a definition of local consistency for constraints involving multiset, set and integer variables. This definition is a generalization of the notion of bounds consistency for integer variables. We show how this local consistency property can be enforced by means of some simple inference rules which tighten bounds on the variables. We also study a number of global constraints on set and multiset variables. Surprisingly, unlike finite domain variables, the decomposition of global constraints over set or multiset variables often does not hinder constraint propagation. © Springer-Verlag 2003.