Bounds of MIN_NCC and MAX_NCC and filtering scheme for graph domain variables

Abstract

Graph domain variables and constraints are an extension of constraint programming introduced by Dooms et al. This approach had been further investigated by Fages in its PhD thesis. On the other hand, Beldiceanu et al. presented a generic filtering scheme for global constraints based on graph properties. This scheme strongly relies on the computation of graph properties' bounds and can be used in the context of graph domain variables and constraints with a few adjustments. Bounds of MIN_NCC and MAX_NCC had been defined for the graph-based representation of global constraint for the path_with_loops graph class. In this note, we generalize those bounds for graph domain variables and for any graph class. We also provide a filtering scheme for any graph class and arbitrary bounds.