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

TL;DR

This paper generalizes bounds for graph-based global constraints and introduces a filtering scheme applicable to various graph classes and bounds, enhancing constraint programming techniques.

Contribution

It extends bounds of MIN_NCC and MAX_NCC to all graph classes and proposes a versatile filtering scheme for graph domain variables.

Findings

Generalized bounds for MIN_NCC and MAX_NCC across all graph classes.

Developed a filtering scheme adaptable to any graph class and bounds.

Facilitated more flexible constraint solving in 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.