A GAC Algorithm for a Class of Global Counting Constraints

Nicolas Beldiceanu (1) , Xavier Lorca (1) , Thierry Petit (2, 1)

1 LINA - Laboratoire d'Informatique de Nantes Atlantique
2 TASC - Theory, Algorithms and Systems for Constraints

This paper presents the constraint class seq bin(N;X;C;B) where N is an integer variable, X is a sequence of integer variables and C and B are two binary constraints. A constraint of the seq bin class enforces the two following conditions: (1) N is equal to the number of times that the constraint C is satised on two consecutive variables in X, and (2) B holds on any pair of consecutive variables in X. Providing that B satises the particular property of neighborhood-substitutability, we come up with a ltering algorithm that achieves generalized arc-consistency (GAC) for seq bin(N;X;C;B). This algorithm can be directly used for the constraints Change, Smooth, Increasing Nvalue, Among and Increasing Among, in time linear in the sum of domain sizes. For all these constraints, this time complexity either improves the best known results, or equals those results.

Domaines: Recherche opérationnelle [math.OC]

Nicolas Beldiceanu, Xavier Lorca, Thierry Petit. A GAC Algorithm for a Class of Global Counting Constraints. 2010. ⟨hal-00517122⟩