Section: New Results

Consistency and Filtering

Participants : Nicolas Beldiceanu, Mats Carlsson, Gilles Chabert, Sophie Demassey, Thierry Petit, Jean-Charles Régin.

Following up on our work on efficient filtering algorithms for common conjunctions of widely used constraints (e.g., among, alldifferent, linear constraint, inequalities constraints) we provide:

1. An $O(nlogn)$ bound consistency filtering algorithm for the conjunction of an alldifferent and a linear inequality constraint. The $O(nlogn)$ complexity is equal to the complexity of the bound consistency algorithm of the alldifferent constraint.

2. A polynomial time bound consistency algorithm for the conjunction of among constraints where the variable and value domains are interval.

Motivated by the need to define more formally incomplete filtering algorithms we have proposed a new theoretical scheme for characterizing, comparing and classifying the intermediary levels of consistency of global constraints.

The corresponding papers, An $O(nlogn)$ Bound Consistency Algorithm for the Conjunction of an alldifferent and an Inequality between a Sum of Variables and a Constant, and its Generalization [17] , The Conjunction of Interval among Constraints [21] and Intermediary Local Consistencies [28] were published at the 20th European Conference on Artificial Intelligence (ECAI 2012 ) as well as at the 9th International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (CPAIOR 2012 ).