Exploring Parameterized Relational Consistency

Consistency properties and algorithms for achieving them are at the heart of the success of Constraint Programming. For non-binary Constraint Satis- faction Problems (CSPs), the relational-consistency property R(i,j)C of (Dechter and van Beek 1997) may add new non-binary constraints to the constraint network, thus modifying its topology. The domain-filtering properties of (Bessiere et al. 2008) filter the domains of the variables and leave the constr aints un- changed but are restricted to combinations of two constraints. We restate the property of m-wise consistency (Gyssens 1986; Jegou 1993) as relational (∗,m)-consistency, R(∗,m)C. R(∗,m)C ensures that any tuple in a relation is consistent in every combination of m constraints. The main contributions of this document are the design of an algorithm for enforcing R(∗,m)C and the evaluation of its effectiveness in a search procedure so lving CSPs. This document thus establishes the usefulness in practice of higher consistency levels in non-binary CSPs.