Christian Bessiere

Among, common and disjoint constraints

Among, Common and Disjoint are global constraints useful in modelling problems involving resources. We study a number of variations of these constraints over integer and set variables. We show how computational complexity can be used to determine whether achieving the highest level of consistency is tractable. For tractable constraints, we present a polynomial propagation algorithm and compare it to logical decompositions with respect to the amount of constraint propagation. For intractable cases, we show in many cases that a propagation algorithm can be adapted from a propagation algorithm of a similar tractable one.

The range constraint: algorithms and implementation

We recently proposed a simple declarative language for specifying a wide range of counting and occurrence constraints. The language uses just two global primitives: the Range constraint, which computes the range of values used by a set of variables, and the Roots constraint, which computes the variables mapping onto particular values. In order for this specification language to be executable, propagation algorithms for the Range and Roots constraints should be developed. In this paper, we focus on the study of the Range constraint. We propose an efficient algorithm for propagating the Range constraint. We also show that decomposing global counting and occurrence constraints using Range is effective and efficient in practice.

Range and Roots: Two common patterns for specifying and propagating counting and occurrence constraints

We propose Range and Roots which are two common patterns useful for specifying a wide range of counting and occurrence constraints. We design specialised propagation algorithms for these two patterns. Counting and occurrence constraints specified using these patterns thus directly inherit a propagation algorithm. To illustrate the capabilities of the Range and Roots constraints, we specify a number of global constraints taken from the literature. Preliminary experiments demonstrate that propagating counting and occurrence constraints using these two patterns leads to a small loss in performance when compared to specialised global constraints and is competitive with alternative decompositions using elementary constraints.