Global reasoning on sets

Finite set constraint systems represent a natural choice to model com-binatorial connguration problems involving set disjointness, covering or partitioning relations. However, for eeciency reasons, alternative formulations based on Finite Domain or 0-1 integer programming are often preferred even though they require much modelling eeort. To ooer a better trade-oo \natural formulation"/eeciency we propose to improve the ee-ciency of set constraint solvers by introducing global reasoning on a class of nite set constraints. These are n-ary constraints like atmost1-incommon, distinct upon sets of known cardinality. In this paper we show how the representation of sets within powersets speciied as set intervals allows us to derive some global pruning based on mathematical and combinatorial analysis formulas. They improve greatly the ltering enforced by bound consistency methods, and allow to detect failure at early stages. Preliminary results are illustrated on the ternary Steiner and a generic distinct problems.