Thierry Petit

A New Characterization of Relevant Intervals for Energetic Reasoning

Energetic Reasoning (ER) is a powerful filtering algorithm for the Cumulative constraint. Unfortunately, ER is generally too costly to be used in practice. One reason of its bad behavior is that many intervals are considered as relevant, although most of them should be ignored. In the literature, heuristic approaches have been developed in order to reduce the number of intervals to consider, leading to a loss of filtering. In this paper, we provide a sharp characterization that allows to reduce the number of intervals by a factor seven without loss of filtering.

An O ( n log n ) bound consistency algorithm for the conjunction of an alldifferent and an Inequality between a Sum of Variables and a Constant , and its generalization

This paper gives an O(n log n) bound-consistency filtering algorithm for the conjunction alldifferent(V0, V1,..., Vn-1) Λ f(V0) ⊕ f(V1) ⊕ ⊕ · · · ⊕ f(Vn-1) ≤ cst, (V0, V1,..., Vn-1, cst ∈ ℕ+), where (ℕ, ⊕) is a commutative group, f is a unary function, and both ⊕ and f are monotone increasing. This complexity is equal to the complexity of the bound-consistency algorithm of the alldifferent constraint.

A Θ(n) bound-consistency algorithm for the increasing sum constraint

Given a sequence of variables X =〈x0, x1,..., xn-1〉, we consider the INCREASINGSUM constraint, which imposes ∀i e [0, n - 2] xi ≤ xi+1, and ΣxieXxi = s. We propose an Θ(n) bound-consistency algorithm for INCREASINGSUM.

A global constraint for a tractable class of temporal optimization problems

This paper is originally motivated by an application where the objective is to generate a video summary, built using intervals extracted from a video source. In this application, the constraints used to select the relevant pieces of intervals are based on Allens algebra. The best state-of-the-art results are obtained with a small set of ad hoc solution techniques, each specific to one combination of the 13 Allens relations. Such techniques require some expertise in Constraint Programming. This is a critical issue for video specialists. In this paper, we design a generic constraint, dedicated to a class of temporal problems that covers this case study, among others. ExistAllen takes as arguments a vector of tasks, a set of disjoint intervals and any of the

THE ORDERED DISTRIBUTE CONSTRAINT

2^{13}

The Ordered Distribute Constraint

213 combinations of Allens relations. ExistAllen holds if and only if the tasks are ordered according to their indexes and for any task at least one relation is satisfied, between the task and at least one interval. We design a propagator that achieves bound-consistency in

A Declarative Paradigm for Robust Cumulative Scheduling

On+m