Abstract. 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.

Abstract. This paper investigates cumulative scheduling in uncertain environments, using constraint programming. We present a new declarative characterization of robustness, which preserves solution quality. We highlight the significance of our framework on a crane assignment problem with business constraints.

The construction of a Quasi-Cyclic Low Density Parity-Check (QC-LDPC) matrix is usually carried out in two steps. In the first step, a prototype matrix is defined according to certain criteria (size, girth, check and variable node degrees, etc.). The second step involves expansion of the prototype matrix. During this last phase, an integer value is assigned to each nonnull position in the prototype matrix corresponding to the rightrotation of the identity matrix. The problem of determining these integer values is complex. State-of-the-art solutions use either some mathematical constructions to guarantee a given girth of the final QC-LDPC code or a random search of values until the target girth is satisfied. In this paper, we propose an alternative/complementary method that reduces the search space by defining large equivalence classes of topologically identical matrices through row and column permutations using additive, structural and multiplicative transformations. Selecting only a single element per equivalence class can reduce the search space by a few orders of magnitude. Then, we use the formalism of constraint programming to list the exhaustive sets of solutions for a given girth and a given expansion factor. An example is presented in all sections of the paper to illustrate the methodology.

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Abstract. 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 Allen's 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 Allen's 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 2 13 combinations of Allen's 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 O(n + m), where n is the number of tasks and m the number of intervals. This propagator is suited to any combination of Allen's relations, without any specific tuning. Therefore, using our framework does not require a strong expertise in Constraint Programming. The experiments, performed on real data, confirm the relevance of our approach.