Section: New Results

New Global Constraints

This year we introduce new generic global constraints that can be respectively used to reformulate a number of constraints where the formulation become easy once some tuples are sorted, and to express temporal relation between two sequence of intervals.

• Some constraint programming solvers and constraint modelling languages feature the sort$(L,P,S)$ constraint, which holds if $S$ is a nondecreasing rearrangement of the list $L$, the permutation being made explicit by the optional list $P$. However, such sortedness constraints do not seem to be used much in practice. We argue that reasons for this neglect are that it is impossible to require the underlying sort to be stable, so that sort cannot be guaranteed to be a total-function constraint, and that $L$ cannot contain tuples of variables, some of which form the key for the sort. To overcome these limitations, we introduce the stable-keysort constraint, decompose it using existing constraints, and propose a propagator. This new constraint enables a powerful modelling idiom, which we illustrate by elegant and scalable models of two problems that are otherwise hard to encode as constraint programs.

• The constraint was initially 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. 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 213 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.