A Quadratic Propagator for the Inter-Distance Constraint, Claude-Guy Quimper, A. López-Ortiz, Gilles Pesant. In proceedings of 21^st National Conference on Artificial Intelligence (AAAI-06). [PDF file]

Abstract.
We present a new propagator achieving bound consistency for the interdistance constraint. This constraint ensures that, among a set of variables X_1, …, X_n, the difference between two variables is at least p. This restriction models, in particular, scheduling problems in which tasks require p contiguous units of a resource to be completed. Until now, the best known propagator for bound consistency had time complexity O(n^3). In this work we propose a quadratic propagator for the same level of consistency. We then show that this theoretical gain gives savings of an order of magnitude in our benchmark of scheduling problems.