SLIDE: A Useful Special Case of the CARDPATH Constraint

We study the CARDPATH constraint. This ensures a given constraint holds a number of times down a sequence of variables. We show that SLIDE, a special case of CARDPATH where the slid constraint must hold always, can be used to encode a wide range of sliding sequence constraints including CARDPATH itself. We consider how to propagate SLIDE and provide a complete propagator for CARDPATH. Since propagation is NP-hard in general, we identify special cases where propagation takes polynomial time. Our experiments demonstrate that using SLIDE to encode global constraints can be as efficient and effective as specialised propagators.