Analysis of a Global Contiguity Constraint

We address a global constraint for enforcing contiguity. Contiguity is the property that all of one kind of object in an array or list are grouped together; it is a one-dimensional discrete form of convexity. We present an implementation of this property in a concurrent constraint programming language. We adapt and apply the constraint propagation framework of [19] to analyse the contiguity property. In particular, the soundness of the implementation is proved and the forms of local consistency that are maintained by the implementation are identified. A complexity analysis shows that the implementation is optimal for achieving arc-consistency. However, an optimal implementation is not given for a stronger consistency condition, and we raise the possibility that an optimal implementation requires meta-level programming.