A Constraint on the Number of Distinct Vectors with Application to Localization

This paper introduces a generalization of the nvalue constraint that bounds the number of distinct values taken by a set of variables.The generalized constraint (called nvector) bounds the number of distinct (multi-dimensional) vectors. The first contribution of this paper is to show that this global constraint has a significant role to play with continuous domains, by taking the example of simultaneous localization and map building (SLAM). This type of problem arises in the context of mobile robotics. The second contribution is to prove that enforcing bound consistency on this constraint is NP-complete. A simple contractor (or propagator) is proposed and applied on a real application.