Networks of qualitative interval relations: combining circuit consistency and path consistency in the search for a solution

We first define the concept of circuit consistency for interval networks. We then provide an example showing that even for atomic networks circuit consistency is not complete. Then we describe how to combine circuit consistency and path consistency in existing search algorithms. Instead of applying path-consistency at each node of the search tree, as do existing algorithms, the idea of our method is to apply path consistency only at nodes of level (n-1)n/2, and circuit consistency in the remaining nodes of the search tree (n is the number of variables of the input network). Circuit consistency filtering is potentially less effective than path consistency filtering; however circuit consistency is computationally one factor less expensive. We provide experiments showing the performances of the search in the two cases (a) when circuit consistency and path consistency are combined and (b) when only path consistency is used.