A New Evaluation of Forward Checking and Its Consequences on Efficiency of Tools for Decomposition of CSPs

In this paper, a new evaluation of the complexity of forward checking for solving non-binary CSPs with finite domains is proposed. Unlike what is done usually, it does not consider the size of domains, but the size of the relations associated to the constraints. It may lead sometimes to define better complexity bounds. By using this first result, we show that the tractability hierarchy proposed in [6] which compares different methods based on a decomposition of constraint networks can be seen from a new viewpoint.