Combining Restarts, Nogoods and Decompositions for Solving CSPs

From a theoretical viewpoint, the (tree-)decomposition methods offer a good approach when the (tree)-width of constraint networks (CSPs) is small. In this case, they have often shown their practical interest. However, sometimes, a bad choice for the root cluster (a tree-decomposition is a tree of clusters) may drastically degrade the performance of the solving. In this paper, we highlight an explanation of this degradation and we propose a solution based on restart techniques. Then, we present a new version of the BTD algorithm (for Backtracking with TreeDecomposition [8]) integrating restart techniques. From a theoretical viewpoint, we prove that reduced nld-nogood can be safely recorded during the search and that their size is smaller than ones recorded by MAC+RST+NG [9]. We also show how structural (no)goods may be exploited when the search restarts from a new root cluster. Finally, from a practical viewpoint, we show experimentally the benefits of using restart techniques for solving CSPs by decomposition methods.