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A Generalized Cyclic-Clustering Approach for Solving Structured CSPs

We propose a new method for solving structured CSPs which generalizes and improves the Cyclic-Clustering approach [Jegou, 1990]. First, the cutset and the tree-decomposition of the constraint network, which are used for taking advantage of the CSP structure, are computed independently of the notion of triangulated induced subgraph. Then, unlike Cyclic-Clustering, our method can try to solve the tree-decomposition part of the problem without having assigned all the variables of the cutset. Regarding the solving of the tree-decomposition part, we use the BTD method [Jegou and Terrioux, 2003] like in [Jegou and Terrioux, 2004]. As BTD records and exploits structural (no)goods, we provide some conditions which make possible the use of structural (no)goods recorded during previous calls of BTD and we implement them in a dedicated version of BTD. By so doing, from a theoretical viewpoint, we can provide a theoretical time complexity bound related to parameters of the cutset and the tree-decomposition and, from a practical viewpoint we expect to detect failures earlier and to avoid more redundancies in the search.