Bounded Backtracking for the Valued Constraint Satisfaction Problems

We propose a new method for solving Valued Constraint Satisfaction Problems based both on backtracking techniques branch and bound and the notion of tree-decomposition of valued constraint networks. This mixed method aims to benefit from the practical efficiency of enumerative algorithms while providing a warranty of a bounded time complexity. Indeed the time complexity of our method is O(d ++1) with w an approximation of the tree-width of the constraint network and d the maximum size of domains. Such a complexity is obtained by exploiting optimal bounds on the subproblems defined from the tree-decomposition. These bounds associated to some partial assignments are called ”structural valued goods”. Recording and exploiting these goods may allow our method to save some time and space with respect to ones required by classical dynamic programming methods. Finally, this method is a natural extension of the BTD algorithm [1] proposed in the classical CSP framework.