Tree Decomposition with Applications to Constraint Processing

This paper concerns the task of removing redundant information from a given knowledge base, and restructuring it in the form of a tree, so as to admit efficient problem solving routines. We offer a novel approach which guarantees the removal of all redundancies that hide a tree structure. We develop a polynomial time algorithm that, given an arbitrary constraint network, generates a precise tree representation whenever such a tree can be extracted from the input network, otherwise, the fact that no tree representation exists is acknowledged, and the tree generated may serve as a good approximation to the original network.