Perfect Constraints Are Tractable

By using recent results from graph theory, including the Strong Perfect Graph Theorem, we obtain a unifying framework for a number of tractable classes of constraint problems. These include problems with chordal microstructure; problems with chordal microstructure complement; problems with tree structure; and the ``all-different'' constraint. In each of these cases we show that the associated microstructure of the problem is a perfect graph, and hence they are all part of the same larger family of tractable problems