In Proceedings of AAAI - 96 . c American Association for Arti cial Intelligence , 1996 . The Constrainedness of Search

We introduce a parameter that measures the \con-strainedness" of an ensemble of combinatorial problems. If problems are over-constrained, they are likely to be insoluble. If problems are under-constrained, they are likely to be soluble. This constrainedness parameter generalizes a number of parameters previously used in diierent NP-complete problem classes. Phase transitions in diierent NP classes can thus be directly compared. This parameter can also be used in a heuristic to guide search. The heuristic captures the intuition of making the most constrained choice rst, since it is often useful to branch into the least constrained subproblem. Many widely disparate heuris-tics can be seen as minimizing constrainedness.