Counting-Based Look-Ahead Schemes for Constraint Satisfaction

The paper presents a new look-ahead scheme for backtracking search for solving constraint satisfaction problems. This look-ahead scheme computes a heuristic for value ordering and domain pruning. The heuristic is based on approximating the number of solutions extending each partial solution. In particular, we investigate a recent partitionbased approximation of tree-clustering algorithms, Iterative Join-Graph Propagation (IJGP), which belongs to the class of belief propagation algorithms that attracted substantial interest due to their success for probabilistic inference. Our empirical evaluation demonstrates that the counting-based heuristic approximated by IJGP yields a scalable, focused search.