New Look-Ahead Schemes for Constraint Satisfaction

This paper presents new look-ahead schemes for backtracking search when solving constraint satisfaction problems. The look-ahead schemes compute a heuristic for value ordering and domain pruning, which influences variable orderings at each node in the search space. As a basis for a heuristic, we investigate two tasks, both harder than the CSP task. The first is finding the solution with min-number of conflicts. The second is counting solutions. Clearly each of these tasks also finds a solution to the CSP problem, if one exists, or decides that the problem is inconsistent. Our plan is to use approximations of these more complex tasks as heuristics for guiding search for a solution of a CSP task. In particular, we investigate two recent partitionbased strategies that approximate variable elimination algorithms, Mini-Bucket-Tree Elimination and Iterative Join-Graph Propagation (ijgp). The latter belong to the class of belief propagation algorithm that attracted substantial interest due to their surprising success for probabilistic inference. Our preliminary empirical evaluation is very encouraging, demonstrating that the countingbased heuristic approximated by by IJGP yields a very focused search even for hard problems.