Improving Exact Solution Counting for Decomposition Methods

The problem of counting solutions in CSP, called #CSP, is an extremely difficult problem that has many applications in Artificial Intelligence. This problem can be addressed by exact methods, but more classically it is solved by approximate methods. Here, we focus primarily on the exact counting. We show how it is possible to improve the methods based on structural decomposition by offering to enhance the search for a new solution which is a critical step for counting, particularly for such methods. Moreover, if the resources in time or in space are insufficient, we show that our approach is still able to provide a lower bound of the result. Experiments on CSP benchmarks show the practical advantage of our approach w.r.t. the best methods of the literature.