A Weighted Counting Algorithm for the Circuit Constraint

Gauthier Pezzoli, Gilles Pesant

Abstract: The Circuit constraint is useful to model many combinatorial problems in Constraint Programming. cp solvers extended with Belief Propagation, such as MiniCPBP, require that constraints be equipped with weighted counting algorithms in order to propagate probability mass functions over domains. This is not yet the case for Circuit. To this purpose we introduce a probabilistic sampling algorithm to count Hamiltonian circuits in a weighted graph. We show that our resulting estimator is unbiased, measure its empirical accuracy, and evaluate its impact on search performance.