On the Forward Checking Algorithm

The forward checking algorithm for solving constraint satisfaction problems is a popular and successful alternative to backtracking. However, its success has largely been determined empirically, and there has been limited work towards a real understanding of why and when forward checking is the superior approach. This paper advances our understanding by showing that forward checking is closely related to backmarking, which is a widely used improvement of ordinary backtracking.This result is somewhat surprising, because (as their names suggest) forward checking is superficially quite different from backtracking and its variants. The result may also help in predicting when forward checking will be the best method. Finally, the paper shows how the relationship to backmarking helps understand a recently introduced improvement to the forward checking algorithm, known as minimal forward checking. We argue that the new algorithm is best viewed as a hybrid combination of backmarking and forward checking.