Minimal Forward Checking

Forward Checking is a highly regarded search method used to solve Constraint Satisfaction Problems. This method performs a limited type of lookahead attempting to nd a failure earlier during a backtracking search. In this paper a new search method, Minimal Forward Checking, is introduced which under certain conditions performs the same amount of constraint checking in the worst case as Forward Checking and retains Forward Check-ing's ability to detect future consistent values. Minimal Forward Checking is a lazy version of Forward Checking that suspends some \forward checks" until they are needed. Minimal Forward Checking is implemented as a marriage of incremental Forward Checking with Backmarking. Experimental evidence gathered from comparisons of the two algorithms on two large samples of randomly generated problems shows that Minimal Forward Checking outperforms Forward Checking especially as the domain sizes increase. The experiments also show that the use of a dynamic variable selection heuristic beneets both of the algorithms.