A Complexity Analysis of Space-Bounded Learning Algorithms for the Constraint Satisfaction Problem

Learning during backtrack search is a space-intensive process that records information (such as additional constraints) in order to avoid redundant work. In this paper, we analyze the effects of polynomial-space-bounded learning on runtime complexity of backtrack search. One space-bounded learning scheme records only those constramts With limited size, and another records arbitrarily large constraints but deletes those that become irrelevant to the portion of the search space being explored. We find that relevance-bounded learning allows better runtime bounds than size-bounded learning on structurally restricted constraint satisfaction problems. Even when restricted to linear space, our relevance-bounded learning algorithm has runtime complexity near that of unrestricted (exponential space-consuming) learning schemes.