Complexity of State-Space Search for Optimal Solutions

Abstract

In the worst case, a state-space search algorithm must explore every node in a state space. Thus the worst-case complexity is linear in the size of the state space. On the other hand, if the lower-bound cost function used by the algorithm is exact, the complexity is linear in the length of the path from the initial node to a goal node. However, these extreme cases rarely occur and thus convey little information about the actual performance of an algorithm. Average-case complexity is therefore a more realistic performance measure. This chapter considers an average-case complexity of a state-space search algorithm. The main purpose of an average-case analysis is to find the relationship between the average-case complexity and the accuracy of lower-bound cost functions used by a search algorithm.

The author thanks American Association for Artificial Intelligence for permission to reprint some of the text and figures in the article “Depth-first vs. best-first search: New results” by Weixiong Zhang and Richard E. Korf which appeared in Proceedings of the 11th National Conference on Artificial Intelligence (AAAI-93), Washington, DC, July 11–15, 1993, pp.769–775, and to Elsevier Science for permission to reprint some of the text and figures in the article “Performance of linear-space search algorithms” by Weixiong Zhang and Richard E. Korf which appeared in Artificial Intelligence, 79(2) (1995) 241–292.