Abstract
This paper analyzes the average number of nodes expanded by A∗ as a function of the accuracy of its heuristic estimates, by treating the errors h∗ - h as random variables whose distribution may vary over the nodes in the graph. The search model consists of an m-ary tree with unit branch costs and a unique goal state situated at a distance N from the root. The main result states that if the typical error grows like φ(h∗) then the mean complexity of A∗ grows approximately like G( N)exp[ cφ( N)], where c is a positive constant and G(N) is O(N 2). Thus, a necessary and sufficient condition for maintaining polynomial search complexity is that A∗ be guided by heuristics with logarithmic precision, e.g. φ( N) = (log N) k . A∗ is shown to make much greater use of its heuristic knowledge than a backtracking procedure would under similar conditions.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
