Probabilistic Analysis of the Complexity of A*

This paper analyzes the 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 distributions may vary over the nodes in the graph. Our model consists of an m -ary tree with unit branch costs and a unique goal state situated at a distance N from the root. Two results are established: (1) for any error distribution, i f A '[ is stochastically more informed than A ~, then A T is stochastically more efficient than A ~., and (2) if the probability that the relative error be bounded away from zero is greater than l /m, then the average complexity of A * is exponential with N, whereas if the probability of zero error is greater than 1 l /m, the average complexity is O(N) .