Average-Case Analysis of Heuristic Search in Tree-Like Networks
A search graph has the form of an m-ary tree with bi-directional arcs of unit cost. There is a goal node at a distance N from the root, and there may be other goal nodes at distances ≥ N from the root. It is assumed that the heuristic estimates of nongoal nodes, after being appropriately normalized, are independent and identically distributed random variables. The heuristic is not required to be admissible. Under what conditions is the expected number of node expansions E(Z) polynomial in N? Earlier efforts by Pearl and others at answering this question have considered search trees with only one goal node. An attempt is made here to develop a general and unified method of analysis applicable to situations with more than one goal node. It is shown that, for most probability distributions on the heuristic estimates, E(Z) is exponential in N; the one major exception being the case when the number of goal nodes is polynomial in N and the normalizing function for the error is logarithmic. Pearl’s contention that the average-case analysis of weighted heuristic search is not too attractive is also verified. It is hoped that the general approach described here will encourage similar studies on search graphs other than trees.
KeywordsGoal Node Heuristic Search Search Tree Solution Path Search Graph
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