Complexity Analysis of Admissible Heuristic Search

Richard E. Korf, Michael Reid

We analyze the asymptotic time complexity of admissible heuristic search algorithms such as A*, IDA*, and depth-first branch-and-bound. Previous analyses relied on an abstract analytical model, and characterize the heuristic function in terms of its accuracy, but do not apply to real problems. In contrast, our analysis allows us to accurately predict the performance of these algorithms on problems such as the sliding-tile puzzles and Rubik’s Cube. The heuristic function is characterized simply by the distribution of heuristic values in the problem space. Contrary to conventional wisdom, our analysis shows that the asymptotic heuristic branching factor is the same as the bruteforce branching factor, and that the effect of a heuristic function is to reduce the effective depth of search, rather than the effective branching factor.

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