Abstract
This paper analyzes Nn,d, the average number of terminal nodes examined by the α-β pruning algorithm in a uniform game-tree of degree n and depth d for which the terminal values are drawn at random from a continuous distribution. It is shown that Nn,d attains the branching factor ℝα−β(n)=ξn/l-ξn where ξn is the positive root of xn+x-l=0. The quantity ξn/1-ξn has previously been identified as a lower bound for all directional algorithms. Thus, the equality ℝα−β(n)=ξn/1-ξn renders α-β asymptotically optimal over the class of directional, game-searching algorithms.
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References
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© 1981 Springer-Verlag Berlin Heidelberg
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Pearl, J. (1981). The solution for the branching factor of the alpha-beta pruning algorithm. In: Even, S., Kariv, O. (eds) Automata, Languages and Programming. ICALP 1981. Lecture Notes in Computer Science, vol 115. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10843-2_41
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DOI: https://doi.org/10.1007/3-540-10843-2_41
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