The solution for the branching factor of the alpha-beta pruning algorithm

  • Judea Pearl
Session 16: S. Even, Chairman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 115)


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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Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • Judea Pearl
    • 1
  1. 1.Cognitive Systems Laboratory School of Engineering and Applied ScienceUniversity of California, Los AngelesLos Angeles

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