The Eigen-Distribution for Multi-Branching Weighted Trees on Independent Distributions

Weiguang Peng, NingNing Peng () and Kazuyuki Tanaka
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Weiguang Peng: Southwest University
NingNing Peng: Wuhan University of Technology
Kazuyuki Tanaka: Tohoku University

Methodology and Computing in Applied Probability, 2022, vol. 24, issue 1, 277-287

Abstract: Abstract Okisaka et al. (2017) investigated the eigen-distribution for multi-branching trees weighted with (a,b) on correlated distributions, which is a weak version of Saks and Wigderson’s (1986) weighted trees. In the present work, we concentrate on the studies of eigen-distribution for multi-branching weighted trees on independent distributions. In particular, we generalize our previous results in Peng et al. (Inform Process Lett 125:41–45, 2017) to weighted trees where the cost of querying each leaf is associated with the leaf and its Boolean value. For a multi-branching weighted tree, we define a directional algorithm and show it is optimal among all the depth-first algorithms with respect to the given independent distribution. For some balanced multi-branching trees weighted with (a,b) on the assumption 0

Keywords: Game trees with weights; Alpha-beta pruning algorithm; Independent distribution; Computational complexity; 03D15 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11009-021-09849-7

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