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

Weiguang Peng, Ning Ning Peng, Kazuyuki Tanaka

## 抄録

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 < r < 1 (r is the probability that the root has value 0), we further prove that if an independent distribution d achieves the distributional complexity, then d turns out to be an independent and identical distribution.

本文言語 English 277-287 11 Methodology and Computing in Applied Probability 24 1 https://doi.org/10.1007/s11009-021-09849-7 Published - 2022 3月 はい

• 統計学および確率
• 数学 (全般)

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