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

Author

Listed:
  • Weiguang Peng

    (Southwest University)

  • NingNing Peng

    (Wuhan University of Technology)

  • Kazuyuki Tanaka

    (Tohoku University)

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

Suggested Citation

  • Weiguang Peng & NingNing Peng & Kazuyuki Tanaka, 2022. "The Eigen-Distribution for Multi-Branching Weighted Trees on Independent Distributions," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 277-287, March.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:1:d:10.1007_s11009-021-09849-7
    DOI: 10.1007/s11009-021-09849-7
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