The eigen-distribution of weighted game trees

Shohei Okisaka, Weiguang Peng, Wenjuan Li, Kazuyuki Tanaka

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)


This paper is devoted to the ongoing study on the equilibrium points of AND-OR trees. Liu and Tanaka (2007, 2007a) characterized the eigen-distributions that achieve the distributional complexity, and among others, they proved the uniqueness of eigen-distribution for a uniform binary tree. Later, Suzuki and Nakamura (2012) showed that the uniqueness fails if only directional algorithms are allowed. Peng et al. (2016) extended the studies on eigen-distributions to balanced multi-branching trees of height 2. But, it remains open whether the uniqueness still holds or not for general multi-branching trees. To this end, we introduce the weighted trees, namely, trees with weighted cost depending on the value of a leaf. Using such models, we prove that for balanced multi-branching trees, the uniqueness of eigen-distribution holds w.r.t. all deterministic algorithms, but fails w.r.t. only directional algorithms.

Original languageEnglish
Title of host publicationCombinatorial Optimization and Applications - 11th International Conference, COCOA 2017, Proceedings
EditorsMeng Han, Hongwei Du, Xiaofeng Gao
PublisherSpringer Verlag
Number of pages12
ISBN (Print)9783319711492
Publication statusPublished - 2017
Event11th International Conference on Combinatorial Optimization and Applications, COCOA 2017 - Shanghai, China
Duration: 2017 Dec 162017 Dec 18

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10627 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other11th International Conference on Combinatorial Optimization and Applications, COCOA 2017


  • Alpha-beta pruning algorithm
  • Computational complexity
  • Game trees with weight
  • Leaf cost function

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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