Eigen-distribution on random assignments for game trees

Chen Guang Liu, Kazuyuki Tanaka

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


In this Letter, we investigate a special distribution, called eigen-distribution, on random assignments for a class of game trees T2k. There are two cases, where the assignments to leaves are independently distributed (ID) and correlated distributed (CD). In the ID case, we prove that the distributional probability ρ{variant} belongs to [frac(sqrt(7) - 1, 3), frac(sqrt(5) - 1, 2)], and ρ{variant} is a strictly increasing function on rounds k ∈ [1, ∞). In the CD case, we propose a reverse assigning technique (RAT) to form two particular sets of assignments, 1-set and 0-set, then show that the E1-distribution (namely, a particular distribution on the assignments of 1-set such that all the deterministic algorithms have the same complexity) is the unique eigen-distribution for T2k in the global distribution.

Original languageEnglish
Pages (from-to)73-77
Number of pages5
JournalInformation Processing Letters
Issue number2
Publication statusPublished - 2007 Oct 16
Externally publishedYes


  • Computational complexity
  • Distributional complexity
  • Eigen-distribution
  • Game tree
  • Randomized algorithms

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Information Systems
  • Computer Science Applications


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