Eigen-distribution on assignments for game trees with random properties

Chenguang Liu, Kazuyuki Tanaka

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


In this paper, we investigate a special distribution, called eigen-distribution, on assignments for game tree Tk 2 with random properties. There are two cases, where the assignments to leaves are independently distributed (ID) and correlated istributed (CD). In ID setting, we prove that the distributional probability % belongs to [√7-1/3, √5-1/2 ], and q is a strictly increasing function on rounds kε2 [1,1). In CD setting, we propose a reverse assigning technique (RAT) to form 1-set and 0-set, then show that E1-distribution (namely, a particular distribution on assignments of 1-set such that the complexity of any deterministic algorithm is equal) is the unique eigen-distribution.

Original languageEnglish
Title of host publicationProceedings of the 2007 ACM Symposium on Applied Computing
PublisherAssociation for Computing Machinery
Number of pages2
ISBN (Print)1595934804, 9781595934802
Publication statusPublished - 2007 Jan 1
Externally publishedYes
Event2007 ACM Symposium on Applied Computing - Seoul, Korea, Republic of
Duration: 2007 Mar 112007 Mar 15

Publication series

NameProceedings of the ACM Symposium on Applied Computing


Other2007 ACM Symposium on Applied Computing
Country/TerritoryKorea, Republic of


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

ASJC Scopus subject areas

  • Software


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