The uniqueness of eigen-distribution under non-directional algorithms

Weiguang Peng; Shohei Okisaka; Wenjuan Li; Kazuyuki Tanaka

The uniqueness of eigen-distribution under non-directional algorithms

Weiguang Peng, Shohei Okisaka, Wenjuan Li, Kazuyuki Tanaka

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

Liu and Tanaka (2007) investigated the eigendistribution, which achieves the distributional complexity, for uniform binary trees. In the present work, we extend their studies to balanced multi-branching trees. We show that an eigen-distibution is equivalent to Eⁱ-distribution with respect to the closed set of all alpha-beta pruning algorithms. The proof is quite different from the uniform binary case given by Suzuki and Nakamura (2012). We also show that for any multibranching tree, Eⁱ-distribution is the unique eigen-distribution with respect to the set of all alpha-beta pruning algorithms.

Original language	English
Pages (from-to)	318-325
Number of pages	8
Journal	IAENG International Journal of Computer Science
Volume	43
Issue number	3
Publication status	Published - 2016

Keywords

AND-OR trees
Alpha-beta pruning algorithms
Balanced trees
Randomized complexity
Uniform trees

ASJC Scopus subject areas

Computer Science(all)

Cite this

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title = "The uniqueness of eigen-distribution under non-directional algorithms",

abstract = "Liu and Tanaka (2007) investigated the eigendistribution, which achieves the distributional complexity, for uniform binary trees. In the present work, we extend their studies to balanced multi-branching trees. We show that an eigen-distibution is equivalent to Ei-distribution with respect to the closed set of all alpha-beta pruning algorithms. The proof is quite different from the uniform binary case given by Suzuki and Nakamura (2012). We also show that for any multibranching tree, Ei-distribution is the unique eigen-distribution with respect to the set of all alpha-beta pruning algorithms.",

keywords = "AND-OR trees, Alpha-beta pruning algorithms, Balanced trees, Randomized complexity, Uniform trees",

author = "Weiguang Peng and Shohei Okisaka and Wenjuan Li and Kazuyuki Tanaka",

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AU - Peng, Weiguang

AU - Okisaka, Shohei

AU - Li, Wenjuan

AU - Tanaka, Kazuyuki

N1 - Funding Information: Manuscript received July 5, 2016. This work was supported in part by the JSPS KAKENHI Grant Number JP26540001 and JP15H03634.

PY - 2016

Y1 - 2016

N2 - Liu and Tanaka (2007) investigated the eigendistribution, which achieves the distributional complexity, for uniform binary trees. In the present work, we extend their studies to balanced multi-branching trees. We show that an eigen-distibution is equivalent to Ei-distribution with respect to the closed set of all alpha-beta pruning algorithms. The proof is quite different from the uniform binary case given by Suzuki and Nakamura (2012). We also show that for any multibranching tree, Ei-distribution is the unique eigen-distribution with respect to the set of all alpha-beta pruning algorithms.

AB - Liu and Tanaka (2007) investigated the eigendistribution, which achieves the distributional complexity, for uniform binary trees. In the present work, we extend their studies to balanced multi-branching trees. We show that an eigen-distibution is equivalent to Ei-distribution with respect to the closed set of all alpha-beta pruning algorithms. The proof is quite different from the uniform binary case given by Suzuki and Nakamura (2012). We also show that for any multibranching tree, Ei-distribution is the unique eigen-distribution with respect to the set of all alpha-beta pruning algorithms.

KW - AND-OR trees

KW - Alpha-beta pruning algorithms

KW - Balanced trees

KW - Randomized complexity

KW - Uniform trees

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The uniqueness of eigen-distribution under non-directional algorithms

Abstract

Keywords

ASJC Scopus subject areas

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