TY - JOUR

T1 - Eigen-distribution on random assignments for game trees

AU - Liu, Chen Guang

AU - Tanaka, Kazuyuki

N1 - Funding Information:
This work is partially supported by the Grant-in-Aid for special research of the 21st century Center of Excellence (COE) program “Exploring new Science by Bridging Particle-Matter Hierarchy” from Ministry of Education, Culture, Sports, Science and Technology.

PY - 2007/10/16

Y1 - 2007/10/16

N2 - 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.

AB - 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.

KW - Computational complexity

KW - Distributional complexity

KW - Eigen-distribution

KW - Game tree

KW - Randomized algorithms

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U2 - 10.1016/j.ipl.2007.05.008

DO - 10.1016/j.ipl.2007.05.008

M3 - Article

AN - SCOPUS:34447643023

VL - 104

SP - 73

EP - 77

JO - Information Processing Letters

JF - Information Processing Letters

SN - 0020-0190

IS - 2

ER -