TY - GEN

T1 - Eigen-distribution on assignments for game trees with random properties

AU - Liu, Chenguang

AU - Tanaka, Kazuyuki

PY - 2007/1/1

Y1 - 2007/1/1

N2 - 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.

AB - 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.

KW - Computational complexity

KW - Distributional complexity

KW - Eigen-distribution

KW - Game trees

KW - Randomized algorithms

UR - http://www.scopus.com/inward/record.url?scp=35248827561&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35248827561&partnerID=8YFLogxK

U2 - 10.1145/1244002.1244020

DO - 10.1145/1244002.1244020

M3 - Conference contribution

AN - SCOPUS:35248827561

SN - 1595934804

SN - 9781595934802

T3 - Proceedings of the ACM Symposium on Applied Computing

SP - 78

EP - 79

BT - Proceedings of the 2007 ACM Symposium on Applied Computing

PB - Association for Computing Machinery

T2 - 2007 ACM Symposium on Applied Computing

Y2 - 11 March 2007 through 15 March 2007

ER -