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Dependence between path-length and size in random digital trees

Published online by Cambridge University Press:  30 November 2017

Michael Fuchs
Affiliation:
National Chiao Tung University
Hsien-Kuei Hwang
Affiliation:
Academia Sinica
Corresponding
E-mail address:

Abstract

We study the size and the external path length of random tries and show that they are asymptotically independent in the asymmetric case but strongly dependent with small periodic fluctuations in the symmetric case. Such an unexpected behavior is in sharp contrast to the previously known results on random tries, that the size is totally positively correlated to the internal path length and that both tend to the same normal limit law. These two dependence examples provide concrete instances of bivariate normal distributions (as limit laws) whose components have correlation either zero or one or periodically oscillating. Moreover, the same type of behavior is also clarified for other classes of digital trees such as bucket digital trees and Patricia tries.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2017 

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