Dependence between External Path-Length and Size in Random Tries
Combinatorics
2016-05-09 v2 Discrete Mathematics
Probability
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 that the internal path length is totally positively correlated to the size and that both tend to the same normal limit law. These two examples provide concrete instances of bivariate normal distributions (as limit laws) whose correlation is , and periodically oscillating.
Keywords
Cite
@article{arxiv.1604.08658,
title = {Dependence between External Path-Length and Size in Random Tries},
author = {Michael Fuchs and Hsien-Kuei Hwang},
journal= {arXiv preprint arXiv:1604.08658},
year = {2016}
}
Comments
To appear in Proceedings of the 27th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, Krakow, Poland, 4-8 July, 2016