Structural complexity of random binary trees

Authors:
J. C. Kieffer;E-H. Yang;W. Szpankowski
Affiliations:
ECE Department, University of Minnesota, Minneapolis, MN;ECE Department, University of Waterloo, Waterloo, Ontario, CA;Computer Science Department, Purdue University, West Lafayette, IN
Venue:
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Year:
2009

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Abstract

For each positive integer n, let Tn be a random rooted full binary tree having 2n-1 vertices. We can view H(Tn), the entropy of Tn as a measure of the structural complexity of tree Tn in the sense that approximately H(Tn) bits suffice to construct Tn. We analyze some random binary tree sequences (Tn: n = 1,2,...) for which the normalized entropies H(Tn)/n converge to a limit as n → ∞, as well as some other sequences (Tn) in which the normalized entropies fail to converge.