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Profiles of random trees: correlation and width of random recursive trees and binary search trees

Part of: Linear inference, regression Combinatorial probability Graph theory

Published online by Cambridge University Press:  01 July 2016

Michael Drmota  and
Hsien-Kuei Hwang
Michael Drmota*
Affiliation:
Technische Universität Wien
Hsien-Kuei Hwang*
Affiliation:
Academia Sinica
*
∗ Postal address: Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Wiedner Hauptstrasse 8-10/118, 1040 Wien, Austria.
∗∗ Postal address: Institute of Statistical Science, Academia Sinica, Taipei, 115, Taiwan. Email address: hkhwang@stat.sinica.edu.tw
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Abstract

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In a tree, a level consists of all those nodes that are the same distance from the root. We derive asymptotic approximations to the correlation coefficients of two level sizes in random recursive trees and binary search trees. These coefficients undergo sharp sign-changes when one level is fixed and the other is varying. We also propose a new means of deriving an asymptotic estimate for the expected width, which is the number of nodes at the most abundant level. Crucial to our methods of proof is the uniformity achieved by singularity analysis.

Keywords

Correlation coefficientrandom recursive treerandom binary search treewidthtotal path lengthsign-change

MSC classification

Primary: 60C05: Combinatorial probability
Secondary: 62J10: Analysis of variance and covariance 05C05: Trees
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 37 , Issue 2 , June 2005 , pp. 321 - 341
Copyright
Copyright © Applied Probability Trust 2005 

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