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On the Subtree Size Profile of Binary Search trees

Published online by Cambridge University Press:  22 January 2010

FLORIAN DENNERT  and
RUDOLF GRÜBEL
FLORIAN DENNERT
Affiliation:
Institut für Mathematische Stochastik, Leibniz Universität Hannover, Postfach 6009, D-30060 Hannover, Germany (e-mail: dennert@stochastik.uni-hannover.de, rgrubel@stochastik.uni-hannover.de)
RUDOLF GRÜBEL
Affiliation:
Institut für Mathematische Stochastik, Leibniz Universität Hannover, Postfach 6009, D-30060 Hannover, Germany (e-mail: dennert@stochastik.uni-hannover.de, rgrubel@stochastik.uni-hannover.de)
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Abstract

For random trees T generated by the binary search tree algorithm from uniformly distributed input we consider the subtree size profile, which maps k ∈ ℕ to the number of nodes in T that root a subtree of size k. Complementing earlier work by Devroye, by Feng, Mahmoud and Panholzer, and by Fuchs, we obtain results for the range of small k-values and the range of k-values proportional to the size n of T. In both cases emphasis is on the process view, i.e., the joint distributions for several k-values. We also show that the dynamics of the tree sequence lead to a qualitative difference between the asymptotic behaviour of the lower and the upper end of the profile.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 19 , Issue 4 , July 2010 , pp. 561 - 578
Copyright
Copyright © Cambridge University Press 2010

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