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Distribution of the Steiner Distance in Generalized M-ary Search Trees

Published online by Cambridge University Press:  24 September 2004

ALOIS PANHOLZER
Affiliation:
Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Wiedner Hauptstraße 8–10, A-1040 Wien, Austria (e-mail: Alois.Panholzer@tuwien.ac.at)

Abstract

In this paper, we show for generalized $M$-ary search trees that the Steiner distance of $p$ randomly chosen nodes in random search trees is asymptotically normally distributed. The special case $p=2$ shows, in particular, that the distribution of the distance between two randomly chosen nodes is asymptotically Gaussian. In the presented generating functions approach, we consider first the size of the ancestor-tree of $p$ randomly chosen nodes. From the obtained Gaussian limiting distribution for this parameter, we deduce the result for the Steiner distance. Since the size of the ancestor-tree is essentially the same as the number of passes in the (generalized) Multiple Quickselect algorithm, the limiting distribution result also holds for this parameter.

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Paper
Copyright
© 2004 Cambridge University Press

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