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Multiway Trees of Maximum and Minimum Probability under the Random Permutation Model

Published online by Cambridge University Press:  12 September 2008

Robert P. Dobrow  and
James Allen Fill
Robert P. Dobrow
Affiliation:
Division of Mathematics and Computer Science, Truman State University, Kirksville, MO 63501, USA (e-mail: bdobrow@mathax.truman.edu)
James Allen Fill
Affiliation:
Department of Mathematical Sciences, The Johns Hopkins University, Baltimore, MD 21218-2692, USA (e-mail: jimfill@jhu.edu)
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Abstract

Multiway trees, also known as m–ary search trees, are data structures generalising binary search trees. A common probability model for analysing the behaviour of these structures is the random permutation model. The probability mass function Q on the set of m–ary search trees under the random permutation model is the distribution induced by sequentially inserting the records of a uniformly random permutation into an initially empty m–ary search tree. We study some basic properties of the functional Q, which serves as a measure of the ‘shape’ of the tree. In particular, we determine exact and asymptotic expressions for the maximum and minimum values of Q and identify and count the trees achieving those values.

Information

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 5 , Issue 4 , December 1996 , pp. 351 - 371
Copyright
Copyright © Cambridge University Press 1996

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