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On Tail Bounds for Random Recursive Trees

Part of: Graph theory Distribution theory - Probability Combinatorial probability

Published online by Cambridge University Press:  04 February 2016

Götz Olaf Munsonius
Götz Olaf Munsonius*
Affiliation:
Goethe University Frankfurt
*
∗ Postal address: Institute of Mathematics, Goethe University Frankfurt, 60054 Frankfurt am Main, Germany. Email address: munsonius@math.uni-frankfurt.de
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Abstract

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We consider a multivariate distributional recursion of sum type, as arises in the probabilistic analysis of algorithms and random trees. We prove an upper tail bound for the solution using Chernoff's bounding technique by estimating the Laplace transform. The problem is traced back to the corresponding problem for binary search trees by stochastic domination. The result obtained is applied to the internal path length and Wiener index of random b-ary recursive trees with weighted edges and random linear recursive trees. Finally, lower tail bounds for the Wiener index of these trees are given.

Keywords

Random treeprobabilistic analysis of algorithmstail boundpath lengthWiener index

MSC classification

Primary: 60C05: Combinatorial probability 05C05: Trees 05C80: Random graphs 60E15: Inequalities; stochastic orderings
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 2 , June 2012 , pp. 566 - 581
Copyright
© Applied Probability Trust 

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