The Annals of Applied Probability

Search trees: Metric aspects and strong limit theorems

Rudolf Grübel

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Abstract

We consider random binary trees that appear as the output of certain standard algorithms for sorting and searching if the input is random. We introduce the subtree size metric on search trees and show that the resulting metric spaces converge with probability 1. This is then used to obtain almost sure convergence for various tree functionals, together with representations of the respective limit random variables as functions of the limit tree.

Article information

Source
Ann. Appl. Probab., Volume 24, Number 3 (2014), 1269-1297.

Dates
First available in Project Euclid: 23 April 2014

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1398258101

Digital Object Identifier
doi:10.1214/13-AAP948

Mathematical Reviews number (MathSciNet)
MR3199986

Zentralblatt MATH identifier
1294.60009

Subjects
Primary: 60B99: None of the above, but in this section
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 68Q25: Analysis of algorithms and problem complexity [See also 68W40] 05C05: Trees

Keywords
Doob–Martin compactification metric trees path length silhouette subtree size metric vector-valued martingales Wiener index

Citation

Grübel, Rudolf. Search trees: Metric aspects and strong limit theorems. Ann. Appl. Probab. 24 (2014), no. 3, 1269--1297. doi:10.1214/13-AAP948. https://projecteuclid.org/euclid.aoap/1398258101


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