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One-sided variations on interval trees

Part of: Limit theorems Graph theory

Published online by Cambridge University Press:  14 July 2016

Yoshiaki Itoh  and
Hosam M. Mahmoud
Yoshiaki Itoh*
Affiliation:
Institute of Statistical Mathematics, Tokyo
Hosam M. Mahmoud*
Affiliation:
George Washington University
*
∗Postal address: Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minatoku, Tokyo 106-8569, Japan. Email address: [email protected]
∗∗Postal address: Department of Statistics, George Washington University, Washington, DC 20052, USA
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Abstract

The binary interval tree is a random structure that underlies interval division and parking problems. Five incomplete one-sided variants of binary interval trees are considered, providing additional flavors and variations on the main applications. The size of each variant is studied, and a Gaussian tendency is proved in each case via an analytic approach. Differential equations on half scale and delayed differential equations arise and can be solved asymptotically by local expansions and Tauberian theorems. Unlike the binary case, in an incomplete interval tree the size determines most other parameters of interest, such as the height or the internal path length.

Keywords

Random graphtreelimit distributionhalf-scale differential equationdelayed differential equationTauberian theorem

MSC classification

Primary: 05C05: Trees 60F05: Central limit and other weak theorems
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 3 , September 2003 , pp. 654 - 670
Copyright
Copyright © Applied Probability Trust 2003 

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