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Average-Case Analysis of Cousins in m-ary Tries

Part of: Graph theory Theory of data Combinatorial probability

Published online by Cambridge University Press:  14 July 2016

Hosam M. Mahmoud  and
Mark Daniel Ward
Hosam M. Mahmoud*
Affiliation:
The George Washington University
Mark Daniel Ward*
Affiliation:
Purdue University
*
∗Postal address: Department of Statistics, The George Washington University, 2140 Pennsylvania Avenue NW, Washington, DC 20052, USA. Email address: hosam@gwu.edu
∗∗Postal address: Department of Statistics, Purdue University, 150 North University Street, West Lafayette, IN 47907-1451, USA. Email address: mdw@purdue.edu
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Abstract

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We investigate the average similarity of random strings as captured by the average number of ‘cousins’ in the underlying tree structures. Analytical techniques including poissonization and the Mellin transform are used for accurate calculation of the mean. The string alphabets we consider are m-ary, and the corresponding trees are m-ary trees. Certain analytic issues arise in the m-ary case that do not have an analog in the binary case.

Keywords

Analysis of algorithmsrandom treerecurrenceMellin transformpoissonizationcombinatorics on wordssimilarity of strings

MSC classification

Secondary: 05C05: Trees 60C05: Combinatorial probability 68P05: Data structures 68P10: Searching and sorting 68P20: Information storage and retrieval
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 3 , September 2008 , pp. 888 - 900
Copyright
Copyright © Applied Probability Trust 2008 

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