DMTCS

2005 International Conference on Analysis of Algorithms

Conrado Martínez (ed.)

DMTCS Conference Volume AD (2005), pp. 95-104


author: Julien Fayolle and Mark Daniel Ward
title: Analysis of the average depth in a suffix tree under a Markov model
keywords: Suffix trees, depth, average analysis, asymptotics, analytic methods
abstract: In this report, we prove that under a Markovian model of order one, the average depth of suffix trees of index
n
is asymptotically similar to the average depth of tries (a.k.a. digital trees) built on
n
independent strings. This leads to an asymptotic behavior of
(logn)/h + C
for the average of the depth of the suffix tree, where
h
is the entropy of the Markov model and
C
is constant. Our proof compares the generating functions for the average depth in tries and in suffix trees; the difference between these generating functions is shown to be asymptotically small. We conclude by using the asymptotic behavior of the average depth in a trie under the Markov model found by Jacquet and Szpankowski ([JaSz91]).
  If your browser does not display the abstract correctly (because of the different mathematical symbols) you may look it up in the PostScript or PDF files.
reference: Julien Fayolle and Mark Daniel Ward (2005), Analysis of the average depth in a suffix tree under a Markov model, in 2005 International Conference on Analysis of Algorithms, Conrado Martínez (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AD, pp. 95-104
bibtex: For a corresponding BibTeX entry, please consider our BibTeX-file.
ps.gz-source: dmAD0109.ps.gz (103 K)
ps-source: dmAD0109.ps (251 K)
pdf-source: dmAD0109.pdf (140 K)

The first source gives you the `gzipped' PostScript, the second the plain PostScript and the third the format for the Adobe accrobat reader. Depending on the installation of your web browser, at least one of these should (after some amount of time) pop up a window for you that shows the full article. If this is not the case, you should contact your system administrator to install your browser correctly.

Due to limitations of your local software, the two formats may show up differently on your screen. If eg you use xpdf to visualize pdf, some of the graphics in the file may not come across. On the other hand, pdf has a capacity of giving links to sections, bibliography and external references that will not appear with PostScript.


Automatically produced on Di Sep 27 10:09:29 CEST 2005 by gustedt