| 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]).
|
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| 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. |
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