2005 International Conference on Analysis of Algorithms
Conrado Martínez (ed.)
DMTCS Conference Volume AD (2005), pp. 95104
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. 95104 
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