2005 International Conference on Analysis of Algorithms
Conrado Martínez (ed.)
DMTCS Conference Volume AD (2005), pp. 257266
author:  Pierre Nicodème 

title:  Average profiles, from tries to suffixtrees 
keywords:  tries, suffixtrees, profile, asymptotics, Mellin transform, saddlepoint method. 
abstract: 
We build upon previous work of [Fayj04]
and [ParSzp05] to study asymptotically the average
internal profile of tries and of suffixtrees. The binary
keys and the strings are built from a Bernoulli source
(p,q)
. We consider the average number
p_k,P(ν)
of internal nodes at depth
k
of a trie whose number of input keys follows a
Poisson law of parameter
ν
. The Mellin transform of the corresponding bivariate
generating function has a major singularity at the origin,
which implies a phase reversal for the saturation rate
p_k,P(ν)/2
as
k
k
reaches the value
2log(ν)/(log(1/p)+log(1/q))
. We prove that the asymptotic average profiles of
random tries and suffixtrees are mostly similar, up to
second order terms, a fact that has been experimentally
observed in [Nic03]; the proof follows from
comparisons to the profile of tries in the Poisson model.

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reference:  Pierre Nicodème (2005), Average profiles, from tries to suffixtrees, in 2005 International Conference on Analysis of Algorithms, Conrado Martínez (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AD, pp. 257266 
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