2005 International Conference on Analysis of Algorithms
Conrado Martínez (ed.)
DMTCS Conference Volume AD (2005), pp. 257-266
| author: | Pierre Nicodème |
|---|---|
| title: | Average profiles, from tries to suffix-trees |
| keywords: | tries, suffix-trees, profile, asymptotics, Mellin transform, saddle-point method. |
| abstract: |
We build upon previous work of [Fayj04]
and [ParSzp05] to study asymptotically the average
internal profile of tries and of suffix-trees. 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 suffix-trees 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 suffix-trees, in 2005 International Conference on Analysis of Algorithms, Conrado Martínez (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AD, pp. 257-266 |
| bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
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