DMTCS Proceedings, 2005 International Conference on Analysis of Algorithms

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DMTCS Conference vol AD (2005), pp. 257-266


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
. We consider the average number
of internal nodes at depth
of a trie whose number of input keys follows a Poisson law of parameter
. 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
reaches the value
. 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
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