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Dichotomic Selection on Words: A Probabilistic Analysis

Ali Akhavi 1 Julien Clément 1 Dimitri Darthenay 1 Loïck Lhote 1 Brigitte Vallée 1
1 Equipe AMACC - Laboratoire GREYC - UMR6072
GREYC - Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen
Abstract : The paper studies the behaviour of selection algorithms that are based on dichotomy principles. On the entry formed by an ordered list L and a searched element x ∈ L, they return the interval of the list L the element x belongs to. We focus here on the case of words, where dichotomy principles lead to a selection algorithm designed by Crochemore, Hancart and Lecroq, which appears to be "quasi-optimal". We perform a probabilistic analysis of this algorithm that exhibits its quasi-optimality on average.
Keywords : coincidence dichotomic selection text algorithms analysis of algorithms average case analysis of algorithms trie suffix array lcp-array information theory depoissonization techniques analytic combinatorics numeration process entropy sources
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Submitted on : Tuesday, June 11, 2019 - 3:11:14 PM
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Ali Akhavi, Julien Clément, Dimitri Darthenay, Loïck Lhote, Brigitte Vallée. Dichotomic Selection on Words: A Probabilistic Analysis. 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019), Jun 2019, Pisa, Italy. pp.19:1-19:19, ⟨10.4230/LIPIcs.CPM.2019.19⟩. ⟨hal-02152162⟩

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