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Analysis of the average depth in a suffix tree under a Markov model

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 $(\log{n})/h + C$ 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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Julien Fayolle, Mark Daniel Ward. Analysis of the average depth in a suffix tree under a Markov model. 2005 International Conference on Analysis of Algorithms, 2005, Barcelona, Spain. pp.95-104. ⟨hal-01184043⟩

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