Julien Fayolle ; Mark Daniel Ward - Analysis of the average depth in a suffix tree under a Markov model

dmtcs:3371 - Discrete Mathematics & Theoretical Computer Science, January 1, 2005, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms - https://doi.org/10.46298/dmtcs.3371
Analysis of the average depth in a suffix tree under a Markov modelArticle

Authors: Julien Fayolle 1; Mark Daniel Ward 2

  • 1 Algorithms
  • 2 Department of mathematics Purdue University

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]).


Volume: DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms
Section: Proceedings
Published on: January 1, 2005
Imported on: May 10, 2017
Keywords: asymptotics,analytic methods,Suffix trees,depth,average analysis,[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG],[INFO.INFO-HC] Computer Science [cs]/Human-Computer Interaction [cs.HC]

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