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Digital Search Trees and Chaos Game Representation

Abstract : In this paper, we consider a possible representation of a DNA sequence in a quaternary tree, in which one can visualize repetitions of subwords (seen as suffixes of subsequences) The CGR-tree turns a sequence of letters into a Digital Search Tree (DST), obtained from the suffixes of the reversed sequence Several results are known concerning the height, the insertion depth for DST built from independent successive random sequences having the same distribution Here the successive inserted words are strongly dependent We give the asymptotic behaviour of the insertion depth and length of branches for the CGR-tree obtained from the suffixes of a reversed i.i.d. or Markovian sequence As a by-product, asymptotic results on the length of longest runs in a Markovian sequence are obtained
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Contributor : Rapport de Recherche Inria <>
Submitted on : Friday, May 19, 2006 - 7:19:02 PM
Last modification on : Thursday, November 15, 2018 - 11:53:37 AM
Long-term archiving on: : Sunday, April 4, 2010 - 8:23:34 PM


  • HAL Id : inria-00070170, version 1



Peggy Cénac, Brigitte Chauvin, Stéphane Ginouillac, Nicolas Pouyanne. Digital Search Trees and Chaos Game Representation. [Research Report] RR-5856, INRIA. 2006, pp.27. ⟨inria-00070170⟩



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