Digital search trees and chaos game representation - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue ESAIM: Probability and Statistics Année : 2009

Digital search trees and chaos game representation

Résumé

In this paper, we consider a possible representation of a DNA sequence in a quaternary tree, in which on can visualize repetitions of subwords. 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 and the insertion depth for DST built from i.i.d. successive sequences. Here, the successive inserted wors are strongly dependent. We give the asymptotic behaviour of the insertion depth and of the length of branches for the CGR-tree obtained from the suffixes of reversed i.i.d. or Markovian sequence. This behaviour turns out to be at first order the same one as in the case of independent words. As a by-product, asymptotic results on the length of longest runs in a Markovian sequence are obtained.
Fichier principal
Vignette du fichier
cgrDst.pdf (345.14 Ko) Télécharger le fichier
Loading...

Dates et versions

hal-00076896 , version 1 (29-05-2006)

Identifiants

Citer

Peggy Cénac, Brigitte Chauvin, Stéphane Ginouillac, Nicolas Pouyanne. Digital search trees and chaos game representation. ESAIM: Probability and Statistics, 2009, 13, pp.15-37. ⟨10.1051/ps:2007043⟩. ⟨hal-00076896⟩
190 Consultations
125 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More