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Limit distributions for multitype branching processes of m -ary search trees

Brigitte Chauvin;  Quansheng Liu;  Nicolas Pouyanne — 2014

Annales de l'I.H.P. Probabilités et statistiques

Let m ≥ 3 be an integer. The so-calledis a discrete time Markov chain which is very popular in theoretical computer science, modelling famous algorithms used in searching and sorting. This random process satisfies a well-known phase transition: when m ≤ 26 , the asymptotic behavior of the process is Gaussian, but for m ≥ 27 it is no longer Gaussian and a limit W D T of a complex-valued martingale arises. In this paper, we consider the multitype branching process which is the continuous time version of the m -ary search...

Digital search trees and chaos game representation

Peggy Cénac;  Brigitte Chauvin;  Stéphane Ginouillac;  Nicolas Pouyanne — 2009

ESAIM: Probability and Statistics

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...

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