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Teasing Apart Two Trees

Published online by Cambridge University Press:  01 November 2007

M. A. STEEL  and
L. A. SZÉKELY
M. A. STEEL
Affiliation:
Biomathematics Research Centre,Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand (e-mail: m.steel@math.canterbury.ac.nz)
L. A. SZÉKELY
Affiliation:
Department of Mathematics, University of South Carolina, Columbia SC, USA (e-mail: szekely@math.sc.edu)
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Abstract

A widely studied model for generating binary sequences is to ‘evolve’ them on a tree according to a symmetric Markov process. We show that under this model distinguishing the true (model) tree from a false one is substantially ‘easier’ (in terms of the sequence length needed) than determining the true tree. The key tool is a new and near-tight Ramsey-type result for binary trees.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 16 , Issue 6 , November 2007 , pp. 903 - 922
Copyright
Copyright © Cambridge University Press 2007

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