François Nicolas

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Given a set of evolutionary trees on a same set of taxa, the maximum agreement subtree problem (MAST), respectively, maximum compatible tree problem (MCT), consists of finding a largest subset of taxa such that all input trees restricted to these taxa are isomorphic, respectively compatible. These problems have several applications in phylogenetics such as(More)
Given a set of leaf-labelled trees with identical leaf sets, the well-known MAST problem consists of finding a subtree homeomorphi-cally included in all input trees and with the largest number of leaves. MAST and its variant called MCT are of particular interest in computational biology. This paper presents positive and negative results on the approximation(More)
Given a finite set of strings, the MEDIAN STRING problem consists in finding a string that minimizes the sum of the edit distances to the strings in the set. Approximations of the median string are used in a very broad range of applications where one needs a representative string that summarizes common information to the strings of the set. It is the case(More)
In metabolomics and other fields dealing with small compounds, mass spectrometry is applied as a sensitive high-throughput technique. Recently, fragmentation trees have been proposed to automatically analyze the fragmentation mass spectra recorded by such instruments. Computationally, this leads to the problem of finding a maximum weight subtree in an(More)
BACKGROUND Variable minisatellites count among the most polymorphic markers of eukaryotic and prokaryotic genomes. This variability can affect gene coding regions, like in the prion protein gene, or gene regulation regions, like for the cystatin B gene, and be associated or implicated in diseases: the Creutzfeld-Jakob disease and the myoclonus epilepsy type(More)
A pure morphic sequence is a right-infinite, symbolic sequence obtained by iterating a letter-to-word substitution. For instance, the Fibonacci sequence and the Thue–Morse sequence, which play an important role in theoretical computer science, are pure morphic. Define a coding as a letter-to-letter substitution. The image of a pure morphic sequence under a(More)