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Evolutionary Bioinformatics

A Reduction Algorithm for Computing The Hybridization Number of Two Trees

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Evolutionary Bioinformatics 2007:3 86-98

Published on 30 May 2007


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Magnus Bordewich1, Simone Linz2,3, Katherine St. John4 and Charles Semple2

1Department of Computer Science, Durham University, Durham DH1 3LE, United Kingdom 2Biomathematics Research Centre, Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand 3Department of Bioinformatics, Heinrich-Heine-University, Düsseldorf, Germany 4Department of Mathematics and Computer Science, Lehman College, City University of New York, USA

Abstract: Hybridization is an important evolutionary process for many groups of species. Thus, conflicting signals in a data set may not be the result of sampling or modeling errors, but due to the fact that hybridization has played a significant role in the evolutionary history of the species under consideration. Assuming that the initial set of gene trees is correct, a basic problem for biologists is to compute this minimum number of hybridization events to explain this set. In this paper, we describe a new reduction-based algorithm for computing the minimum number, when the initial data set consists of two trees. Although the two-tree problem is NP-hard, our algorithm always gives the exact solution and runs efficiently on many real biological problems. Previous algorithms for the two-tree problem either solve a restricted version of the problem or give an answer with no guarantee of the closeness to the exact solution. We illustrate our algorithm on a grass data set. This new algorithm is freely available for application at either http://www.bi.uni-duesseldorf.de/~linz or http://www.math.canterbury.ac.nz/~cas83.



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