On the Approximability of Comparing Genomes with Duplicates

Abstract : A central problem in comparative genomics consists in computing a (dis-)similarity measure between two genomes. A large number of such measures has been proposed in the recent past: breakpoints, common intervals, SAD etc. In their initial definitions, all these measures suppose that genomes contain no duplicates. However, we now know that genes can be duplicated within the same genome. One possible approach to overcome this difficulty is to establish a matching between genes of both genomes in order to optimize the studied measure. Then, after a gene relabeling according to this matching and a deletion of the unmatched signed genes, two genomes without duplicates are obtained and the measure can be computed. In this paper, we are interested in three measures (number of breakpoints, common intervals or conserved intervals) and three models of matching (exemplar, maximum and non-maximum matching). We prove that, for each model and each measure, computing a matching between two genomes that optimizes the measure is APX-Hard. We show that this result remains true even for two genomes G1 and G2 such that G1 contains no duplicates and no gene of G2 appears more than twice. Finally, we propose a 4-approximation algorithm for a fourth measure, the number of adjacencies, under the maximum matching model, in the case where genomes contain the same number of duplications of each gene.
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Pré-publication, Document de travail
Rapport de recherche. 2007
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Sébastien Angibaud, Guillaume Fertin, Irena Rusu. On the Approximability of Comparing Genomes with Duplicates. Rapport de recherche. 2007. 〈hal-00159893〉

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