Abstract
In this paper, we are interested in the algorithmic complexity of computing (dis)similarity measures between two genomes when they contain duplicated genes. In that case, there are usually two main ways to compute a given (dis)similarity measure M between two genomes G 1 and G 2: the first model, that we will call the matching model, consists in computing a one-to-one correspondence between genes of G 1 and genes of G 2, in such a way that M is optimized in the resulting permutation. The second model, called the exemplar model, consists in keeping in G 1 (resp. G 2) exactly one copy of each gene, thus deleting all the other copies, in such a way that M is optimized in the resulting permutation. We present here different results concerning the algorithmic complexity of computing three different similarity measures (number of common intervals, MAD number and SAD number) in those two models, basically showing that the problem becomes NP-completeness for each of them as soon as genomes contain duplicates. In the case of MAD and SAD, we actually prove that, under both models, both MAD and SAD problems are APX-hard.
Work partially supported by the French-Italian Galileo Project PAI 08484VH and the French-Québec 60th CPCFQ.
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Chauve, C., Fertin, G., Rizzi, R., Vialette, S. (2006). Genomes Containing Duplicates Are Hard to Compare. In: Alexandrov, V.N., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds) Computational Science – ICCS 2006. ICCS 2006. Lecture Notes in Computer Science, vol 3992. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11758525_105
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DOI: https://doi.org/10.1007/11758525_105
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