Genomes Containing Duplicates Are Hard to Compare
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.
KeywordsSimilarity Measure Duplicate Gene Algorithmic Complexity Match Model Exemplar Model
- 1.Blin, G., Chauve, C., Fertin, G.: The breakpoint distance for signed sequences. In: 1st Int. Conference on Algorithms and Computational Methods for Biochemical and Evolutionary Networks, CompBioNets 2004. Texts in Algorithms, vol. 3, pp. 3–16. KCL Publications (2004)Google Scholar
- 3.Bryant, D.: The complexity of calculating exemplar distances. In: Sankoff, D., Nadeau, J. (eds.) Comparative Genomics: Empirical and Analytical Approaches to Gene Order Dynamics, Map Alignment, and the Evolution of Gene Families, pp. 207–212. Kluwer Acad. Pub., Dordrecht (2000)Google Scholar
- 9.Cam Thach, N.: Algorithms for calculating exemplar distances. Honours Year Project Report, National University of Singapore (2005)Google Scholar