The Reversal Median Problem, Common Intervals, and Mitochondrial Gene Orders
An important problem for phylogenetic investigations that are based on gene orders is to find for three given gene orders a fourth gene order that has a minimum sum of reversal distances to the three given gene orders. This problem is called Reversal Median problem (RMP). The RMP is studied here under the constraint that common (combinatorial) structures are preserved which are modeled as common intervals. An existing branch-and-bound algorithm for RMP is extended here so that it can solve the RMP with common intervals optimally. This algorithm is applied to mitochondrial gene order data for different animal taxa. It is shown that common intervals occur often for most taxa and that many common intervals are destroyed when the RMP is solved optimally with standard methods that do not consider common intervals.
KeywordsGene Order Test Instance Dynamic Constraint Animal Taxon Common Interval
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- 4.Sankoff, D.: Edit distance for genome comparison based on non-local operations. In: Apostolico, A., Galil, Z., Manber, U., Crochemore, M. (eds.) CPM 1992. LNCS, vol. 644, pp. 121–135. Springer, Heidelberg (1992)Google Scholar
- 7.Moret, B.M.E., Tang, J., Warnow, T.: Reconstructing phylogenies from gene-content and gene-order data. Mathematics of Evolution and Phylogeny. In: Gascuel, O. (ed.), pp. 321–352. Oxford University Press, Oxford (2004)Google Scholar
- 8.Bourque, G., Pevzner, P.A.: Genome-Scale Evolution: Reconstructing Gene Orders in the Ancestral Species. Genome Res. 12(1), 26–36 (2002)Google Scholar
- 9.Blanchette, M., Bourque, G., Sankoff, D.: Breakpoint phylogenies. Genome Informatics, 25–34 (1997)Google Scholar
- 11.Bernt, M., Merkle, D., Middendorf, M.: Genome Rearrangement Based on Reversals that Preserve Conserved Intervals. IEEE/ACM Transactions on Computational Biology and Bioinformatics (to appear)Google Scholar
- 15.Hannenhalli, S., Pevzner, P.: Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals. In: Proc. 27th Ann. ACM Symp. on Theory of Comput., pp. 178–189 (1995)Google Scholar
- 16.Boore, J.L.: Mitochondrial database (2005), http://evogen.jgi.doe.gov/