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Issue No.03 - July-September (2008 vol.5)
pp: 332-347
Matthias Bernt , University of Leipzig, Leipzig
Martin Middendorf , University of Leipzig, Leipzig
ABSTRACT
Genomic rearrangement operations can be very useful to infer the phylogenetic relationship of gene orders representing species. We study the problem of finding potential ancestral gene orders for the gene orders of given taxa, such that the corresponding rearrangement scenario has a minimal number of reversals, and where each of the reversals has to preserve the common intervals of the given input gene orders. Common intervals identify sets of genes that occur consecutively in all input gene orders. The problem of finding such an ancestral gene order is called the preserving reversal median problem (pRMP). A tree-based data structure for the representation of the common intervals of all input gene orders is used in our exact algorithm TCIP for solving the pRMP. It is known that the minimum number of reversals to transform one gene order into another can be computed in polynomial time, whereas the corresponding problem with the restriction that common intervals should not be destroyed is already NP-hard. It is shown theoretically that TCIP can solve a large class of pRMP instances in polynomial time. Empirically we show the good performance of TCIP on biological and artificial data.
INDEX TERMS
Biology and genetics, Permutations and combinations
CITATION
Matthias Bernt, Martin Middendorf, "Solving the Preserving Reversal Median Problem", IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol.5, no. 3, pp. 332-347, July-September 2008, doi:10.1109/TCBB.2008.39
REFERENCES
[1] G. Bourque and P.A. Pevzner, “Genome-Scale Evolution: Reconstructing Gene Orders in the Ancestral Species,” Genome Research, vol. 12, no. 1, pp. 26-36, 2002.
[2] B. Moret, A. Siepel, J. Tang, and T. Liu, “Inversion Medians Outperform Breakpoint Medians in Phylogeny Reconstruction from Gene-Order Data,” Proc. Second Int'l Workshop Algorithms in Bioinformatics (WABI '02), pp. 521-536, 2002.
[3] B. Moret, J. Tang, and T. Warnow, Mathematics of Evolution and Phylogeny, ch. Reconstructing Phylogenies from Gene-Content and Gene-Order Data, pp. 321-352, Oxford Univ. Press, 2005.
[4] M. Bernt, D. Merkle, and M. Middendorf, “Using Median Sets for Inferring Phylogenetic Trees,” Bioinformatics, vol. 23, no. 2, pp.e129-e135, 2007.
[5] A. Bergeron and J. Stoye, “On the Similarity of Sets of Permutations and Its Applications to Genome Comparison,” J.Computational Biology, vol. 13, no. 7, pp. 1345-1354, 2006.
[6] T. Uno and M. Yagiura, “Fast Algorithms to Enumerate All Common Intervals of Two Permutations,” Algorithmica, vol. 2, no. 26, pp. 290-309, 2000.
[7] S. Heber and J. Stoye, “Finding All Common Intervals of $k$ Permutations,” Proc. 12th Ann. Symp. Combinatorial Pattern Matching (CPM '01), pp. 207-218, 2001.
[8] G. Didier, “Common Intervals of Two Sequences,” Proc. Third Int'l Workshop Algorithms in Bioinformatics (WABI '03), pp. 17-24, 2003.
[9] T. Schmidt and J. Stoye, “Quadratic Time Algorithms for Finding Common Intervals in Two and More Sequences,” Proc. 15th Ann. Symp. Combinatorial Pattern Matching (CPM '04), pp. 347-358, 2004.
[10] A. Bergeron, M. Blanchette, A. Chateau, and C. Chauve, “Reconstructing Ancestral Gene Orders Using Conserved Intervals,” Proc. Fourth Int'l Workshop Algorithms in Bioinformatics (WABI '04), pp. 14-25, 2004.
[11] M. Bernt, D. Merkle, and M. Middendorf, “Genome Rearrangement Based on Reversals that Preserve Conserved Intervals,” IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 3, no. 3, pp. 275-288, July-Sept. 2006.
[12] S. Bérard, A. Bergeron, and C. Chauve, “Conservation of Combinatorial Structures in Evolution Scenarios,” Proc. Second RECOMB Comparative Genomics Satellite Workshop (RCG '04), pp. 1-15, 2004.
[13] M. Bernt, D. Merkle, and M. Middendorf, “The Reversal Median Problem, Common Intervals, and Mitochondrial Gene Orders,” Computational Life Sciences II—Proc. Second Int'l Symp. CompLife, pp. 52-63, 2006.
[14] Y. Diekmann, M.-F. Sagot, and E. Tannier, “Evolution under Reversals: Parsimony and Conservation of Common Intervals,” IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 4, pp. 301-309, 2007.
[15] M. Figeac and J. Varré, “Sorting by Reversals with Common Intervals,” Proc. Fourth Int'l Workshop Algorithms in Bioinformatics (WABI '04), pp. 26-37, 2004.
[16] S. Hannenhalli and P. Pevzner, “Transforming Cabbage into Turnip: Polynomial Algorithm for Sorting Signed Permutations by Reversals,” Proc. 27th Ann. ACM Symp. Theory of Computing (STOC '95), pp. 178-189, 1995.
[17] A. Bergeron, J. Mixtacki, and J. Stoye, “Reversal Distance without Hurdles and Fortresses,” Proc. 15th Ann. Symp. Combinatorial Pattern Matching (CPM '04), pp. 388-399, 2004.
[18] E. Tannier, A. Bergeron, and M.-F. Sagot, “Advances in Sorting by Reversals,” Discrete Applied Math., vol. 155, no. 6-7, p. 888, 2006.
[19] A. Caprara, “The Reversal Median Problem,” INFORMS J. Computing, vol. 15, no. 1, pp. 93-113, 2003.
[20] A. Siepel and B. Moret, “Finding an Optimal Inversion Median: Experimental Results,” Proc. First Int'l Workshop Algorithms in Bioinformatics (WABI '01), pp. 189-203, 2001.
[21] M. Bernt, D. Merkle, and M. Middendorf, “A Parallel Algorithm for Solving the Reversal Median Problem,” Proc. Parallel Processing and Applied Math.-Bio-Computing Workshop (PBC '05), pp. 1089-1096, 2005.
[22] S. Bérard, A. Bergeron, C. Chauve, and C. Paul, “Perfect Sorting by Reversals Is Not Always Difficult,” IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 4, no. 1, pp. 4-16, Jan. 2007.
[23] R. Eres, G.M. Landau, and L. Parida, “A Combinatorial Approach to Automatic Discovery of Cluster-Patterns,” Proc. Third Int'l Workshop Algorithms in Bioinformatics (WABI '03), pp. 139-150, 2003.
[24] A. Bergeron, C. Chauve, F. de Montgolfier, and M. Raffinot, “Computing Common Intervals of $K$ Permutations, with Applications to Modular Decomposition of Graphs,” Proc. 13th Ann. European Symp. Algorithms (ESA '05), pp. 779-790, 2005.
[25] A. Bergeron, C. Chauve, F. de Montgolfier, and M. Raffinot, “Computing Common Intervals of $K$ Permutations, with Applications to Modular Decomposition of Graphs,” SIAM J. Discrete Math., to appear.
[26] J. Boore, Mitochondrial Gene Arrangement Database, www.hapmap.orghttp://dx.doi.org/10.1038/ nature04072http://dx.doi.org/10.1038/nature04338http:/ evogen.jgi.doe.gov/, 2006.
[27] M. Cosner, R. Jansen, B. Moret, L. Raubeson, L.-S. Wang, T. Warnow, and S. Wyman, “An Empirical Comparison of Phylogenetic Methods on Chloroplast Gene Order Data in Campanulaceae,” Comparative Genomics: Empirical and Analytical Approaches to Gene Order Dynamics, Map Alignment, and the Evolution of Gene Families, pp. 99-121, Kluwer Academic Publishers, 2000.
[28] D. Bader, B. Moret, and M. Yan, “A Linear-Time Algorithm for Computing Inversion Distance between Signed Permutations with an Experimental Study,” J. Computational Biology, vol. 5, no. 8, pp.483-491, 2001.
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