Abstract
Studying rearrangements from gene order data is a standard approach in evolutionary analysis. Gene order data are usually modeled as signed permutations. The computation of the minimal number of reversals between two signed permutations produced a lot of literature during the last decade. Algorithms designed were first approximative, then polynomial and were further improved to give a linear one. Several extensions were investigated authorizing for example deletion or insertion of genes during the sorting process. We propose to revisit the ’sorting by reversals’ problem by adding constraints on allowed reversals. We do not allow to break conserved clusters of genes usually called Common Intervals. We show that this problem is NP-complete. Assuming special conditions, we propose a polynomial algorithm.
Omitted proofs are given as supplementary material at http://www.lifl.fr/~figeac/supplementary_material/srac_appendix.pdf
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References
Ajana, Y., Lefebvre, J.F., Tillier, E., El-Mabrouk, N.: Exploring the set of all minimal sequences of reversals - an application to test the replication-directed reversal hypothesis. In: Guigó, R., Gusfield, D. (eds.) WABI 2002. LNCS, vol. 2452, p. 300. Springer, Heidelberg (2002)
Bader, D., Moret, B., Yan, M.: A linear time algorithm for computing inversion distance between signed permutations with an expermimental study. Journal of (2000)
Bergeron, A., Chauve, C., Hartman, T., St-Onge, K.: On the properties of sequences of reversals that sort a signed permutation. In: Proceedings of JOBIM, JOBIM (2002)
Bergeron, A.: A very elementary presentation of the hannenhalli-pevzner theory. In: Amir, A., Landau, G.M. (eds.) CPM 2001. LNCS, vol. 2089, p. 106. Springer, Heidelberg (2001)
Caprara, A.: Sorting by reversals is difficult. ACM RECOMB (1997)
Cosner, M.E., Jansen, R.K., Moret, B.M.E., Raubeson, L.A., Wang, L., Warnow, T., Wyman, S.K.: An empirical comparison between bpanalysis and mpbe on the campanulaceae chloroplast genome dataset. Comparative Genomics (2000)
El-Mabrouk, N.: Sorting signed permutations by reversals and insertions/deletions of contiguous segments. Journal of Discrete Algorithms (2000)
Eriksen, N. (1+epsilon)-approximation of sorting by reversals and transpositions. In: Gascuel, O., Moret, B.M.E. (eds.) WABI 2001. LNCS, vol. 2149, p. 227. Springer, Heidelberg (2001)
Hannenhalli, S., Pevzner, P.: To cut.. or not to cut (applications of comparative physical maps in molecular evolution). In: Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 304–313 (1996)
Hannenhalli, S., Pevzner, P.A.: Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals. In: STOC (1995)
Heber, S., Stoye, J.: Algorithms for finding gene clusters. In: Gascuel, O., Moret, B.M.E. (eds.) WABI 2001. LNCS, vol. 2149, p. 252. Springer, Heidelberg (2001)
Kececioglu, J., Sankoff, D.: Exact and approximation algorithms for sorting by reversals, with application to genome rearrangement. Algorithmica 13, 180–210 (1995)
Pevzner, P., Tesler, G.: Transforming men into mice: the nadeau-taylor chromosomal breakage model revisited. In: RECOMB (2003)
Sankoff, D.: Short inversions and conserved gene clusters. Bioinformatics 18(10), 1305–1308 (2002)
Uno, T., Yagiura, M.: Fast algorithms to enumerate all common intervals of two permutations. Algorithmica (2000)
Walter, M.E., Dias, Z., Meidanis, J.: Reversal and transposition distance of linear chromosomes. In: SPIRE (1998)
Wang, L.S., Warnow, T.: New polynomial time methods for whole-genome phylogeny reconstruction. In: Proc. 33rd Symp. on Theory of Comp. (2001) (to appear)
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Figeac, M., Varré, JS. (2004). Sorting by Reversals with Common Intervals. In: Jonassen, I., Kim, J. (eds) Algorithms in Bioinformatics. WABI 2004. Lecture Notes in Computer Science(), vol 3240. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30219-3_3
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DOI: https://doi.org/10.1007/978-3-540-30219-3_3
Publisher Name: Springer, Berlin, Heidelberg
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