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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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
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