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Exploring the Solution Space of Sorting by Reversals, with Experiments and an Application to Evolution

Marília D.V. Braga 1 Marie-France Sagot 1 Celine Scornavacca 2 Eric Tannier 3 
1 Baobab
PEGASE - Département PEGASE [LBBE]
2 MAB - Méthodes et Algorithmes pour la Bioinformatique
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : In comparative genomics, algorithms that sort permutations by reversals are often used to propose evolutionary scenarios of rearrangements between species. One of the main problems of such methods is that they give one solution while the number of optimal solutions is huge, with no criteria to discriminate among them. Bergeron et al. started to give some structure to the set of optimal solutions, in order to be able to deliver more presentable results than only one solution or a complete list of all solutions. However, no algorithm exists so far to compute this structure except through the enumeration of all solutions, which takes too much time even for small permutations. Bergeron et al. state as an open problem the design of such an algorithm. We propose in this paper an answer to this problem, that is, an algorithm which gives all the classes of solutions and counts the number of solutions in each class, with a better theoretical and practical complexity than the complete enumeration method. We give an example of how to reduce the number of classes obtained, using further constraints. Finally, we apply our algorithm to analyse the possible scenarios of rearrangement between mammalian sex chromosomes.
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Submitted on : Friday, July 16, 2021 - 12:31:42 PM
Last modification on : Friday, August 5, 2022 - 3:02:17 PM
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Marília D.V. Braga, Marie-France Sagot, Celine Scornavacca, Eric Tannier. Exploring the Solution Space of Sorting by Reversals, with Experiments and an Application to Evolution. IEEE/ACM Transactions on Computational Biology and Bioinformatics, Institute of Electrical and Electronics Engineers, 2008, 5 (3), pp.348-356. ⟨10.1109/TCBB.2008.16⟩. ⟨hal-00428206⟩



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