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| HAL: hal-00649761, version 1 |
| DOI: 10.1142/S1793830911001280 |
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| Discrete Mathematics, Algorithms and Applications 3, 3 (2011) 369-392 |
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| Average-case analysis of perfect sorting by reversals |
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Mathilde Bouvel 1Cédric Chauve 2 |
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| (2011) |
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| Perfect sorting by reversals, a problem originating in computational genomics, is the process of sorting a signed permutation to either the identity or to the reversed identity permutation, by a sequence of reversals that do not break any common interval. Bérard et al. (2007) make use of strong interval trees to describe an algorithm for sorting signed permutations by reversals. Combinatorial properties of this family of trees are essential to the algorithm analysis. Here, we use the expected value of certain tree parameters to prove that the average run-time of the algorithm is at worst, polynomial, and additionally, for sufficiently long permutations, the sorting algorithm runs in polynomial time with probability one. Furthermore, our analysis of the subclass of commuting scenarios yields precise results on the average length of a reversal, and the average number of reversals. A preliminary version of this work appeared in the proceedings of Combinatorial Pattern Matching (CPM) 2009, Lectures Notes in Computer Science, vol. 5577, pp. 314--325, Springer. |
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| 1: | Laboratoire Bordelais de Recherche en Informatique (LaBRI) |
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CNRS : UMR5800 – Université Sciences et Technologies - Bordeaux I – École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB) – Université Victor Segalen - Bordeaux II |
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| 2: | Department of Mathematics |
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Simon Fraser University |
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| 3: | Department of Mathematics |
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Simon Fraser University |
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| 4: | Laboratoire d'informatique de l'école polytechnique (LIX) |
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CNRS : UMR7161 – Polytechnique - X |
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| Subject | : | Mathematics/Combinatorics Computer Science/Bioinformatics Life Sciences/Quantitative Methods |
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| Algorithm analysis – genome rearrangements – tree parameters – simple permutations |
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| Attached file list to this document: | |||||
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| hal-00649761, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00649761 | |
| oai:hal.archives-ouvertes.fr:hal-00649761 | |
| From: Mathilde Bouvel | |
| Submitted on: Thursday, 8 December 2011 15:31:41 | |
| Updated on: Monday, 11 March 2013 17:47:22 | |
