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Sorting by reversals in subquadratic time

Eric Tannier 1 Marie-France Sagot 1
1 HELIX - Computer science and genomics
Inria Grenoble - Rhône-Alpes, LBBE - Laboratoire de Biométrie et Biologie Evolutive - UMR 5558
Abstract : The problem of sorting by signed reversals is inspired by a genome rearrangement problem in computational molecular biology. Given two genomes represented as signed permutations of the same elements (e.g. orthologous genes), the problem consists in finding a most parsimonious scenario of reversals that transforms one genome into the other. We propose a method for sorting a signed permutation by reversals in time O(n). The best known algorithms run in time O(n^2), the main obstacle to an improvement being a costly operation of detection of so-called «safe» reversals. We bypass this detection and, using the same data structure as a previous random approximation algorithm, we achieve the same subquadratic complexity for finding an exact optimal solution. This answers an open question by Ozery-Flato and Shamir whether a subquadratic complexity could ever be achieved for solving the problem.
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https://hal.inria.fr/inria-00071486
Contributor : Rapport de Recherche Inria <>
Submitted on : Tuesday, May 23, 2006 - 5:43:19 PM
Last modification on : Monday, February 10, 2020 - 4:36:45 PM
Long-term archiving on: : Sunday, April 4, 2010 - 10:18:36 PM

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  • HAL Id : inria-00071486, version 1

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Eric Tannier, Marie-France Sagot. Sorting by reversals in subquadratic time. [Research Report] RR-5097, INRIA. 2004. ⟨inria-00071486⟩

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