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Reports (Research Report) Year : 2004

Sorting by reversals in subquadratic time

Eric Tannier
Marie-France Sagot


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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Dates and versions

inria-00071486 , version 1 (23-05-2006)


  • HAL Id : inria-00071486 , version 1


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