Sorting Signed Permutations by Inversions in O(nlogn) Time

  • Krister M. Swenson
  • Vaibhav Rajan
  • Yu Lin
  • Bernard M. E. Moret
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5541)

Abstract

The study of genomic inversions (or reversals) has been a mainstay of computational genomics for nearly 20 years. After the initial breakthrough of Hannenhalli and Pevzner, who gave the first polynomial-time algorithm for sorting signed permutations by inversions, improved algorithms have been designed, culminating with an optimal linear-time algorithm for computing the inversion distance and a subquadratic algorithm for providing a shortest sequence of inversions—also known as sorting by inversions. Remaining open was the question of whether sorting by inversions could be done in O(nlogn) time.

In this paper, we present a qualified answer to this question, by providing two new sorting algorithms, a simple and fast randomized algorithm and a deterministic refinement. The deterministic algorithm runs in time O(nlogn + kn), where k is a data-dependent parameter. We provide the results of extensive experiments showing that both the average and the standard deviation for k are small constants, independent of the size of the permutation. We conclude (but do not prove) that almost all signed permutations can be sorted by inversions in O(nlogn) time.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Krister M. Swenson
    • 1
  • Vaibhav Rajan
    • 1
  • Yu Lin
    • 1
  • Bernard M. E. Moret
    • 1
  1. 1.Laboratory for Computational Biology and BioinformaticsEPFL (École Polytechnique Fédérale de Lausanne)Switzerland

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