Sorting Signed Permutations by Inversions in O(nlogn) Time

  • Authors:

  • Krister M. Swenson;Vaibhav Rajan;Yu Lin;Bernard M. Moret

  • Affiliations:

  • Laboratory for Computational Biology and Bioinformatics, EPFL (École Polytechnique Fédérale de Lausanne), Switzerland;Laboratory for Computational Biology and Bioinformatics, EPFL (École Polytechnique Fédérale de Lausanne), Switzerland;Laboratory for Computational Biology and Bioinformatics, EPFL (École Polytechnique Fédérale de Lausanne), Switzerland;Laboratory for Computational Biology and Bioinformatics, EPFL (École Polytechnique Fédérale de Lausanne), Switzerland

  • Venue:
  • RECOMB 2'09 Proceedings of the 13th Annual International Conference on Research in Computational Molecular Biology
  • Year:
  • 2009

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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 (n logn ) 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 (n logn + 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 (n logn ) time.