Average-Case Analysis of Perfect Sorting by Reversals

  • Mathilde Bouvel
  • Cedric Chauve
  • Marni Mishna
  • Dominique Rossin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5577)


A sequence of reversals that takes a signed permutation to the identity is perfect if it preserves all common intervals between the permutation and the identity. The problem of computing a parsimonious perfect sequence of reversals is believed to be NP-hard, as the more general problem of sorting a signed permutation by reversals while preserving a given subset of common intervals is NP-hard. The only published algorithms that compute a parsimonious perfect reversals sequence have an exponential time complexity. Here we show that, despite this worst-case analysis, with probability one, sorting can be done in polynomial time. Further, we find asymptotic expressions for the average length and number of reversals in commuting permutations, an interesting sub-class of signed permutations.


Internal Vertex Prime Vertex Prime Node Identity Permutation Common Interval 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Mathilde Bouvel
    • 1
  • Cedric Chauve
    • 2
  • Marni Mishna
    • 2
  • Dominique Rossin
    • 1
  1. 1.CNRS, Université Paris Diderot, LIAFAParisFrance
  2. 2.Department of MathematicsSimon Fraser UniversityBurnabyCanada

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