Listing All Sorting Reversals in Quadratic Time

  • Krister M. Swenson
  • Ghada Badr
  • David Sankoff
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6293)


We describe an average-case O(n 2) algorithm to list all reversals on a signed permutation π that, when applied to π, produce a permutation that is closer to the identity. This algorithm is optimal in the sense that, the time it takes to write the list is Ω(n 2) in the worst case.


Negative Element Frame Element Quadratic Time Circular Permutation Signed Permutation 
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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Krister M. Swenson
    • 1
    • 2
  • Ghada Badr
    • 3
  • David Sankoff
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of OttawaCanada
  2. 2.LaCIM, UQAMMontréal QuébecCanada
  3. 3.SITE, School of Information Technology and EngineeringUniversity of OttawaCanada

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