Listing all sorting reversals in quadratic time

Authors:
Krister M. Swenson;Ghada Badr;David Sankoff
Affiliations:
Department of Mathematics and Statistics, University of Ottawa, Ontario, Canada and LaCIM, UQAM, Montréal, Québec, Canada;School of Information Technology and Engineering, University of Ottawa, Ontario, Canada;Department of Mathematics and Statistics, University of Ottawa, Ontario, Canada
Venue:
WABI'10 Proceedings of the 10th international conference on Algorithms in bioinformatics
Year:
2010

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Abstract

We describe an average-case O(n2) algorithm to list all reversals on a signed permutation π that, when applied to &pi, 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(n2) in the worst case.