Average-Case Analysis of Perfect Sorting by Reversals

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 worstcase 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. Published in the Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching (CPM 2009), Lille (France), June 22–24, 2009. Volume 5577 of Lecture Notes in Computer Science, pp. 314–325,...

• Type: Conference
• Year: 2009
• Where: CPM
• Authors: Mathilde Bouvel, Cedric Chauve, Marni Mishna, Dominique Rossin
• Keywords: Common Intervals, CPM 2009, Discrete Geometry, Parsimonious Perfect Reversals, Signed Permutations