Average-case analysis of perfect sorting by reversals [article]

Mathilde Bouvel, Cedric Chauve, Marni Mishna, Dominique Rossin
2009 arXiv   pre-print
A sequence of reversals that takes a signed permutation to the identity is perfect if at no step a common interval is broken. Determining a parsimonious perfect sequence of reversals that sorts a signed permutation is NP-hard. 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.
arXiv:0901.2847v1 fatcat:xpoqu5tu3zccpdfgztpiynhgni