Average-case analysis of perfect sorting by reversals
Combinatorics
2009-05-18 v1 Data Structures and Algorithms
Quantitative Methods
Abstract
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.
Cite
@article{arxiv.0901.2847,
title = {Average-case analysis of perfect sorting by reversals},
author = {Mathilde Bouvel and Cedric Chauve and Marni Mishna and Dominique Rossin},
journal= {arXiv preprint arXiv:0901.2847},
year = {2009}
}