Average-Case Analysis of Perfect Sorting by Reversals

Authors:
Mathilde Bouvel;Cedric Chauve;Marni Mishna;Dominique Rossin
Affiliations:
CNRS, Université Paris Diderot, LIAFA, Paris, France;Department of Mathematics, Simon Fraser University, Burnaby, Canada;Department of Mathematics, Simon Fraser University, Burnaby, Canada;CNRS, Université Paris Diderot, LIAFA, Paris, France
Venue:
CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
Year:
2009

Citing 13
Cited 1

Finding pattern matchings for permutations

Information Processing Letters
Beyond islands (extended abstract): runs in clone-probe matrices

RECOMB '97 Proceedings of the first annual international conference on Computational molecular biology
Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals

Journal of the ACM (JACM)
Advances on sorting by reversals

Discrete Applied Mathematics
Perfect Sorting by Reversals Is Not Always Difficult

IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Evolution under Reversals: Parsimony and Conservation of Common Intervals

IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
A more efficient algorithm for perfect sorting by reversals

Information Processing Letters
Computing Common Intervals of $K$ Permutations, with Applications to Modular Decomposition of Graphs

SIAM Journal on Discrete Mathematics
Perfect DCJ Rearrangement

RECOMB-CG '08 Proceedings of the international workshop on Comparative Genomics
Hurdles Hardly Have to Be Heeded

RECOMB-CG '08 Proceedings of the international workshop on Comparative Genomics
Poisson adjacency distributions in genome comparison

Bioinformatics
Analytic Combinatorics

Analytic Combinatorics
Conservation of combinatorial structures in evolution scenarios

RCG'04 Proceedings of the 2004 RECOMB international conference on Comparative Genomics

Preserving inversion phylogeny reconstruction

WABI'12 Proceedings of the 12th international conference on Algorithms in Bioinformatics

Quantified Score

Hi-index	0.00

Visualization

Abstract

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 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.