Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Sorting by reversals is difficult
RECOMB '97 Proceedings of the first annual international conference on Computational molecular biology
A Faster and Simpler Algorithm for Sorting Signed Permutations by Reversals
SIAM Journal on Computing
A Very Elementary Presentation of the Hannenhalli-Pevzner Theory
CPM '01 Proceedings of the 12th Annual Symposium on Combinatorial Pattern Matching
WABI '02 Proceedings of the Second International Workshop on Algorithms in Bioinformatics
Inversion Medians Outperform Breakpoint Medians in Phylogeny Reconstruction from Gene-Order Data
WABI '02 Proceedings of the Second International Workshop on Algorithms in Bioinformatics
Improved bounds on sorting with length-weighted reversals
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Genome Rearrangement Based on Reversals that Preserve Conserved Intervals
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Reversal and transposition medians
Theoretical Computer Science
A very elementary presentation of the Hannenhalli-Pevzner theory
Discrete Applied Mathematics - 12th annual symposium on combinatorial pattern matching (CPM)
Comparing bacterial genomes from linear orders of patterns
Discrete Applied Mathematics
Improved bounds on sorting by length-weighted reversals
Journal of Computer and System Sciences
Parking Functions, Labeled Trees and DCJ Sorting Scenarios
RECOMB-CG '09 Proceedings of the International Workshop on Comparative Genomics
A very elementary presentation of the Hannenhalli-Pevzner theory
Discrete Applied Mathematics
On the similarity of sets of permutations and its applications to genome comparison
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
Recovering true rearrangement events on phylogenetic trees
RECOMB-CG'07 Proceedings of the 2007 international conference on Comparative genomics
Listing all sorting reversals in quadratic time
WABI'10 Proceedings of the 10th international conference on Algorithms in bioinformatics
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Listing all parsimonious reversal sequences: new algorithms and perspectives
RECOMB-CG'10 Proceedings of the 2010 international conference on Comparative genomics
Complexity decompositions in the problem of comparison of polytene chromosome banding sequences
Pattern Recognition and Image Analysis
Efficient sampling of transpositions and inverted transpositions for bayesian MCMC
WABI'06 Proceedings of the 6th international conference on Algorithms in Bioinformatics
Evolution of tandemly repeated sequences through duplication and inversion
RCG'06 Proceedings of the RECOMB 2006 international conference on Comparative Genomics
Genome rearrangement in mitochondria and its computational biology
RCG'04 Proceedings of the 2004 RECOMB international conference on Comparative Genomics
Complexity decompositions in the problem of comparison of polytene chromosome banding sequences
Pattern Recognition and Image Analysis
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The problem of estimating evolutionary distance from differences in gene order has been distilled to the problem of finding the reversal distance between two signed permutations. During the last decade, much progress was made both in computing reversal distance and in finding a minimum sequence of sorting reversals. For most problem instances, however, many minimum sequences of sorting reversals exist, and obtaining the complete set can be useful in exploring the space of genome rearrangements (e.g., in pursuit of solutions to higher-level problems). The problem of finding all minimum sequences of sorting reversals reduces easily to the problem of finding all sorting reversals of one permutation with respect to another. We derive an efficient algorithm to solve this latter problem, and present experimental results indicating that our algorithm offers a dramatic improvement over the best known alternative. It should be noted that in asymptotic terms the new algorithm does not represent a significant improvement: it requires O(n3) time (where n is the permutation size), while the problem can now be solved trivially in &THgr;(n3) time.