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
SIAM Journal on Discrete Mathematics
Faster and simpler algorithm for sorting signed permutations by reversals
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
An algorithm to enumerate all sorting reversals
Proceedings of the sixth annual international conference on Computational biology
A Very Elementary Presentation of the Hannenhalli-Pevzner Theory
CPM '01 Proceedings of the 12th Annual Symposium on Combinatorial Pattern Matching
CPM '96 Proceedings of the 7th Annual Symposium on Combinatorial Pattern Matching
Transforming men into mice (polynomial algorithm for genomic distance problem)
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Improved bounds on sorting with length-weighted reversals
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Improved bounds on sorting by length-weighted reversals
Journal of Computer and System Sciences
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Finding All Sorting Tandem Duplication Random Loss Operations
CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
Parking Functions, Labeled Trees and DCJ Sorting Scenarios
RECOMB-CG '09 Proceedings of the International Workshop on Comparative Genomics
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
The solution space of sorting by reversals
ISBRA'07 Proceedings of the 3rd international conference on Bioinformatics research and applications
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
Finding all sorting tandem duplication random loss operations
Journal of Discrete Algorithms
Identifying evolutionarily conserved segments among multiple divergent and rearranged genomes
RCG'04 Proceedings of the 2004 RECOMB international conference on Comparative Genomics
The distribution of inversion lengths in bacteria
RCG'04 Proceedings of the 2004 RECOMB international conference on Comparative Genomics
Approximating the number of Double Cut-and-Join scenarios
Theoretical Computer Science
Evolution of genome organization by duplication and loss: an alignment approach
RECOMB'12 Proceedings of the 16th Annual international conference on Research in Computational Molecular Biology
Heuristics for the Sorting by Length-Weighted Inversion Problem
Proceedings of the International Conference on Bioinformatics, Computational Biology and Biomedical Informatics
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Given two genomes, the problem of sorting by reversals is to explain the evolution of these genomes from a common ancestor by a minimal sequence of reversals. The Hannenhalli and Pevzner (HP) algorithm [8] gives the reversal distance and outputs one possible sequence of reversals. However, there is usually a very large set of such minimal solutions. To really understand the mechanism of reversals, it is important to have access to that set of minimal solutions. We develop a new method that allows the user to choose one or several solutions, based on different criteria. In particular, it can be used to sort genomes by weighted reversals. This requires a characterization of all "safe" reversals, as defined in the HP theory. We describe a procedure that outputs the set of all safe reversals at each step of the sorting procedure in time O(n3), and we show how to characterize a large set of such reversals in a more efficient way. We also describe a linear algorithm allowing to generate a random genome of a given reversal distance. We use our methods to verify the hypothesis that, in bacteria, most reversals act on segments surrounding one of the two endpoints of the replication axis [12].