Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals
Journal of the ACM (JACM)
Finding All Common Intervals of k Permutations
CPM '01 Proceedings of the 12th Annual Symposium on Combinatorial Pattern Matching
An algorithmic view of gene teams
Theoretical Computer Science
Advances on sorting by reversals
Discrete Applied Mathematics
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Revisiting t. uno and m. yagiura's algorithm
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Perfect sorting by reversals is not always difficult
WABI'05 Proceedings of the 5th International conference on Algorithms in Bioinformatics
A more efficient algorithm for perfect sorting by reversals
Information Processing Letters
RECOMB-CG '08 Proceedings of the international workshop on Comparative Genomics
Solving the Preserving Reversal Median Problem
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Average-Case Analysis of Perfect Sorting by Reversals
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
The solution space of sorting by reversals
ISBRA'07 Proceedings of the 3rd international conference on Bioinformatics research and applications
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In comparative genomics, gene order data is often modeled as signed permutations. A classical problem for genome comparison is to detect common intervals in permutations, that is, genes that are colocalized in several species, indicating that they remained grouped during evolution. A second largely studied problem related to gene order is to compute a minimum scenario of reversals that transforms a signed permutation into another. Several studies began to mix the two problems and it was observed that their results are not always compatible: Often, parsimonious scenarios of reversals break common intervals. If a scenario does not break any common interval, it is called perfect. In two recent studies, Bérard et al. defined a class of permutations for which building a perfect scenario of reversals sorting a permutation was achieved in polynomial time and stated as an open question whether it is possible to decide, given a permutation, if there exists a minimum scenario of reversals that is perfect. In this paper, we give a solution to this problem and prove that this widens the class of permutations addressed by the aforementioned studies. We implemented and tested this algorithm on gene order data of chromosomes from several mammal species and we compared it to other methods. The algorithm helps to choose among several possible scenarios of reversals and indicates that the minimum scenario of reversals is not always the most plausible.