Formulations and hardness of multiple sorting by reversals
RECOMB '99 Proceedings of the third annual international conference on Computational molecular biology
Finding All Common Intervals of k Permutations
CPM '01 Proceedings of the 12th Annual Symposium on Combinatorial Pattern Matching
Edit Distances for Genome Comparisons Based on Non-Local Operations
CPM '92 Proceedings of the Third Annual Symposium on Combinatorial Pattern Matching
Computing common intervals of K permutations, with applications to modular decomposition of graphs
ESA'05 Proceedings of the 13th annual European conference on Algorithms
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Using PQ trees for comparative genomics
CPM'05 Proceedings of the 16th annual conference on Combinatorial Pattern Matching
Evolution under Reversals: Parsimony and Conservation of Common Intervals
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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This paper investigates the problem of conservation of combinatorial structures in genome rearrangement scenarios. We characterize a class of signed permutations for which one can compute in polynomial time a reversal scenario that conserves all common intervals, and that is parsimonious among such scenarios. Figeac and Varré (WABI 2004) announced that the general problem is NP-hard. We show that there exists a class of permutations for which this computation can be done in linear time with a very simple algorithm, and, for a larger class of signed permutations, the computation can be achieved in subquadratic time. We apply these methods to permutations obtained from the X chromosomes of the human, mouse and rat.