Sorting by bounded permutations
Sorting by bounded permutations
SIAM Journal on Discrete Mathematics
Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals
Journal of the ACM (JACM)
Sorting permutations by tanspositions
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Discrete Mathematics
A New Approach for Approximating the Transposition Distance
SPIRE '00 Proceedings of the Seventh International Symposium on String Processing Information Retrieval (SPIRE'00)
A simpler and faster 1.5-approximation algorithm for sorting by transpositions
Information and Computation
Working on the problem of sorting by transpositions on genome rearrangements
CPM'03 Proceedings of the 14th annual conference on Combinatorial pattern matching
A 1.375-approximation algorithm for sorting by transpositions
WABI'05 Proceedings of the 5th International conference on Algorithms in Bioinformatics
A new tight upper bound on the transposition distance
WABI'05 Proceedings of the 5th International conference on Algorithms in Bioinformatics
Edit Distances and Factorisations of Even Permutations
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
A variant of the tandem duplication — random loss model of genome rearrangement
Theoretical Computer Science
Constraint Programming Models for Transposition Distance Problem
BSB '09 Proceedings of the 4th Brazilian Symposium on Bioinformatics: Advances in Bioinformatics and Computational Biology
Posets and permutations in the duplication-loss model: Minimal permutations with d descents
Theoretical Computer Science
Whole mirror duplication-random loss model and pattern avoiding permutations
Information Processing Letters
Minimal permutations with d descents
European Journal of Combinatorics
An improved 1.375-approximation algorithm for the transposition distance problem
Proceedings of the First ACM International Conference on Bioinformatics and Computational Biology
Bounds on the transposition distance for lonely permutations
BSB'10 Proceedings of the Advances in bioinformatics and computational biology, and 5th Brazilian conference on Bioinformatics
Unitary Toric Classes, the Reality and Desire Diagram, and Sorting by Transpositions
SIAM Journal on Discrete Mathematics
Sorting by transpositions is difficult
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
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The problem of sorting by transpositions asks for a sequence of adjacent interval exchanges that sorts a permutation and is of the shortest possible length. The distance of the permutation is defined as the length of such a sequence. Despite the apparently intuitive nature of this problem, introduced in 1995 by Bafna and Pevzner, the complexity of both finding an optimal sequence and computing the distance remains open today. In this paper, we establish connections between two different graph representations of permutations, which allows us to compute the distance of a few nontrivial classes of permutations in linear time and space, bypassing the use of any graph structure. By showing that every permutation can be obtained from one of these classes, we prove a new tight upper bound on the transposition distance. Finally, we give improved bounds on some other families of permutations and prove formulas for computing the exact distance of other classes of permutations, again in polynomial time.