Sorting permutations by block-interchanges
Information Processing Letters
SIAM Journal on Discrete Mathematics
Sorting permutations by tanspositions
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
The string edit distance matching problem with moves
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Discrete Mathematics
Sorting Strings by Reversals and by Transpositions
SIAM Journal on Discrete Mathematics
Sorting by Prefix Transpositions
SPIRE 2002 Proceedings of the 9th International Symposium on String Processing and Information Retrieval
Edit Distance with Move Operations
CPM '02 Proceedings of the 13th Annual Symposium on Combinatorial Pattern Matching
Subsequence and Run Heuristics for Sorting by Transpositions
Subsequence and Run Heuristics for Sorting by Transpositions
Reversals and Transpositions Over Finite Alphabets
SIAM Journal on Discrete Mathematics
New Bounds and Tractable Instances for the Transposition Distance
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
A 1.375-Approximation Algorithm for Sorting by Transpositions
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Faster algorithms for sorting by transpositions and sorting by block interchanges
ACM Transactions on Algorithms (TALG)
Bounding Prefix Transposition Distance for Strings and Permutations
HICSS '08 Proceedings of the Proceedings of the 41st Annual Hawaii International Conference on System Sciences
Edit Distances and Factorisations of Even Permutations
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Pattern matching with address errors: Rearrangement distances
Journal of Computer and System Sciences
A simpler and faster 1.5-approximation algorithm for sorting by transpositions
Information and Computation
Efficient computations of l1and l∞rearrangement distances
SPIRE'07 Proceedings of the 14th international conference on String processing and information retrieval
Combinatorics of Genome Rearrangements
Combinatorics of Genome Rearrangements
Reversal distance for strings with duplicates: linear time approximation using hitting set
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
A new and faster method of sorting by transpositions
CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching
Bounding prefix transposition distance for strings and permutations
Theoretical Computer Science
A new approximation algorithm for cut-and-paste sorting of unsigned circular permutations
Journal of Computer and System Sciences
A (1+ε)-approximation algorithm for sorting by short block-moves
Theoretical Computer Science
Proceedings of the International Conference on Bioinformatics, Computational Biology and Biomedical Informatics
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In comparative genomics, a transposition is an operation that exchanges two consecutive sequences of genes in a genome. The transposition distance, that is, the minimum number of transpositions needed to transform a genome into another, can be considered as a relevant evolutionary distance. The problem of computing this distance when genomes are represented by permutations, called the SORTING BY TRANSPOSITIONS problem (SBT), has been introduced by Bafna and Pevzner [3] in 1995. It has naturally been the focus of a number of studies, but the computational complexity of this problem has remained undetermined for 15 years. In this paper, we answer this long-standing open question by proving that the SORTING BY TRANSPOSITIONS problem is NP-hard. As a corollary of our result, we also prove that the following problem from [10] is NP-hard: given a permutation π, is it possible to sort π using db(π)/3 permutations, where db(π) is the number of breakpoints of π?