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Sorting permutations by transpositions is an important problem in genome rearrangements. A transposition is a rearrangement operation in which a segment is cut out of the permutation and pasted in a different location. The complexity of this problem is still open and it has been a 10-year-old open problem to improve the best known 1.5-approximation algorithm. In this paper, we provide a 1.375-approximation algorithm for sorting by transpositions. The algorithm is based on a new upper bound on the diameter of 3-permutations. In addition, we present some new results regarding the transposition diameter: We improve the lower bound for the transposition diameter of the symmetric group and determine the exact transposition diameter of simple permutations.
Computational biology, genome rearrangements, sorting permutations by transpositions.

T. Hartman and I. Elias, "A 1.375-Approximation Algorithm for Sorting by Transpositions," in IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 3, no. , pp. 369-379, 2006.
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