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A 1.375-Approximation Algorithm for Sorting by Transpositions

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2 Author(s)
Elias, I. ; Dept. of Numerical Anal. & comput. Sci., R. Inst. of Technol., Stockholm ; Hartman, T.

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

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Computational Biology and Bioinformatics, IEEE/ACM Transactions on  (Volume:3 ,  Issue: 4 )