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A 1.375-Approximation Algorithm for Sorting by Transpositions
October-December 2006 (vol. 3 no. 4)
pp. 369-379
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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Index Terms:
Computational biology, genome rearrangements, sorting permutations by transpositions.
Isaac Elias, Tzvika Hartman, "A 1.375-Approximation Algorithm for Sorting by Transpositions," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 3, no. 4, pp. 369-379, Oct.-Dec. 2006, doi:10.1109/TCBB.2006.44
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