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Sorting a Permutation by Transpositions (SPbT) is an important problem inBioinformtics. In this paper, we improve the running time of the best knownapproximation algorithm for SPbT. We use the permutation tree data structure ofFeng and Zhu and improve the running time of the 1.375 Approximation Algorithmfor SPbT of Elias and Hartman to $O(n\log n)$. The previous running time of EHalgorithm was $O(n^2)$.

The 1.375 Approximation Algorithm for Sorting by Transpositions Can Run in O(nlogn) Time