On the 1.375-approximation algorithm for sorting by transpositions in O(n logn) time

Abstract

Sorting by Transpositions is an NP-hard problem. Elias and Hartman proposed a 1.375-approximation algorithm, the best ratio so far, which runs in O(n 2) time. Firoz et al. proposed an improvement to the running time, from O(n2) down to O(n logn), using Feng and Zhu's permutation trees. We provide counter-examples to the correctness of Firoz et al.'s strategy, showing that it is not possible to reach a component by sufficient extensions using the method proposed by them. © 2013 Springer International Publishing.