A Faster 1.375-Approximation Algorithm for Sorting by Transpositions

Sorting by Transpositions is an NP-hard problem for which several polynomial time approximation algorithms have been developed. Hartman and Shamir (2006) developed a 1.5-approximation algorithm, whose running time was improved to O(n logn) by Feng and Zhu (2007) with a data structure they defined, the permutation tree. Elias and Hartman (2006) developed a 1.375-approximation algorithm that runs in O(n 2) time. In this paper, we propose the first correct adaptation of this algorithm to run in O(n logn) time.

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