# The 1.375 Approximation Algorithm for Sorting by Transpositions Can Run in $O(n\log n)$ Time

## TL;DR

This paper improves the efficiency of the best known approximation algorithm for Sorting by Transpositions in bioinformatics, reducing its runtime from quadratic to near-linear using a permutation tree data structure.

## Contribution

The paper demonstrates that the 1.375 approximation algorithm for SPbT can be implemented in O(n log n) time, significantly enhancing its practical applicability.

## Key findings

- Reduced the algorithm's runtime from O(n^2) to O(n log n)
- Utilized the permutation tree data structure for efficiency
- Maintained the approximation ratio of 1.375

## Abstract

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