A 1.5-Approximation Algorithm for Sorting by Transpositions and Transreversals

One of the most promising ways to determine evolutionary distance between two organisms is to compare the order of appearance of orthologous genes in their genomes. The resulting genome rearrangement problem calls for finding a shortest sequence of rearrangement operations that sorts one genome into the other. In this paper we provide a 1.5-approximation algorithm for the problem of sorting by transpositions and transreversals, improving on a five years old 1.75 ratio for this problem. Our algorithm is also faster than current approaches and requires \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$O(n^{3/2} \sqrt{\log{n}})$\end{document} time for n genes.