On the Sorting by Reversals and Transpositions Problem

Andre Rodrigues Oliveira (University of Campinas, Brazil)

Ulisses Dias (University of Campinas, Brazil)

Zanoni Dias (University of Campinas, Brazil)

Abstract: Reversals and transpositions are two classic genome rearrangement operations. Reversals occur when a chromosome breaks at two locations called breakpoints and the DNA between the breakpoints is reversed. Transpositions occur when two adjacent blocks of elements exchange position. This paper presents a polynomial-time approximation algorithm for the Sorting by Reversals and Transpositions Problem. Our algorithm applies to both signed and unsigned versions of the problem, and it treats both cases in a unified manner. We prove an approximation factor of 2 for signed permutations and 2k for the unsigned case, where k is the approximation factor of the algorithm used for cycle decomposition, but in our practical experiments our algorithm found results with approximation ratio better than 1.5 in more than 99% of the signed permutations and better than 1.8 in more than 97% of the unsigned permutations. Our analysis also shows that our algorithm outperforms any other approach known to date.

Keywords: approximation algorithms, genome rearrangement, sorting by reversals and transpositions

Categories: F.2.0, G.2.3