An improved 1.375-approximation algorithm for the transposition distance problem

In this work, we deal with transposition events, which are large scale mutational events where a block of genes moves from a region of a chromosome to another region within the same chromosome. The transposition distance is the minimum number of transpositions which transform one genome into another. This problem is still open and the best known approximation ratio is 1.375 [3]. Recently, Dias and Dias [2] presented an extension of the 1.5-approximation algorithm presented by Bafna and Pevzner [1]. The extended version achieves good results in practice, but keeps the original 1.5 approximation ratio. One of the extensions is based on a look-ahead strategy and the impact on time complexity and solution quality was controversial. We conclude in this paper that look-ahead does not worth the increase in time complexity. Our main contribution is an 1.375-approximation algorithm based on Elias and Hartman [3] approach and on the extended version of Dias and Dias [2]. We intend to provide a method comparable with Dias and Dias regarding solution quality in practical experiments, but improving their approximation ratio.