A new approach for approximating the transposition distance

One of the proposed ways to compare genomes or other large DNA molecules is by computing a rearrangement distance, defined as the minimum number of rearrangement events necessary to transform one molecule into another taking into account only the relative order of similar genes. In this work, we study the problem of computing the transposition distance between two linear gene orders, represented by permutations. To help solve it, we present a very simple structure, the breakpoint diagram, and a 2.25-approximation algorithm for the problem based on this structure. While there are better approximation algorithms, they are based on more complex data structures. Our algorithm was implemented in the C programming language and we show experimental results obtained with it on all permutations of up to 11 genes, plus selected permutations of higher size.