Sorting by Reversals, Generalized Transpositions, and Translocations Using Permutation Groups

In this article, we consider the problem of sorting a linear/circular, multi-chromosomal genome by reversals, block-interchanges (i.e., generalized transpositions), and translocations (including fusions and fissions) where the used operations can be weighted differently, which aims to find a sequence of reversal, block-interchange, and translocation operations such that the sum of these operation weights in the sequence is minimum. It is known that this sorting problem can be solved in polynomial time on the basis of breakpoint graphs, when block-interchanges are weighted 2 (or >= 3) and the others are weighted 1. In this study, we design a novel and easily implemented algorithm for this problem by utilizing the permutation group theory in algebra.