Advances on sorting by reversals

Abstract

The problem of sorting signed permutations by reversals is inspired by genome rearrangement problems in computational molecular biology. Given two genomes represented as signed permutations of the same elements (e.g. orthologous genes), the problem consists in finding a most parsimonious scenario of reversals that transforms one genome into the other. Following the first polynomial solution of this problem, several improvements, simplifications, generalizations, tutorials or surveys have been published on the subject. While the reversal distance problem—i.e. the problem of computing the minimum number of reversals in a sorting sequence, without giving the sequence itself—seems to be well explored, the problem of giving a scenario realizing the distance still raises some open questions, one of which by Ozery-Flato and Shamir about whether an algorithm with subquadratic time complexity could ever be achieved for solving the problem. We give a positive answer to this question by describing an algorithm of time complexity O ( n 3 / 2 log n ) .