Perfect Sorting by Reversals

Abstract

In computational biology, gene order data is often modelled as signed permutations. A classical problem in genome comparison is to detect conserved segments in a permutation, that is, genes that are co-localised in several species, indicating that they remained grouped during evolution. A second largely studied problem related to gene order data is to compute a minimum scenario of reversals that transforms a signed permutation into another. Several studies began to mix the two problems, and it was observed that their results are not always compatible: often parsimonious scenarios of reversals break conserved segments. In a recent study, Bérard, Bergeron and Chauve stated as an open question whether it was possible to design a polynomial time algorithm to decide if there exists a minimum scenario of reversals that transforms a genome into another while keeping the clusters of co-localised genes together. In this paper, we give this polynomial algorithm, and thus generalise the theoretical result of the aforementioned paper.

This work is funded by the French program ACI “New interfaces of Mathematics: Mathematical and algorithmical aspects of biochemical and evolutionary networks”, and by the INRIA coordinated action ARC “Integrated Biological Networks”.