Listing all parsimonious reversal sequences: new algorithms and perspectives

In comparative genomics studies, finding a minimum length sequences of reversals, so-called sorting by reversals, has been the topic of a huge literature. Since there are many minimum length sequences, another important topic has been the problem of listing all parsimonious sequences between two genomes, called the All Sorting Sequences by Reversals (ASSR) problem. In this article, we revisit the ASSR problem for uni-chromosomal genomes when no duplications are allowed and when the relative order of the genes is known. We put the current body of work in perspective by illustrating the fundamental framework that is common for all of them, a perspective that allows us for the first time to theoretically compare their running times. The article also proposes an improved framework that empirically speeds up all known algorithms.