ON TWO VARIATIONS OF THE REVERSAL MEDIAN PROBLEM

Abstract

We have developed an exact algorithm that solves certain instances of the Reversal Median Problem (RMP) when provided with additional input – the optimal sorting sequences between every pair of genomes. Our algorithm is able to provide an exact solution (the median genome) or determine that it is not able to do so for every instance of the problem. We have also proven the correctness of the algorithm in a theorem. RMP is the problem of finding an ancestral genome (the median) given the gene orders of three genomes. It is commonly encountered when constructing phylogeny, and is NP-hard. Two variations of the RMP were considered. In the first variation, we are given one sorting sequence for each pair of genomes. And in the second variation, we make use of a compact representation of all possible optimal sorting sequences for each pair of genomes that was developed by Braga et al.