The Syntenic Diameter of the Space of N-Chromosome Genomes

A number of distance measures have recently been proposed for the purpose of determining evolutionary similarity among genomes of dieren t species. For each of these measures, a natu- ral but often dicult problem is to determine the diameter of the space it denes: What is the maximum distance between any pair of genomes? In this work we study the syntenic distance between genomes, introduced by Ferretti, Nadeau, and Sanko as a way to approximate evolu- tionary distance between species for which the gene order within chromosomes is not necessarily known. We show that the diameter of the space of n-chromosome genomes, with respect to the syntenic distance, is exactly 2n 4. The proof of this result is based on a surprising connection between genome rearrangements and the study of gossip problems in communication networks.