Gossip is synteny: Incomplete gossip and the syntenic distance between genomes

The syntenic distance between two genomes is given by the minimum number of fusions, fissions, and translocations required to transform one into the other, ignoring the order of genes within chromosomes. Computing this distance is NP-hard. In the present work, we give a tight connection between syntenic distance and the incomplete gossip problem, a novel generalization of the classical gossip problem. In this problem, there are n gossipers, each with a unique piece of initial information; they communicate by phone calls in which the two participants exchange all their information. The goal is to minimize the total number of phone calls necessary to inform each gossiper of his set of relevant gossip which he desires to learn. As an application of the connection between syntenic distance and incomplete gossip, we derive an O(2 log ) algorithm to exactly compute the syntenic distance between two genomes with at most n chromosomes each. Our algorithm requires O(n + 2 log ) time when this distance is d, improving the O(n + 2 2)) running time of the best previous exact algorithm.