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

Abstract

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 O(n log n) ) algorithm to exactly compute the syntenic distance between two genomes with at most n chromosomes each. Our algorithm requires O(n 2 + 2 O(d log d) ) time when this distance is d, improving the O(n 2 + 2 O(d 2 ) ) running time of the best previous exact algorithm.

On generalized gossiping and broadcasting

“…For a tree communication graph they minimize the number of calls or number of rounds required. Liben-Nowell [23] generalizes this work by defining for each gossiper i the set of relevant gossip that they need to learn. This is just like our multi-source multicast problem with ∆ = N , except that the communication model is different, as well as the objective function.…”

“…For example, the paper by Liben-Nowell [23] considers a problem very similar to multi-source multicast with ∆ = N . However, the model that he uses is different than the one that we use.…”

“…Several other papers use the same telephone call model [2,7,14,18,30]. Liben-Nowell [23] gives an exponential time exact algorithm for the problem.…”

Polynomial-time Algorithm for Translocation Syntenic Distance

“…Data of exact gene sequence in genomes are generally unavailable whereas the chromosomal assignment of genes is more studied. This makes syntenic distance more convenient to consider in computing for genomic distance 13 .…”

“…Liben-Nowell gave an analysis of this algorithm and presented further some structural properties of the minimum syntenic distance problem such as monotonicity and non-redundancy 12 . Years later, he was able to provide an improved approximation algorithm using the Gossip Problem 13 .…”