The \emph{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
\emph{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 \emph{relevant gossip}
which he desires to learn.
As an application of the connection between syntenic distance and
incomplete gossip, we derive an \smash{$O(2^{O(n \log n)})$} algorithm
to exactly compute the syntenic distance between two genomes with at
most $n$ chromosomes each. Our algorithm requires \smash{$O(n^2 +
2^{O(d \log d)})$} time when this distance is $d$, improving the
\smash{$O(n^2 + 2^{O(d^2)})$} running time of the best previous exact
algorithm.