  Information dissemination is a fundamental problem in parallel and
distributed computing. In its simplest variant, the broadcasting problem, a
message has to be spread among all nodes of a graph. A prominent communication
protocol for this problem is based on the random phone call model (Karp et al.,
FOCS 2000). In each step, every node opens a communication channel to a
randomly chosen neighbor for bi-directional communication.
  Motivated by replicated databases and peer-to-peer networks, Berenbrink et
al., ICALP 2010, considered the gossiping problem in the random phone call
model. There, each node starts with its own message and all messages have to be
disseminated to all nodes in the network. They showed that any $O(\log n)$-time
algorithm in complete graphs requires $\Omega(\log n)$ message transmissions
per node to complete gossiping, w.h.p, while for broadcasting the average
number of transmissions per node is $O(\log\log n)$.
  It is known that the $O(n\log\log n)$ bound on the number of transmissions
required for randomized broadcasting in complete graphs cannot be achieved in
sparse graphs even if they have best expansion and connectivity properties. In
this paper, we analyze whether a similar influence of the graph density also
holds w.r.t. the performance of gossiping. We study analytically and
empirically the communication overhead generated by randomized gossiping in
random graphs and consider simple modifications of the random phone call model
in these graphs. Our results indicate that, unlike in broadcasting, there is no
significant difference between the performance of randomized gossiping in
complete graphs and sparse random graphs. Furthermore, our simulations indicate
that by tuning the parameters of our algorithms, we can significantly reduce
the communication overhead compared to the traditional push-pull approach in
the graphs we consider.
