On the efficiency of multicast

The average number of joint hops in a shortest-path multicast tree from a root to m arbitrary chosen group member nodes is studied. A general theory for all graphs, hence including the graph representation of the Internet, is presented which quantifies the multicast reduction in network links compared to m times unicast. For two special types of graphs, the random graph G_p(N) and the k-ary tree, exact and asymptotic results are derived. Comparing these explicit results with previously published Internet measurements indicates that the number of routers in the Internet that can be reached from a root grows exponentially in the number of hops with an effective degree of approximately 3.2