Multicast tree structure and the power law

In this paper, we investigate structural properties of multicast trees that give rise to the so-called multicast power law. The law asserts that the ratio R(n) of the average number of links in a multicast tree connecting the source to n destinations to the average number of links in a unicast path, satisfies asymptotically R(n)≈cn^φ, 0<φ<1. In order to obtain a better insight, we first analyze some simple multicast tree topologies, which under appropriately chosen parameters give rise to the multicast power law. The asymptotic analysis of R(n) in this case indicates that it is very difficult to infer the validity of power law by observing graphs of R(n) alone. Next we introduce a new metric, "reachability degree," which is easy to measure and applicable to general networks where multicast trees are constructed as subtrees of a given spanning tree which we call Global Multicast Tree. The reachability degree is indicative of the structure of the Global Multicast Tree. We show that this metric provides a more reliable means for inferring the validity of the power law. Finally, we perform experiments on real and simulated networks to demonstrate the use of the new metric.