On multicast trees: structure and size estimation

This work presents a thorough investigation of the structure of multicast trees cut from the Internet and power-law topologies. Based on both generated topologies and real Internet data, we characterize the structure of such trees and show that they obey the rank-degree power law; that most high degree tree nodes are concentrated in a low diameter neighborhood; and that the sub-tree size also obeys a power law. Our most surprising empirical finding suggests that there is a linear ratio between the number of high degree network nodes, namely nodes whose tree degree is higher than some constant, and the number of leaf nodes in the multicast tree (clients). We also derive this ratio analytically. Based on this finding, we develop the Fast Algorithm, that estimates the number of clients, and show that it converges faster than one round trip delay from the root to a randomly selected client.