On randomized broadcasting in star graphs

One of the most frequently studied problems in the context of information dissemination in communication networks is the broadcasting problem. In this paper, we study the following robust, simple, and scalable randomized broadcasting protocol: At some time t an information is placed at one of the nodes of a graph G, and in the succeeding steps, each informed node choses one of its neighbors in G uniformly at random, and sends the information to this neighbor. We show that this algorithm spreads an information to all nodes in a Star graph Sn of dimension n within O(log(N)) steps, with high probability, where N denotes the number of nodes in Sn. In our proofs, we apply some methods which may be of independent interest, and extend the results of [10] concerning randomized broadcasting in hypercubic graphs