Random Information Spread in Networks

Let G = (V, E) be an undirected loopless graph with possible parallel edges and s, t V . Assume that s is labelled at the initial time step and that every labelled vertex copies its labelling to neighbouring vertices along edges with one labelled endpoint independently with probability p in one time step. In this paper, we establish the equivalence between the expected s-t first arrival time of the above spread process and the notion of the stochastic shortest s-t path. Moreover, we give a short discussion of analytical results on special graphs including the complete graph and s-t series-parallel graphs. Finally we propose some lower bounds for the expected s-t first arrival time. Keywords. random processes on graphs, stochastic shortest s-t path, s-t reliability polynomial, virus propagation in networks

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Raymond Lapus, Frank Simon, Peter Tittmann
• Keywords: Arrival Time, CORR 2010, Education, Shortest S-t Path, Stochastic Shortest