Minimizing Expected Broadcast Time in Unreliable Networks

When communication lines in an interconnection network are prone to random transmission failures, the time required to broadcast a message throughout the network from a given source vertex is uncertain. We view this broadcast time in such unreliable networks as a random variable dependent on the strategy employed by individual nodes to inform their neighbours, and we seek to describe those strategies which minimize its expected value. Two major results are the complete characterization of optimal deterministic broadcast strategies in unreliable star networks, and proof that each arborescence network has a unique optimal randomized strategy. Our introductory treatment of this problem combines aspects of Markov chains, convexity theory, and the coupon collector’s problem. We hope and expect these tools to prove valuable as work continues on several open problems.