Reliable Broadcast with Respect to Topology Knowledge

We study the Reliable Broadcast problem in incomplete networks against a Byzantine adversary. We examine the problem under the

locally bounded adversary model

of Koo (2004) and the

general adversary model

of Hirt and Maurer (1997) and explore the tradeoff between the level of topology knowledge and the solvability of the problem.

We refine the local pair-cut technique of Pelc and Peleg (2005) in order to obtain impossibility results for every level of topology knowledge and any type of corruption distribution. On the positive side we devise protocols that match the obtained bounds and thus, exactly characterize the classes of graphs in which Reliable Broadcast is possible.

Among others, we show that Koo’s Certified Propagation Algorithm (CPA) is

unique

against locally bounded adversaries in

ad hoc

networks, that is, it can tolerate as many local corruptions as any other non-faulty algorithm; this settles an open question posed by Pelc and Peleg. We also provide an adaptation of CPA against general adversaries and show its uniqueness. To the best of our knowledge this is the first optimal algorithm for Reliable Broadcast in generic topology

ad hoc

networks against general adversaries.