Lower Bounds on Generic Broadcast Algorithms

This paper establishes tight lower bounds on the time complexity of algorithms solving the generic broadcast problem. Generic broadcast assumes a symmetric, non-reflexive conflict relation on the set of messages, and requires ordered delivery only for conflicting messages. The lower bounds established in this paper relate the resilience of generic broadcast algorithms (i.e., the total number of failures f the algorithms can tolerate) to their time complexity in runs in which oracles are not used. The paper shows that (a) to deliver messages in one round, no failures can be tolerated, (b) to deliver messages in two rounds, at most f < n/3 failures can be tolerated, where n is the number of processes in the system, and (c) to deliver messages in three rounds, at most f < n/2 failures can be tolerated.