View article

In this paper, we study the complexity of gossip in an asynchronous, message-passing fault-prone distributed system. In short, we show that an adaptive adversary can significantly hamper the spreading of a rumor, while an oblivious adversary cannot. This latter fact implies that there exist message-efficient asynchronous (randomized) consensus protocols, in the context of an oblivious adversary.

In more detail, we summarize our results as follows. If the adversary is adaptive, we show that a randomized asynchronous gossip algorithm cannot terminate in fewer than O(f(d + delta)) time steps unless Omega(n+f²) messages are exchanged, where n is the total number of processes, f is the number of tolerated crash failures, d is the maximum communication delay for the specific execution in question, and delta is the bound on relative process speeds in the specific execution. The lower bound result is to be contrasted …