On the cost of fault-tolerant consensus when there are no faults

Abstract

We consider the consensus problem in an asynchronous model enriched with unreliable failure detectors and in the partial synchrony model. We consider algorithms that solve consensus and tolerate crash failures and/or message omissions. We prove tight lower bounds on the number of communication steps performed by such algorithms in failure-free executions. We present in a unified framework a number of related lower bound results. Thus, we shed light on the relationships among different known lower and upper bounds, and at the same time, illustrate a general technique for obtaining simple and elegant lower bound proofs. We also illustrate matching upper bounds: we algorithms that achieve the lower bound.