Communication-efficient leader election and consensus with limited link synchrony

We study the degree of synchrony required to implement the leader election failure detector Ω and to solve consensus in partially synchronous systems. We show that in a system with n processes and up to f process crashes, one can implement Ω and solve consensus provided there exists some (unknown) correct process with f outgoing links that are eventually timely. In the special case where f = 1, an important case in practice, this implies that to implement Ω and solve consensus it is sufficient to have just one eventually timely link -- all the other links in the system, Θ(n²) of them, may be asynchronous. There is no need to know which link p → q is eventually timely, when it becomes timely, or what is its bound on message delay. Surprisingly, it is not even required that the source p or destination q of this link be correct: either p or q may actually crash, in which case the link p → q is eventually timely in a trivial way, and it is useless for sending messages. We show that these results are in a sense optimal: even if every process has f - 1 eventually timely links, neither Ω nor consensus can be solved. We also give an algorithm that implements Ω in systems where some correct process has f outgoing links that are eventually timely, such that eventually only f links carry messages, and we show that this is optimal. For f = 1, this algorithm ensures that all the links, except for one, eventually become quiescent.