Consensus in rooted dynamic networks with short-lived stability

We consider the problem of solving consensus using deterministic algorithms in a synchronous dynamic network with unreliable, directional point-to-point links, which are under the control of a message adversary. In contrast to the large body of existing work that focuses on message adversaries that pick the communication graphs from a predefined set of candidate graphs arbitrarily, we consider message adversaries that also allow to express eventual properties, like stable periods that occur only eventually. Such message adversaries can model systems that exhibit erratic boot-up phases or recover after repeatedly occurring, massive transient faults. We precisely determine how much eventual stability is necessary and sufficient, and provide an optimal consensus algorithm. Unlike in the case of longer stability periods, where standard algorithms can be adapted for solving consensus, different algorithmic techniques are needed in the case of short-lived stability.