This paper is devoted to deterministic consensus in synchronous dynamic networks with unidirectional links, which are under the control of an omniscient message adversary. Motivated by unpredictable node/system initialization times and long-lasting periods of massive transient faults, we consider message adversaries that guarantee periods of less erratic message loss only eventually: We present a tight bound of 2D+1 for the termination time of consensus under a message adversary that eventually guarantees a single vertex-stable root component with dynamic network diameter D, as well as a simple algorithm that matches this bound. It effectively halves the termination time 4D+1 achieved by an existing consensus algorithm, which also works under our message adversary. We also introduce a generalized, considerably stronger variant of our message adversary, and show that our new algorithm, unlike the existing one, still works correctly under it.
@article{arxiv.1508.00851,
title = {Fast Consensus under Eventually Stabilizing Message Adversaries},
author = {Manfred Schwarz and Kyrill Winkler and Ulrich Schmid},
journal= {arXiv preprint arXiv:1508.00851},
year = {2015}
}