Fast Consensus under Eventually Stabilizing Message Adversaries

Abstract

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.