Fast Consensus under Eventually Stabilizing Message Adversaries

TL;DR

This paper introduces a new deterministic consensus algorithm for dynamic networks with message adversaries that eventually stabilize, reducing termination time and working under stronger adversary models.

Contribution

It presents a tight bound of 2D+1 for consensus termination time under an eventually stabilizing message adversary and provides an algorithm that achieves this bound, improving over previous results.

Findings

Achieves consensus in 2D+1 rounds under the specified adversary.

Halves the previous termination time of 4D+1 rounds.

Works correctly under a stronger, generalized adversary model.

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.