Consensus in Rooted Dynamic Networks with Short-Lived Stability

TL;DR

This paper investigates the minimal stability duration needed for deterministic consensus algorithms to succeed in dynamic, unreliable networks with directional links, revealing new bounds and methods for systems with transient faults.

Contribution

It identifies the shortest stability period necessary and sufficient for consensus, introducing novel algorithms that do not rely on waiting for long stability phases.

Findings

Short-lived stability phases can suffice for consensus under certain conditions.

Standard algorithms require longer stability periods, while new methods work with minimal stability.

The results are applicable to systems with frequent transient faults and erratic startup behaviors.

Abstract

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 a large body of existing work that focuses on oblivious message adversaries where the communication graphs are picked from a predefined set, we consider message adversaries where guarantees about stable periods that occur only eventually can be expressed. We reveal to what extent such eventual stability is necessary and sufficient, that is, we present the shortest period of stability that permits solving consensus, a result that should prove quite useful in systems that exhibit erratic boot-up phases or recover after repeatedly occurring, massive transient faults. Contrary to the case of longer stability periods, where we show how standard algorithmic techniques for solving consensus can be employed, the short-lived nature of the stability phase forces us to use more unusual algorithmic methods that avoid waiting explicitly for the stability period to occur.