Geodesic stability for memoryless binary long-lived consensus

TL;DR

This paper investigates the stability of memoryless binary long-lived consensus in distributed systems, proposing a conjecture, identifying classes of optimal colorings, and establishing new lower bounds for stability measures.

Contribution

It introduces a conjecture on geodesic stability, identifies classes of colorings that achieve this bound, and improves lower bounds for all colorings in the binary memoryless case.

Findings

Proposes a conjecture on stability in the binary memoryless case.

Identifies two classes of colorings that attain the conjectured stability bound.

Establishes improved lower bounds for all colorings and a related stability parameter.

Abstract

The determination of the stability of the long-lived consensus problem is a fundamental open problem in distributed systems. We concentrate on the memoryless binary case with geodesic paths. We offer a conjecture on the stability in this case, exhibit two classes of colourings which attain this conjectured bound, and improve the known lower bounds for all colourings. We also introduce a related parameter, which measures the stability only for certain geodesics, and for which we also prove lower bounds.