Consensus Through Knot Discovery in Asynchronous Dynamic Networks

TL;DR

This paper introduces the Knot Identification Problem as a means to achieve consensus in asynchronous, dynamic networks with potentially disconnected states, providing conditions for solvability and an algorithmic solution.

Contribution

It formalizes the Knot Identification Problem for dynamic networks, establishes necessary and sufficient conditions for its solution, and presents a new algorithm KIA with performance evaluation.

Findings

Knot must be observable by all processes

First observed knot must be consistent across processes

Algorithm KIA effectively solves the problem

Abstract

We state the Problem of Knot Identification as a way to achieve consensus in dynamic networks. The network adversary is asynchronous and not oblivious. The network may be disconnected throughout the computation. We determine the necessary and sufficient conditions for the existence of a solution to the Knot Identification Problem: the knots must be observable by all processes and the first observed knot must be the same for all processes. We present an algorithm KIA that solves it. We conduct KIA performance evaluation.