Finite time distributed averaging over ring networks

TL;DR

This paper introduces a finite-time distributed consensus algorithm specifically designed for ring networks, enabling all agents to reach the average estimate in a predictable number of steps based on network size.

Contribution

The paper presents a novel finite-time consensus algorithm optimized for ring networks, with explicit iteration bounds depending on the number of agents.

Findings

Convergence in n steps for even number of agents

Convergence in 3n steps for odd number of agents

Algorithm guarantees finite-time consensus

Abstract

We consider a multi-agent system where each agent has its own estimate of a given quantity and the goal is to reach consensus on the average. To this purpose, we propose a distributed consensus algorithm that guarantees convergence to the average in a finite number of iterations. The algorithm is tailored to ring networks with bidirectional pairwise communications. If the number of agents $m$ is even, say $m=2n$, then, the number of iterations needed is equal to $n$, which in this case is the diameter of the network, whereas the number of iterations grows to $3n$ if the number of agents is odd and equal to $m=2n+1$.