# Distributed finite-time termination for consensus algorithm in switching topologies

arXiv: https://arxiv.org/abs/1909.00059 · HTML: https://mlsanity.com/paper/1909.00059/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Aug 2019.

## Built on by (most cited first, 1 of 1)

- [Distributed Difference of Convex Optimization](https://mlsanity.com/paper/2407.16728/) (2024)

## Abstract (arXiv)

In this article, we present a finite time stopping criterion for consensus algorithms in networks with dynamic communication topology. Recent results provide asymptotic convergence to the consensus algorithm. However, the asymptotic convergence of these algorithms pose a challenge in the practical settings where the response from agents is required in finite time. To this end, we propose a Maximum-Minimum protocol which propagates the global maximum and minimum values of agent states (while running consensus algorithm) in the network. We establish that global maximum and minimum values are strictly monotonic even for a dynamic topology and can be utilized to distributively ascertain the closeness to convergence in finite time. We show that each node can have access to the global maximum and minimum by running the proposed Maximum-Minimum protocol and use it as a finite time stopping criterion for the otherwise asymptotic consensus algorithm. The practical utility of the algorithm is illustrated through experiments where each agent is instantiated by a NodeJS socket.io server.