# A Scalable Max-Consensus Protocol For Noisy Ultra-Dense Networks

## TL;DR

ScalableMax is a new wireless communication protocol that efficiently achieves max-consensus in dense networks by exploiting interference, with logarithmic resource growth and robustness to noise, enhanced by an error correction extension.

## Contribution

Introduces ScalableMax, a scalable max-consensus protocol leveraging interference and multicast in dense networks, with an error correction extension for noisy conditions.

## Key findings

- Resource growth is logarithmic with network size in dense settings.
- ScalableMax handles additive noise effectively in high SNR regimes.
- ScalableMax-EC reduces error rates at the expense of more resources.

## Abstract

We introduce \emph{ScalableMax}, a novel communication scheme for achieving max-consensus in a network of multiple agents which harnesses the interference in the wireless channel as well as its multicast capabilities. In a sufficiently dense network, the amount of communication resources required grows logarithmically with the number of nodes, while in state-of-the-art approaches, this growth is at least linear. ScalableMax can handle additive noise and works well in a high SNR regime. For medium and low SNR, we propose the \emph{ScalableMax-EC} scheme, which extends the ideas of ScalableMax by introducing a novel error correction scheme. It achieves lower error rates at the cost of using more channel resources. However, it preserves the logarithmic growth with the number of agents in the system.