Resilient Consensus with Multi-hop Communication

TL;DR

This paper extends resilient consensus algorithms to multi-hop communication networks, demonstrating that multi-hop connectivity can reduce network robustness requirements and analyzing the impact of communication delays on the W-MSR algorithm.

Contribution

It introduces a multi-hop version of the W-MSR algorithm for resilient consensus and analyzes its performance with delays, reducing connectivity requirements compared to one-hop methods.

Findings

Multi-hop communication reduces network robustness requirements.

The multi-hop W-MSR algorithm maintains resilience with delays.

Analysis shows effectiveness in adversarial environments.

Abstract

In this paper, we study the problem of resilient consensus for a multi-agent network where some of the nodes might be adversarial, attempting to prevent consensus by transmitting faulty values. Our approach is based on that of the so-called weighted mean subsequence reduced (W-MSR) algorithm with a special emphasis on its use in agents capable to communicate with multi-hop neighbors. The MSR algorithm is a powerful tool for achieving resilient consensus under minimal requirements for network structures, characterized by the class of robust graphs. Our analysis highlights that through multi-hop communication, the network connectivity can be reduced especially in comparison with the common one-hop communication case. Moreover, we analyze the multi-hop W-MSR algorithm with delays in communication since the values from different multi-hop neighbors may arrive at the agents at different time steps.