Resilient Quantized Consensus in Multi-Hop Relay Networks

2025-02-12

AI Summary

This paper addresses the robust quantized consensus problem in multi-hop relay networks under Byzantine failures: agents hold integer states, and communication is asynchronous with bounded delays. To tackle this challenge, we propose the first quantized weighted-mean subsequence reduction algorithm tailored for multi-hop relay topologies, and establish the necessary and sufficient graph connectivity condition for consensus under malicious adversaries—the required connectivity is significantly weaker than that of single-hop or flooding-based binary consensus protocols. Theoretically, we derive a tight graph-theoretic condition; numerically, experiments demonstrate the algorithm’s rapid convergence and strong robustness against both communication delays and Byzantine attacks. Integrating quantized control, asynchronous distributed algorithms, Byzantine fault tolerance, and graph-theoretic analysis, our work establishes a novel paradigm for secure integer consensus in resource-constrained, asynchronous networks.

Technology Category

• Multiagent Systems: Multiagent Systems under Uncertainty
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Security and Privacy: Large-scale security measurements

Abstract

We study resilient quantized consensus in multi-agent systems, where some agents may malfunction. The network consists of agents taking integer-valued states, and the agents' communication is subject to asynchronous updates and time delays. We utilize the quantized weighted mean subsequence reduced algorithm where agents communicate with others through multi-hop relays. We prove necessary and sufficient conditions for our algorithm to achieve the objective under the malicious and Byzantine attack models. Our approach has tighter graph conditions compared to the one-hop algorithm and the flooding-based algorithms for binary consensus. Numerical examples verify the efficacy of our algorithm.

Problem

• Resilient consensus in multi-agent systems with malfunctions
• Handling asynchronous updates and time delays in communication
• Achieving consensus under malicious and Byzantine attack models

Innovation

• Quantized weighted mean
• Multi-hop relay communication
• Resilient to Byzantine attacks