Byzantine fault-tolerant distributed set intersection with redundancy
Shuo Liu, Nitin H. Vaidya
TL;DR
This work analyzes Byzantine fault-tolerant distributed set intersection and its ties to Byzantine optimization. It introduces $2f$-redundancy as a core solvability property and derives necessary and sufficient conditions on centralized and decentralized architectures, including generalized graphs and asynchronous regimes. The authors show how redundancy translates between set intersection and optimization, offering constructive algorithms (centralized and decentralized) and extending results to constrained/unconstrained and asynchronous settings. The results unify fault-tolerant intersection and optimization under a common graph-theoretic framework, enabling robust multi-agent inference on heterogeneous networks with Byzantine adversaries.
Abstract
In this report, we study the problem of Byzantine fault-tolerant distributed set intersection and the importance of redundancy in solving this problem. Specifically, consider a distributed system with $n$ agents, each of which has a local set. There are up to $f$ agents that are Byzantine faulty. The goal is to find the intersection of the sets of the non-faulty agents. We derive the Byzantine set intersection problem from the Byzantine optimization problem. We present the definition of $2f$-redundancy, and identify the necessary and sufficient condition if the Byzantine set intersection problem can be solved if a certain redundancy property is satisfied, and then present an equivalent condition. We further extend our results to arbitrary communication graphs in a decentralized setting. Finally, we present solvability results for the Byzantine optimization problem, inspired by our findings on Byzantine set intersection. The results we provide are for synchronous and asynchronous systems both.