A Graph-Relaxed Method for Byzantine-Resilient Distributed Multidimensional Consensus

In recent years, multi-agent systems have attracted considerable attention, particularly with regard to their security dimensions in presence of Byzantine attacks. However, existing Byzantine-resilient algorithms rely on relatively strong network connectivity conditions, raising the question of whether these requirements can be relaxed while balancing performance trade-offs. To address this, we partition the full state of each agent into multiple blocks and leverage an essentially cyclic rule for each block update, based on which a filter-based block consensus algorithm is proposed. This approach not only relaxes network connectivity requirements but also reduces bandwidth usage per update, making it suitable for a wider range of networks. Theoretical analysis demonstrates that the algorithm achieves linear consensus speed, ensuring fast and robust aggregation among nodes despite Byzantine agents.