A simple median-based resilient consensus algorithm

This paper studies the problem of reaching consensus resiliently in the presence of misbehaving nodes. We design a consensus algorithm where, at each time-step, each node updates its value as a weighted average of its own value and the median of its neighbors' values. This algorithm requires no global information about the network, and is computationally lightweight. We develop a novel graph property that we term excess robustness, and use this property to characterize the ability of the median algorithm to succeed under various fault models. We also provide a construction for excess robust graphs. We show that the sensitivity of this algorithm varies greatly under different fault models, and make connections to related ideas from the literature on contagion and graphical games.