Average consensus via max consensus

Since intuition states that it is simple and fast to compute maxima over networks, we aim at understanding the limits of computing averages over networks through computing maxima. We thus build on top of max-consensus based networks' cardinality estimation protocols a novel estimation strategy that infers averages through computing maxima of opportunely and locally generated random initial conditions. We motivate the max-consensus strategy explaining why it satisfies practical requirements, we characterize completely its statistical properties, and we analyze when and under which conditions it performs favorably against classical linear consensus strategies in static Cayley graphs.