  We introduce \emph{ScalableMax}, a novel communication scheme for achieving
max-consensus in a network of multiple agents which harnesses the interference
in the wireless channel as well as its multicast capabilities. In a
sufficiently dense network, the amount of communication resources required
grows logarithmically with the number of nodes, while in state-of-the-art
approaches, this growth is at least linear. ScalableMax can handle additive
noise and works well in a high SNR regime. For medium and low SNR, we propose
the \emph{ScalableMax-EC} scheme, which extends the ideas of ScalableMax by
introducing a novel error correction scheme. It achieves lower error rates at
the cost of using more channel resources. However, it preserves the logarithmic
growth with the number of agents in the system.
