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The authors study the convergence of the average consensus algorithm in wireless networks in the presence of interference. It is well-known that convergence of the consensus algorithm improves with network connectivity. However, from a networking standpoint, highly connected wireless networks may have lower throughput because of increased interference. This raises an interesting question: What is the effect of increased network connectivity on the convergence of the consensus algorithm, given that this connectivity comes at the cost of lower network throughput? They address this issue for two types of networks: regular lattices with periodic boundary conditions, and a hierarchical network where a backbone of nodes arranged as a regular lattice supports a collection of randomly placed nodes.
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