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The authors study the convergence of the average consensus algorithm in wireless networks in the presence of interference. For regular lattices with periodic boundary conditions, they characterise the convergence properties of an optimal Time Division Multiple Access (TDMA) protocol that maximises the speed of convergence on these networks. They provide analytical upper and lower bounds for the convergence rate for these networks. Their results show that in an interference-limited scenario, the fastest converging interconnection topology for the consensus algorithm crucially depends on the geometry of node placement.
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