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Iterative distributed algorithms are studied for computing arithmetic averages over networks of agents
connected through memoryless broadcast erasure channels. These algorithms do not require the agents
to have any knowledge about the global network structure or size. Almost sure convergence to state
agreement is proved, and the communication and computational complexities of the algorithms are
analyzed. Both the number of transmissions and the number of computations performed by each agent of
the network are shown to grow not faster than poly-logarithmically in the desired precision. The impact of
the graph topology on the algorithms’ performance is analyzed as well. Moreover, it is shown how, in the
presence of noiseless communication feedback, one can modify the algorithms, significantly improving
their performance versus complexity trade-off
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