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In this paper, the authors develop the theory of High Dimensional Consensus (HDC), a general class of distributed algorithms in large-scale networks. HDC relies only on local information, local communication, and low-order computation, and, hence, is ideally suited to implement network tasks under resource constraints, e.g., in sparse networks with a limited computation budget. HDC, in general, is iterative because the underlying sparsity of the network limits the information flow. Each HDC iteration is a simple (linear or non-linear) update at each node in the network.
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