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We establish a tight max-flow min-cut theorem for multi-commodity routing in random geometric graphs. We show that, as the number of nodes in the network n tends to infinity, the maximum concurrent flow (MCF) and the minimum cut-sparsity scale as ??(n2r3(n)/k), for a random choice of k = ??(n) source-destination pairs, where n and r(n) are the number of nodes and the communication range in the network...
We establish a tight max-flow min-cut theorem for multicommodity routing in random geometric graphs. We show that, as the number of nodes in the network n tends to infinity, the maximum concurrent flow (MCF) and the minimum cut-capacity scale as Theta(n2r3(n)/k) for a random choice of k ges Theta(n) source-destination pairs, where r(n) is the communication range in the network. We exploit the fact,...
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