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Characterizing network capacity is one of the central problems in network information theory. While this problem is in general unsolved, there has been considerable success in two research fronts. The first one focuses on single-flow multi-hop networks, in which one source sends the same message to one or more destinations. In this scenario, all destination nodes require the same message, and there is effectively only one information stream in the network. Starting from the max-flow min-cut theorem of Ford-Fulkerson, there has been significant progress on this problem.
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