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Lexicographically optimal balanced networks

We consider the problem of allocating bandwidth between two endpoints of a backbone network so that no parts of the network are unnecessarily loaded. We formulate the problem as lexicographic optimization, and develop algorithms for its solution. The solution consists of (a) identifying a cut in the network where the optimal load can be determined on all the links of the cut, and (b) considering the same problem in each of the subnetworks to which the cut is dividing the original network.