An algorithm for solving min‐cost or max‐flow multicommodity flow problems is described. It is a specialization of the simplex method, which takes advantage of the special structure of the multicommodity problem. The only nongraph or nonadditive operations in a cycle involve the inverse of a working basis, whose dimension is the number of currently saturated arcs. Efficient relations for updating this inverse are derived.
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Hartman et al. (1971) studied this question.