Abstract
Several classes of multicommodity networks have been shown to have the property that they can be transformed to equivalent uncapacitated single commodity flow problems. We show that many of these networks can be further reduced to smaller, semi-capacitated flow problems using the inverse of a result of Ford and Fulkerson. This appears to be a useful computationally-oriented tool for developing practically efficient algorithms. These concepts are also used to establish a generalization of a previous result concerning multicommodity transportation problems.
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Evans, J.R. On equivalent representations of certain multicommodity networks as single commodity flow problems. Mathematical Programming 15, 92–99 (1978). https://doi.org/10.1007/BF01609003
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DOI: https://doi.org/10.1007/BF01609003