Abstract

AbstractSeveral synthesis methods to construct a flow network with the minimum sum of edge capacities for a given terminal capacity matrix have already been presented. However, there are networks that cannot be constructed by the known method.For the case where the given terminal capacity matrix is called elementary terminal capacity matrix, a synthesis method is presented that can construct any undirected flow network with the minimum sum of edge capacities. This paper is based on that synthesis method and presents a synthesis method that can construct any undirected flow network with the minimum sum of edge capacities for a given terminal capacity matrix with that matrix as the terminal capacity matrix.

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