On a generalized minimax realization problem on flow networks

If a matrix, which represents the capacities between vertices for every vertex pair, is given, then the necessary and sufficient conditions are known for the existence of networks satisfying given conditions. However, it is rare that the capacities between all vertex pairs are given. Therefore we give a matrix which is not always the terminal capacity matrix, and we discuss the realization of the matrix. In this case, we consider minimizing the differences between capacities in the network and elements of the matrix. In this paper, we generalize the concept of difference and propose an algorithm to construct the network