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This paper presents a method for the inverse fractional matching problem. We show that the dual of this inverse problem can be transformed into the circulation flow problem on a directed bipartite graph which can be solved easily. We also give an algorithm to obtain the primal optimum solution of the inverse problem from its dual optimum solution by solving a shortest path problem. Furthermore, we generalize this method to solve the inverse symmetric transportation problem.doi:10.1017/s0334270000010572 fatcat:mqrlklbewzh4zjc7tdkdx5ufrq