On Inverse Problems of Optimum Perfect Matching

As far as we know, for most polynomially solvable network optimization problems, their inverse problems under l1 or l∞ norm have been studied, except the inverse maximum-weight matching problem in non-bipartite networks. In this paper we discuss the inverse problem of maximum-weight perfect matching in a non-bipartite network under l1 and l∞ norms. It has been proved that the inverse maximum-weight perfect matching under l∞ norm can be formulated as a maximum-mean alternating cycle problem of an undirected network, and can be solved in polynomial time by a binary search algorithm and in strongly polynomial time by an ascending algorithm, and under l1 norm it can be solved by the ellipsoid method. Therefore, inverse problems of maximum-weight perfect matching under l1 and l∞ norms are solvable in polynomial time.