Abstract
As far as we know, for most polynomially solvable network optimization problems, their inverse problems under l 1 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 l 1 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 l 1 norm it can be solved by the ellipsoid method. Therefore, inverse problems of maximum-weight perfect matching under l 1 and l ∞ norms are solvable in polynomial time.
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Liu, Z., Zhang, J. On Inverse Problems of Optimum Perfect Matching. Journal of Combinatorial Optimization 7, 215–228 (2003). https://doi.org/10.1023/A:1027305419461
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DOI: https://doi.org/10.1023/A:1027305419461