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On Inverse Problems of Optimum Perfect Matching

Author

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  • Zhenhong Liu

    (Institute of Systems Science, Academia Sinica)

  • Jianzhong Zhang

    (City University of Hong Kong)

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.

Suggested Citation

  • Zhenhong Liu & Jianzhong Zhang, 2003. "On Inverse Problems of Optimum Perfect Matching," Journal of Combinatorial Optimization, Springer, vol. 7(3), pages 215-228, September.
    • Handle: RePEc:spr:jcomop:v:7:y:2003:i:3:d:10.1023_a:1027305419461
    DOI: 10.1023/A:1027305419461
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    References listed on IDEAS

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    1. Cai Mao-Cheng & Yanjun Li, 1997. "Inverse Matroid Intersection Problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 45(2), pages 235-243, June.
    2. Jianzhong Zhang & Zhongfan Ma, 1999. "Solution Structure of Some Inverse Combinatorial Optimization Problems," Journal of Combinatorial Optimization, Springer, vol. 3(1), pages 127-139, July.
    3. Wei, Quanling & Zhang, Jianzhong & Zhang, Xiangsun, 2000. "An inverse DEA model for inputs/outputs estimate," European Journal of Operational Research, Elsevier, vol. 121(1), pages 151-163, February.
    4. Jianzhong Zhang & Mao Cai, 1998. "Inverse problem of minimum cuts," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 47(1), pages 51-58, February.
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    Cited by:

    1. Qin Wang & Tianyu Yang & Longshu Wu, 0. "General restricted inverse assignment problems under $$l_1$$l1 and $$l_\infty $$l∞ norms," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-16.
    2. Clemens Heuberger, 2004. "Inverse Combinatorial Optimization: A Survey on Problems, Methods, and Results," Journal of Combinatorial Optimization, Springer, vol. 8(3), pages 329-361, September.
    3. Qin Wang & Tianyu Yang & Longshu Wu, 2022. "General restricted inverse assignment problems under $$l_1$$ l 1 and $$l_\infty $$ l ∞ norms," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 2040-2055, October.

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