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General restricted inverse assignment problems under $$l_1$$l1 and $$l_\infty $$l∞ norms

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  • Qin Wang

    (China Jiliang University)

  • Tianyu Yang

    (China Jiliang University)

  • Longshu Wu

    (China Jiliang University)

Abstract

In this paper, we study the general restricted inverse assignment problems, in which we can only change the costs of some specific edges of an assignment problem as less as possible, so that a given assignment becomes the optimal one. Under $$l_1$$l1 norm, we formulate this problem as a linear programming. Then we mainly consider two cases. For the case when the specific edges are only belong to the given assignment, we show that this problem can be reduced to some variations of the minimum cost flow problems. For the case when every specific edge does not belong to the given assignment, we show that this problem can be solved by a minimum cost circulation problem. In both cases, we present some combinatorial algorithms which are strongly polynomial. We also study this problem under the $$l_\infty $$l∞ norm. We propose a binary search algorithm and prove that the optimal solution can be obtained in polynomial time.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v::y::i::d:10.1007_s10878-020-00577-1
    DOI: 10.1007/s10878-020-00577-1
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    References listed on IDEAS

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    1. Zhenhong Liu & Jianzhong Zhang, 2003. "On Inverse Problems of Optimum Perfect Matching," Journal of Combinatorial Optimization, Springer, vol. 7(3), pages 215-228, September.
    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.
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