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Weighted inverse maximum perfect matching problems under the Hamming distance

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  • Longcheng Liu
  • Enyu Yao

Abstract

Given an undirected network G(V, E, c) and a perfect matching M 0 , the inverse maximum perfect matching problem is to modify the cost vector as little as possible such that the given perfect matching M 0 can form a maximum perfect matching. The modification can be measured by different norms. In this paper, we consider the weighted inverse maximum perfect matching problems under the Hamming distance, where we use the weighted Hamming distance to measure the modification of the edges. We consider both of the sum-type and the bottleneck-type problems. For the general case of the sum-type case, we show it is NP-hard. For the bottleneck-type, we present a strongly polynomial algorithm which can be done in O(m · n 3 ). Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Longcheng Liu & Enyu Yao, 2013. "Weighted inverse maximum perfect matching problems under the Hamming distance," Journal of Global Optimization, Springer, vol. 55(3), pages 549-557, March.
    • Handle: RePEc:spr:jglopt:v:55:y:2013:i:3:p:549-557
    DOI: 10.1007/s10898-012-9901-8
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    References listed on IDEAS

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    1. Yong He & Binwu Zhang & Enyu Yao, 2005. "Weighted Inverse Minimum Spanning Tree Problems Under Hamming Distance," Journal of Combinatorial Optimization, Springer, vol. 9(1), pages 91-100, February.
    2. Binwu Zhang & Jianzhong Zhang & Yong He, 2005. "The Center Location Improvement Problem Under the Hamming Distance," Journal of Combinatorial Optimization, Springer, vol. 9(2), pages 187-198, March.
    3. Longcheng Liu & Enyu Yao, 2007. "A Weighted Inverse Minimum Cut Problem Under The Bottleneck Type Hamming Distance," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 24(05), pages 725-736.
    4. 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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    Cited by:

    1. Xianyue Li & Xichao Shu & Huijing Huang & Jingjing Bai, 2019. "Capacitated partial inverse maximum spanning tree under the weighted Hamming distance," Journal of Combinatorial Optimization, Springer, vol. 38(4), pages 1005-1018, November.

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