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Partial inverse maximum spanning tree problem under the Chebyshev norm

Author

Listed:
  • Xianyue Li

    (Lanzhou University)

  • Ruowang Yang

    (Lanzhou University)

  • Heping Zhang

    (Lanzhou University)

  • Zhao Zhang

    (Zhejiang Normal University)

Abstract

Given an edge weighted graph, and an acyclic edge set, the target of the partial inverse maximum spanning tree problem (PIMST) is to get a new weight function such that the given set is included in some maximum spanning tree associated with the new function, and the difference between the two functions is minimum. In this paper, we research PIMST under the Chebyshev norm. Firstly, the definition of extreme optimal solution is introduced, and its some properties are gained. Based on these properties, a polynomial scale optimal value candidate set is obtained. Finally, strongly polynomial-time algorithms for solving this problem are proposed. Thus, the computational complexity of PIMST is completely solved.

Suggested Citation

  • Xianyue Li & Ruowang Yang & Heping Zhang & Zhao Zhang, 2022. "Partial inverse maximum spanning tree problem under the Chebyshev norm," Journal of Combinatorial Optimization, Springer, vol. 44(5), pages 3331-3350, December.
    • Handle: RePEc:spr:jcomop:v:44:y:2022:i:5:d:10.1007_s10878-022-00903-9
    DOI: 10.1007/s10878-022-00903-9
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    References listed on IDEAS

    as
    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.
    2. 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.
    3. Xianyue Li & Zhao Zhang & Ding-Zhu Du, 2018. "Partial inverse maximum spanning tree in which weight can only be decreased under $$l_p$$ l p -norm," Journal of Global Optimization, Springer, vol. 70(3), pages 677-685, March.
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    5. Dorit S. Hochbaum, 2003. "Efficient Algorithms for the Inverse Spanning-Tree Problem," Operations Research, INFORMS, vol. 51(5), pages 785-797, October.
    6. Xiucui Guan & Xinyan He & Panos M. Pardalos & Binwu Zhang, 2017. "Inverse max $$+$$ + sum spanning tree problem under Hamming distance by modifying the sum-cost vector," Journal of Global Optimization, Springer, vol. 69(4), pages 911-925, December.
    7. Hui Wang & Xiucui Guan & Qiao Zhang & Binwu Zhang, 2021. "Capacitated inverse optimal value problem on minimum spanning tree under bottleneck Hamming distance," Journal of Combinatorial Optimization, Springer, vol. 41(4), pages 861-887, May.
    8. Xianyue Li & Zhao Zhang & Ruowang Yang & Heping Zhang & Ding-Zhu Du, 2020. "Approximation algorithms for capacitated partial inverse maximum spanning tree problem," Journal of Global Optimization, Springer, vol. 77(2), pages 319-340, June.
    9. Cai, Mao-Cheng & Duin, C.W. & Yang, Xiaoguang & Zhang, Jianzhong, 2008. "The partial inverse minimum spanning tree problem when weight increase is forbidden," European Journal of Operational Research, Elsevier, vol. 188(2), pages 348-353, July.
    10. Omar Ben-Ayed & Charles E. Blair, 1990. "Computational Difficulties of Bilevel Linear Programming," Operations Research, INFORMS, vol. 38(3), pages 556-560, June.
    11. Zhao Zhang & Shuangshuang Li & Hong-Jian Lai & Ding-Zhu Du, 2016. "Algorithms for the partial inverse matroid problem in which weights can only be increased," Journal of Global Optimization, Springer, vol. 65(4), pages 801-811, August.
    12. Xiucui Guan & Panos Pardalos & Xia Zuo, 2015. "Inverse Max + Sum spanning tree problem by modifying the sum-cost vector under weighted $$l_\infty $$ l ∞ Norm," Journal of Global Optimization, Springer, vol. 61(1), pages 165-182, January.
    13. Binwu Zhang & Xiucui Guan & Panos M. Pardalos & Hui Wang & Qiao Zhang & Yan Liu & Shuyi Chen, 2021. "The lower bounded inverse optimal value problem on minimum spanning tree under unit $$l_{\infty }$$ l ∞ norm," Journal of Global Optimization, Springer, vol. 79(3), pages 757-777, March.
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