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Capacitated inverse optimal value problem on minimum spanning tree under bottleneck Hamming distance

Author

Listed:
  • Hui Wang

    (Southeast University)

  • Xiucui Guan

    (Southeast University)

  • Qiao Zhang

    (Southeast University)

  • Binwu Zhang

    (Hohai University)

Abstract

We consider the capacitated inverse optimal value problem on minimum spanning tree under Hamming distance. Given a connected undirected network $$G=(V,E)$$ G = ( V , E ) and a spanning tree $$T^0$$ T 0 , we aim to modify the weights of the edges such that $$T^0$$ T 0 is not only the minimum spanning tree under the new weights but also the weight of $$T^0$$ T 0 is equal to a given value K. The objective is to minimize the modification cost under bottleneck Hamming distance. We add a lower bound l and an upper bound u on the modification of weights and consider three cases (uncapacitated, lower bounded, capacitated) of the problem based on the bound vectors. Suppose $$l=-\,\infty , u=+\,\infty $$ l = - ∞ , u = + ∞ in the uncapacitated problem, $$l>-\,\infty , u=+\,\infty $$ l > - ∞ , u = + ∞ in the lower bounded problem and $$l>-\,\infty , u - ∞ , u

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:41:y:2021:i:4:d:10.1007_s10878-021-00721-5
    DOI: 10.1007/s10878-021-00721-5
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Xiaoguang Yang & Jianzhong Zhang, 2007. "Some inverse min-max network problems under weighted l 1 and l ∞ norms with bound constraints on changes," Journal of Combinatorial Optimization, Springer, vol. 13(2), pages 123-135, February.
    4. 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.
    5. P. T. Sokkalingam & Ravindra K. Ahuja & James B. Orlin, 1999. "Solving Inverse Spanning Tree Problems Through Network Flow Techniques," Operations Research, INFORMS, vol. 47(2), pages 291-298, April.
    6. 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.
    7. 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.
    8. 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.
    9. Dorit S. Hochbaum, 2003. "Efficient Algorithms for the Inverse Spanning-Tree Problem," Operations Research, INFORMS, vol. 51(5), pages 785-797, October.
    10. 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.
    11. 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.
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    Cited by:

    1. 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.
    2. Qiao Zhang & Xiucui Guan & Junhua Jia & Xinqiang Qian & Panos M. Pardalos, 2023. "The restricted inverse optimal value problem on shortest path under $$l_1$$ l 1 norm on trees," Journal of Global Optimization, Springer, vol. 86(1), pages 251-284, May.

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