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The lower bounded inverse optimal value problem on minimum spanning tree under unit $$l_{\infty }$$ l ∞ norm

Author

Listed:
  • Binwu Zhang

    (Hohai University
    Hohai University)

  • Xiucui Guan

    (Southeast University)

  • Panos M. Pardalos

    (University of Florida
    Higher School of Economics)

  • Hui Wang

    (Southeast University)

  • Qiao Zhang

    (Southeast University)

  • Yan Liu

    (Hohai University
    Hohai University)

  • Shuyi Chen

    (Hohai University)

Abstract

We consider the lower bounded inverse optimal value problem on minimum spanning tree under unit $$l_{\infty }$$ l ∞ norm. Given an edge weighted connected undirected network $$G=(V,E,\varvec{w})$$ G = ( V , E , w ) , a spanning tree $$T^0$$ T 0 , a lower bound vector $$\varvec{l}$$ l and a value K, we aim to find a new weight vector $$\bar{\varvec{w}}$$ w ¯ respecting the lower bound such that $$T^0$$ T 0 is a minimum spanning tree under the vector $$\bar{\varvec{w}}$$ w ¯ with weight K, and the objective is to minimize the modification cost under unit $$l_{\infty }$$ l ∞ norm. We present a mathematical model of the problem. After analyzing optimality conditions of the problem, we develop a strongly polynomial time algorithm with running time O(|V||E|). Finally, we give an example to demonstrate the algorithm and present the numerical experiments.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:79:y:2021:i:3:d:10.1007_s10898-020-00947-3
    DOI: 10.1007/s10898-020-00947-3
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    References listed on IDEAS

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    1. Timothy C. Y. Chan & Taewoo Lee & Daria Terekhov, 2019. "Inverse Optimization: Closed-Form Solutions, Geometry, and Goodness of Fit," Management Science, INFORMS, vol. 65(3), pages 1115-1135, March.
    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.
    4. 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.
    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. 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.
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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. 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.

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