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Partial inverse maximum spanning tree in which weight can only be decreased under $$l_p$$ l p -norm

Author

Listed:
  • Xianyue Li

    (Lanzhou University)

  • Zhao Zhang

    (Zhejiang Normal University)

  • Ding-Zhu Du

    (University of Texas at Dallas)

Abstract

The maximum or minimum spanning tree problem is a classical combinatorial optimization problem. In this paper, we consider the partial inverse maximum spanning tree problem in which the weight function can only be decreased. Given a graph, an acyclic edge set, and an edge weight function, the goal of this problem is to decrease weights as little as possible such that there exists with respect to function containing the given edge set. If the given edge set has at least two edges, we show that this problem is APX-Hard. If the given edge set contains only one edge, we present a polynomial time algorithm.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:70:y:2018:i:3:d:10.1007_s10898-017-0554-5
    DOI: 10.1007/s10898-017-0554-5
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    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 & 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. 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.
    3. 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.
    4. Junhua Jia & Xiucui Guan & Qiao Zhang & Xinqiang Qian & Panos M. Pardalos, 2022. "Inverse max+sum spanning tree problem under weighted $$l_{\infty }$$ l ∞ norm by modifying max-weight vector," Journal of Global Optimization, Springer, vol. 84(3), pages 715-738, November.
    5. 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.
    6. 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.
    7. Javad Tayyebi & Ali Reza Sepasian, 2020. "Partial inverse min–max spanning tree problem," Journal of Combinatorial Optimization, Springer, vol. 40(4), pages 1075-1091, November.

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