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Capacitated partial inverse maximum spanning tree under the weighted Hamming distance

Author

Listed:
  • Xianyue Li

    (Lanzhou University)

  • Xichao Shu

    (Lanzhou University)

  • Huijing Huang

    (Lanzhou University)

  • Jingjing Bai

    (Lanzhou University)

Abstract

Given an edge weighted graph, and an acyclic edge set, the goal of partial inverse maximum spanning tree problem is to modify the weight function as little as possible such that there exists a maximum spanning tree with respect to the new weight function containing the given edge set. In this paper, we consider this problem with capacitated constraint under the weighted Hamming distance. Under the weighted sum Hamming distance, if the given edge set has at least two edges, we show that this problem is APX-Hard even without the capacitated constraint; if the given edge set contains only one edge, we present a strongly polynomial time algorithm to solve it. Under the weighted bottleneck Hamming distance, we present an algorithm with time complexity $$O(m\log ^2 m)$$ O ( m log 2 m ) , where m is the number of edges of the given graph.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:38:y:2019:i:4:d:10.1007_s10878-019-00433-x
    DOI: 10.1007/s10878-019-00433-x
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    References listed on IDEAS

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    8. 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.
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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. 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.
    3. 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.
    4. 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.

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