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Weighted Inverse Minimum Spanning Tree Problems Under Hamming Distance

Author

Listed:
  • Yong He

    (Zhejiang University)

  • Binwu Zhang

    (Zhejiang University)

  • Enyu Yao

    (Zhejiang University)

Abstract

In this paper, we consider weighted inverse minimum spanning tree problems under Hamming distance. Three models are considered: unbounded case, unbounded case with forbidden edges, and general bounded case. In terms of the method for minimum-weight node cover problem on bipartite graph, we present their respective strongly polynomial algorithms.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:9:y:2005:i:1:d:10.1007_s10878-005-5486-1
    DOI: 10.1007/s10878-005-5486-1
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    References listed on IDEAS

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    1. Jianzhong Zhang & Zhongfan Ma, 1999. "Solution Structure of Some Inverse Combinatorial Optimization Problems," Journal of Combinatorial Optimization, Springer, vol. 3(1), pages 127-139, July.
    2. 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.
    3. Jianzhong Zhang & Zhenhong Liu, 2002. "A General Model of Some Inverse Combinatorial Optimization Problems and Its Solution Method Under l ∞ Norm," Journal of Combinatorial Optimization, Springer, vol. 6(2), pages 207-227, June.
    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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    Citations

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    Cited by:

    1. Longcheng Liu & Jianzhong Zhang, 2006. "Inverse maximum flow problems under the weighted Hamming distance," Journal of Combinatorial Optimization, Springer, vol. 12(4), pages 395-408, December.
    2. 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.
    3. 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.
    4. Binwu Zhang & Jianzhong Zhang & Yong He, 2005. "The Center Location Improvement Problem Under the Hamming Distance," Journal of Combinatorial Optimization, Springer, vol. 9(2), pages 187-198, March.
    5. 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.
    6. 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.
    7. 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.
    8. Binwu Zhang & Jianzhong Zhang & Liqun Qi, 2006. "The shortest path improvement problems under Hamming distance," Journal of Combinatorial Optimization, Springer, vol. 12(4), pages 351-361, December.
    9. Binwu Zhang & Xiucui Guan & Panos M. Pardalos & Chunyuan He, 2018. "An Algorithm for Solving the Shortest Path Improvement Problem on Rooted Trees Under Unit Hamming Distance," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 538-559, August.
    10. 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.
    11. 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.
    12. 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.
    13. Jiang, Yiwei & Liu, Longcheng & Wu, Biao & Yao, Enyu, 2010. "Inverse minimum cost flow problems under the weighted Hamming distance," European Journal of Operational Research, Elsevier, vol. 207(1), pages 50-54, November.
    14. 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.
    15. 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.
    16. 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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