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The shortest path improvement problems under Hamming distance

Author

Listed:
  • Binwu Zhang

    (Hohai University)

  • Jianzhong Zhang

    (The Chinese University of Hong Kong)

  • Liqun Qi

    (Hong Kong Polytechnic University)

Abstract

In this paper, we consider the shortest path improvement problems under Hamming distance (SPIH), where the weights of edges can be modified only within given intervals. Two models are considered: the general SPIH problem and the SPIH problem with a single pair of required vertices. For the first problem, we show that it is strongly NP-hard. For the second problem, we show that even if the network is a chain network, it is still NP-hard.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:12:y:2006:i:4:d:10.1007_s10878-006-9000-1
    DOI: 10.1007/s10878-006-9000-1
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    Cited by:

    1. 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.
    2. 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.

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