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The inverse connected p-median problem on block graphs under various cost functions

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  • Kien Trung Nguyen

    (Teacher College, Can Tho University)

  • Nguyen Thanh Hung

    (Teacher College, Can Tho University)

Abstract

We address the problem of modifying vertex weights of a block graph at minimum total cost so that a predetermined set of p connected vertices becomes a connected p-median on the perturbed block graph. This problem is the so-called inverse connected p-median problem on block graphs. We consider the problem on a block graph with uniform edge lengths under various cost functions, say rectilinear norm, Chebyshev norm, and bottleneck Hamming distance. To solve the problem, we first find an optimality criterion for a set that is a connected p-median. Based on this criterion, we can formulate the problem as a convex or quasiconvex univariate optimization problem. Finally, we develop combinatorial algorithms that solve the problems under the three cost functions in $$O(n\log n)$$ O ( n log n ) time, where n is the number of vertices in the underlying block graph.

Suggested Citation

  • Kien Trung Nguyen & Nguyen Thanh Hung, 2020. "The inverse connected p-median problem on block graphs under various cost functions," Annals of Operations Research, Springer, vol. 292(1), pages 97-112, September.
    • Handle: RePEc:spr:annopr:v:292:y:2020:i:1:d:10.1007_s10479-020-03651-3
    DOI: 10.1007/s10479-020-03651-3
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    References listed on IDEAS

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    1. Kien Trung Nguyen, 2016. "Inverse 1-Median Problem on Block Graphs with Variable Vertex Weights," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 944-957, March.
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    4. Liying Kang & Jianjie Zhou & Erfang Shan, 2018. "Algorithms for connected p-centdian problem on block graphs," Journal of Combinatorial Optimization, Springer, vol. 36(1), pages 252-263, July.
    5. Burkard, Rainer E. & Galavii, Mohammadreza & Gassner, Elisabeth, 2010. "The inverse Fermat-Weber problem," European Journal of Operational Research, Elsevier, vol. 206(1), pages 11-17, October.
    6. Nguyen, Kien Trung & Chassein, André, 2015. "The inverse convex ordered 1-median problem on trees under Chebyshev norm and Hamming distance," European Journal of Operational Research, Elsevier, vol. 247(3), pages 774-781.
    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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    11. Kien Trung Nguyen & Huong Nguyen-Thu & Nguyen Thanh Hung, 2018. "On the complexity of inverse convex ordered 1-median problem on the plane and on tree networks," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(2), pages 147-159, October.
    12. Kien Trung Nguyen, 2019. "The inverse 1-center problem on cycles with variable edge lengths," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(1), pages 263-274, March.
    13. 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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