IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v292y2020i1d10.1007_s10479-020-03651-3.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-020-03651-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10479-020-03651-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kien Nguyen & Lam Anh, 2015. "Inverse $$k$$ k -centrum problem on trees with variable vertex weights," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(1), pages 19-30, August.
    2. 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.
    3. Dorit S. Hochbaum, 2003. "Efficient Algorithms for the Inverse Spanning-Tree Problem," Operations Research, INFORMS, vol. 51(5), pages 785-797, October.
    4. 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.
    5. 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.
    6. 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.
    7. Ravindra K. Ahuja & James B. Orlin, 2001. "Inverse Optimization," Operations Research, INFORMS, vol. 49(5), pages 771-783, October.
    8. 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.
    9. 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.
    10. 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.
    11. Egon Balas & Eitan Zemel, 1980. "An Algorithm for Large Zero-One Knapsack Problems," Operations Research, INFORMS, vol. 28(5), pages 1130-1154, October.
    12. Elisabeth Gassner, 2012. "An inverse approach to convex ordered median problems in trees," Journal of Combinatorial Optimization, Springer, vol. 23(2), pages 261-273, February.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nguyen, Kien Trung & Hung, Nguyen Thanh, 2021. "The minmax regret inverse maximum weight problem," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    2. Esmaeil Afrashteh & Behrooz Alizadeh & Fahimeh Baroughi & Kien Trung Nguyen, 2018. "Linear Time Optimal Approaches for Max-Profit Inverse 1-Median Location Problems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(05), pages 1-22, October.
    3. Alizadeh, Behrooz & Afrashteh, Esmaeil, 2020. "Budget-constrained inverse median facility location problem on tree networks," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    4. 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.
    5. 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.
    6. 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.
    7. Le Xuan Dai & Kien Trung Nguyen & Le Phuong Thao & Pham Thi Vui, 2024. "Some robust inverse median problems on trees with interval costs," Computational Management Science, Springer, vol. 21(2), pages 1-25, December.
    8. Behrooz Alizadeh & Somayeh Bakhteh, 2017. "A modified firefly algorithm for general inverse p-median location problems under different distance norms," OPSEARCH, Springer;Operational Research Society of India, vol. 54(3), pages 618-636, September.
    9. Timothy C. Y. Chan & Tim Craig & Taewoo Lee & Michael B. Sharpe, 2014. "Generalized Inverse Multiobjective Optimization with Application to Cancer Therapy," Operations Research, INFORMS, vol. 62(3), pages 680-695, June.
    10. Chassein, André & Goerigk, Marc, 2018. "Variable-sized uncertainty and inverse problems in robust optimization," European Journal of Operational Research, Elsevier, vol. 264(1), pages 17-28.
    11. Jonathan Yu-Meng Li, 2021. "Inverse Optimization of Convex Risk Functions," Management Science, INFORMS, vol. 67(11), pages 7113-7141, November.
    12. 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.
    13. 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.
    14. 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.
    15. Behrooz Alizadeh & Esmaeil Afrashteh & Fahimeh Baroughi, 2018. "Combinatorial Algorithms for Some Variants of Inverse Obnoxious Median Location Problem on Tree Networks," Journal of Optimization Theory and Applications, Springer, vol. 178(3), pages 914-934, September.
    16. Trung Kien Nguyen & Nguyen Thanh Hung & Huong Nguyen-Thu, 2020. "A linear time algorithm for the p-maxian problem on trees with distance constraint," Journal of Combinatorial Optimization, Springer, vol. 40(4), pages 1030-1043, November.
    17. Abumoslem Mohammadi & Javad Tayyebi, 2019. "Maximum Capacity Path Interdiction Problem with Fixed Costs," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(04), pages 1-21, August.
    18. Zeynep Erkin & Matthew D. Bailey & Lisa M. Maillart & Andrew J. Schaefer & Mark S. Roberts, 2010. "Eliciting Patients' Revealed Preferences: An Inverse Markov Decision Process Approach," Decision Analysis, INFORMS, vol. 7(4), pages 358-365, December.
    19. Vincent Mousseau & Özgür Özpeynirci & Selin Özpeynirci, 2018. "Inverse multiple criteria sorting problem," Annals of Operations Research, Springer, vol. 267(1), pages 379-412, August.
    20. T. R. Wang & N. Pedroni & E. Zio & V. Mousseau, 2020. "Identification of Protective Actions to Reduce the Vulnerability of Safety‐Critical Systems to Malevolent Intentional Acts: An Optimization‐Based Decision‐Making Approach," Risk Analysis, John Wiley & Sons, vol. 40(3), pages 565-587, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:292:y:2020:i:1:d:10.1007_s10479-020-03651-3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.