IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v347y2025i3d10.1007_s10479-024-06361-2.html
   My bibliography  Save this article

The absolute quickest 1-center problem on a cycle and its reverse problem

Author

Listed:
  • Kien Trung Nguyen

    (Can Tho University)

Abstract

The concept of the quickest path refers to the path with the minimum transmission time, considering both its length and capacity. We investigate the problem of finding a point on a cycle such that the maximum quickest distance from any vertex to that point is minimized. We refer to this problem as the quickest 1-center problem on cycles. First, we solve the problem on paths in linear time based on the optimality criterion. Then, we address the problem on cycles in $$O(n^2)$$ O ( n 2 ) time by leveraging the solution approach on the induced path in each iteration, where n is the number of vertices. We also consider the problem of reducing the quickest distance objective at a predetermined vertex of a cycle as much as possible by augmenting the edge capacities within a given budget. This problem is called the reverse quickest 1-center problem on cycles. We develop a combinatorial algorithm that solves the problem in $$O(n^2)$$ O ( n 2 ) time by solving each subproblem in linear time.

Suggested Citation

  • Kien Trung Nguyen, 2025. "The absolute quickest 1-center problem on a cycle and its reverse problem," Annals of Operations Research, Springer, vol. 347(3), pages 1473-1491, April.
    • Handle: RePEc:spr:annopr:v:347:y:2025:i:3:d:10.1007_s10479-024-06361-2
    DOI: 10.1007/s10479-024-06361-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-024-06361-2
    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/s10479-024-06361-2?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. Michael Hart Moore, 1976. "On the Fastest Route for Convoy-Type Traffic in Flowrate-Constrained Networks," Transportation Science, INFORMS, vol. 10(2), pages 113-124, May.
    2. Marta Pascoal & M. Captivo & João Clímaco, 2006. "A comprehensive survey on the quickest path problem," Annals of Operations Research, Springer, vol. 147(1), pages 5-21, October.
    3. Tran Hoai Ngoc Nhan & Kien Trung Nguyen & Huong Nguyen-Thu, 2023. "The Minmax Regret Reverse 1-Median Problem on Trees with Uncertain Vertex Weights," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 40(03), pages 1-17, June.
    4. Ali Reza Sepasian & Javad Tayyebi, 2020. "Further Study on Reverse 1-Center Problem on Trees," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(06), pages 1-18, December.
    5. Punnen, Abraham P., 1991. "A linear time algorithm for the maximum capacity path problem," European Journal of Operational Research, Elsevier, vol. 53(3), pages 402-404, August.
    6. Marianov, Vladimir & Eiselt, H.A., 2024. "Fifty Years of Location Theory - A Selective Review," European Journal of Operational Research, Elsevier, vol. 318(3), pages 701-718.
    7. Roghayeh Etemad & Behrooz Alizadeh, 2018. "Reverse selective obnoxious center location problems on tree graphs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(3), pages 431-450, June.
    8. Zhang, Jianzhong & Liu, Zhenhong & Ma, Zhongfan, 2000. "Some reverse location problems," European Journal of Operational Research, Elsevier, vol. 124(1), pages 77-88, July.
    9. Xinqiang Qian & Xiucui Guan & Junhua Jia & Qiao Zhang & Panos M. Pardalos, 2023. "Vertex quickest 1-center location problem on trees and its inverse problem under weighted $$l_\infty $$ l ∞ norm," Journal of Global Optimization, Springer, vol. 85(2), pages 461-485, February.
    10. Herminia Calvete & Lourdes del-Pozo & José Iranzo, 2012. "Algorithms for the quickest path problem and the reliable quickest path problem," Computational Management Science, Springer, vol. 9(2), pages 255-272, May.
    11. 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. Calvete, Herminia I. & del-Pozo, Lourdes & Iranzo, José A., 2018. "Dealing with residual energy when transmitting data in energy-constrained capacitated networks," European Journal of Operational Research, Elsevier, vol. 269(2), pages 602-620.
    2. Sedeño-Noda, Antonio & González-Barrera, Jonathan D., 2014. "Fast and fine quickest path algorithm," European Journal of Operational Research, Elsevier, vol. 238(2), pages 596-606.
    3. Mehdi Ghiyasvand & Azam Ramezanipour, 2018. "Solving the MCQP, MLT, and MMLT problems and computing weakly and strongly stable quickest paths," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 68(2), pages 217-230, June.
    4. 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.
    5. 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.
    6. Yi Zhang & Liwei Zhang & Yue Wu, 2014. "The augmented Lagrangian method for a type of inverse quadratic programming problems over second-order cones," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 45-79, April.
    7. Herminia Calvete & Lourdes del-Pozo & José Iranzo, 2012. "Algorithms for the quickest path problem and the reliable quickest path problem," Computational Management Science, Springer, vol. 9(2), pages 255-272, May.
    8. Elisabeth Gassner, 2008. "The inverse 1-maxian problem with edge length modification," Journal of Combinatorial Optimization, Springer, vol. 16(1), pages 50-67, July.
    9. Forghani-elahabad, Majid & Mahdavi-Amiri, Nezam, 2015. "An efficient algorithm for the multi-state two separate minimal paths reliability problem with budget constraint," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 472-481.
    10. Jianzhong Zhang & Liwei Zhang & Xiantao Xiao, 2010. "A Perturbation approach for an inverse quadratic programming problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(3), pages 379-404, December.
    11. Melchiori, Anna & Sgalambro, Antonino, 2020. "A branch and price algorithm to solve the Quickest Multicommodity k-splittable Flow Problem," European Journal of Operational Research, Elsevier, vol. 282(3), pages 846-857.
    12. Nguyen Thanh Toan & Huy Minh Le & Kien Trung Nguyen, 2024. "The reverse selective balance center location problem on trees," OPSEARCH, Springer;Operational Research Society of India, vol. 61(1), pages 483-497, March.
    13. Ashutosh Sharma & Rajiv Kumar & Manar Wasif Abu Talib & Saurabh Srivastava & Razi Iqbal, 2019. "Network modelling and computation of quickest path for service-level agreements using bi-objective optimization," International Journal of Distributed Sensor Networks, , vol. 15(10), pages 15501477198, October.
    14. Lindong Liu & Xiangtong Qi & Zhou Xu, 2024. "Stabilizing Grand Cooperation via Cost Adjustment: An Inverse Optimization Approach," INFORMS Journal on Computing, INFORMS, vol. 36(2), pages 635-656, March.
    15. Libura, Marek, 2007. "On the adjustment problem for linear programs," European Journal of Operational Research, Elsevier, vol. 183(1), pages 125-134, November.
    16. 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.
    17. Gassner, Elisabeth, 2009. "Up- and downgrading the 1-center in a network," European Journal of Operational Research, Elsevier, vol. 198(2), pages 370-377, October.
    18. 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.
    19. Nguyen, Kien Trung & Hung, Nguyen Thanh, 2021. "The minmax regret inverse maximum weight problem," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    20. Urmila Pyakurel & Tanka Nath Dhamala & Stephan Dempe, 2017. "Efficient continuous contraflow algorithms for evacuation planning problems," Annals of Operations Research, Springer, vol. 254(1), pages 335-364, July.

    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:347:y:2025:i:3:d:10.1007_s10479-024-06361-2. 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.