IDEAS home Printed from https://ideas.repec.org/a/spr/snopef/v4y2023i1d10.1007_s43069-022-00189-x.html
   My bibliography  Save this article

Online Mixed Ring Covering Problem with Two Nodes

Author

Listed:
  • Man Xiao

    (Yunnan University)

  • Weidong Li

    (Yunnan University)

  • Xiaofei Liu

    (Yunnan University)

Abstract

In this paper, we study the online mixed ring covering problem, where the ring contains two nodes and undirected and bidirected links. A sequence of flows arrives one by one, where each flow has a traffic demand for each pair of nodes in the ring. The objective is to maximize the minimum load of the ring link, where the load of a link is the total demand of the flows sent to that link. We consider the problem in three different scenarios: splittable, integer splittable and unsplittable. When the demands are splittable, we present an optimal online algorithm with a competitive ratio that is no more than $$\frac{4}{3}$$ 4 3 . When the demands are integer splittable, we present an optimal online algorithm with a competitive ratio that is no more than 2. When the demands are unsplittable, we prove that the lower bound for this case is $$\infty$$ ∞ , and few researchers have provided this result. Then, we consider a special case of the online mixed ring covering problem when the demands are unsplittable, which has a buffer size of K, where K is the number of flows temporarily stored in the buffer. We prove that the competitive ratio for any positive integer K is at least 2. For $$K=1$$ K = 1 , we present an online algorithm with a competitive ratio that is no more than 3. For $$K=2$$ K = 2 , we present an online algorithm with a competitive ratio that is no more than $$\frac{3+\sqrt{5}}{2}\approx 2.618$$ 3 + 5 2 ≈ 2.618 .

Suggested Citation

  • Man Xiao & Weidong Li & Xiaofei Liu, 2023. "Online Mixed Ring Covering Problem with Two Nodes," SN Operations Research Forum, Springer, vol. 4(1), pages 1-20, March.
    • Handle: RePEc:spr:snopef:v:4:y:2023:i:1:d:10.1007_s43069-022-00189-x
    DOI: 10.1007/s43069-022-00189-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s43069-022-00189-x
    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/s43069-022-00189-x?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. Young-Soo Myung & Hu-Gon Kim & Dong-Wan Tcha, 1997. "Optimal Load Balancing on Sonet Bidirectional Rings," Operations Research, INFORMS, vol. 45(1), pages 148-152, February.
    2. Qingqin Nong & Jinjiang Yuan & Yixun Lin, 2009. "The weighted link ring loading problem," Journal of Combinatorial Optimization, Springer, vol. 18(1), pages 38-50, July.
    3. Yingli Ran & Yishuo Shi & Changbing Tang & Zhao Zhang, 2020. "A primal-dual algorithm for the minimum partial set multi-cover problem," Journal of Combinatorial Optimization, Springer, vol. 39(3), pages 725-746, April.
    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. Yingli Ran & Xiaohui Huang & Zhao Zhang & Ding-Zhu Du, 2021. "Approximation algorithm for minimum power partial multi-coverage in wireless sensor networks," Journal of Global Optimization, Springer, vol. 80(3), pages 661-677, July.
    2. Yingli Ran & Zhao Zhang & Shaojie Tang & Ding-Zhu Du, 2021. "Breaking the r max Barrier: Enhanced Approximation Algorithms for Partial Set Multicover Problem," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 774-784, May.
    3. Y Shim & S A Gabriel & A Desai & P Sahakij & S Milner, 2008. "A fast heuristic method for minimizing traffic congestion on reconfigurable ring topologies," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(4), pages 521-539, April.
    4. Qingqin Nong & Jinjiang Yuan & Yixun Lin, 2009. "The weighted link ring loading problem," Journal of Combinatorial Optimization, Springer, vol. 18(1), pages 38-50, July.
    5. Hanif D. Sherali & J. Cole Smith & Youngho Lee, 2000. "Enhanced Model Representations for an Intra-Ring Synchronous Optical Network Design Problem Allowing Demand Splitting," INFORMS Journal on Computing, INFORMS, vol. 12(4), pages 284-298, November.
    6. Meunier, Frédéric & Pradeau, Thomas, 2014. "The uniqueness property for networks with several origin–destination pairs," European Journal of Operational Research, Elsevier, vol. 237(1), pages 245-256.
    7. Khodakaram Salimifard & Sara Bigharaz, 2022. "The multicommodity network flow problem: state of the art classification, applications, and solution methods," Operational Research, Springer, vol. 22(1), pages 1-47, March.
    8. Jianping Li & Weidong Li & Lusheng Wang, 2012. "A polynomial time approximation scheme for embedding a directed hypergraph on a weighted ring," Journal of Combinatorial Optimization, Springer, vol. 24(3), pages 319-328, October.
    9. Cole Smith, J., 2004. "Algorithms for distributing telecommunication traffic on a multiple-ring SONET-based network," European Journal of Operational Research, Elsevier, vol. 154(3), pages 659-672, May.
    10. Fortz, Bernard & Soriano, Patrick & Wynants, Christelle, 2003. "A tabu search algorithm for self-healing ring network design," European Journal of Operational Research, Elsevier, vol. 151(2), pages 280-295, December.

    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:snopef:v:4:y:2023:i:1:d:10.1007_s43069-022-00189-x. 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.