IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v18y2009i1d10.1007_s10878-007-9136-7.html
   My bibliography  Save this article

The weighted link ring loading problem

Author

Listed:
  • Qingqin Nong

    (Ocean University of China)

  • Jinjiang Yuan

    (Zhengzhou University)

  • Yixun Lin

    (Zhengzhou University)

Abstract

In the weighted link ring loading problem, we are given an n-node undirected ring network. Each of its links is associated with a weight. Traffic demands are given for each pair of nodes in the ring. The load of a link is the sum of the flows routed through the link, and the weighted load of a link is the product of its weight and the smallest integer not less than its load. The objective of the problem is to find a routing scheme such that the maximum weighted load on the ring is minimized. In this paper we consider three variants: (i) demands may be split into two parts, and then each part is sent in a different direction; (ii) demands are allowed to be split into two parts but restricted to be integrally split; (iii) each demand must be entirely routed in either of the two directions, clockwise or counterclockwise. We first prove that the first variant is polynomially solvable. We then present a pseudo-polynomial time algorithm for the second one. Finally, for the third one, whose NP-hardness can be drawn from the result in the literature, we derive a polynomial-time approximation scheme (PTAS).

Suggested Citation

  • 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.
  • Handle: RePEc:spr:jcomop:v:18:y:2009:i:1:d:10.1007_s10878-007-9136-7
    DOI: 10.1007/s10878-007-9136-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-007-9136-7
    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/s10878-007-9136-7?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. Gruia Călinescu & Peng-Jun Wan, 2002. "Traffic Partition in WDM/SONET Rings to Minimize SONET ADMs," Journal of Combinatorial Optimization, Springer, vol. 6(4), pages 425-453, December.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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:jcomop:v:18:y:2009:i:1:d:10.1007_s10878-007-9136-7. 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.