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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
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    References listed on IDEAS

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    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.
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    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.

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