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Mathematical programming approaches for dual multicast routing problem with multilayer risk cost

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  • Zhe Liang
  • Chungmok Lee
  • W. Chaovalitwongse

Abstract

This paper addresses a dual multicast routing problem with shared risk link group (SRLG) diverse costs (DMR-SRLGD) that arises from large-scale distribution of realtime multicast data (e.g., internet protocol TV, videocasting, online games, stock price update). The goal of this problem is to find two redundant multicast trees, each from one of the two sources to every destination at a minimum cost. The cost of the problem contains two parts: the multicast routing cost and the shard common risk cost. Such common risk could cause the failures of multiple links simultaneously. Therefore, the DMR-SRLGD ensures the availability and reliability of multicast service. We formulate an edge-based model for the DMR-SRLGD. In addition, we also propose a path-based model that rises from the Dantzig-Wolfe decomposition of the edge-based model, and develop a column-generation framework to solve the linear relaxation of the path-based formulation. We then employ a branch-and-price solution method to find integer solutions to DMR-SRLGD. We also extend both edge-based and path-based models to handle the complex quality of service requirements. The computational results show the edge-based model is superior than the path-based model for the easy and small test instances, whereas the path-based model provides better solutions in a timely fashion for hard or large test instances. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Zhe Liang & Chungmok Lee & W. Chaovalitwongse, 2013. "Mathematical programming approaches for dual multicast routing problem with multilayer risk cost," Annals of Operations Research, Springer, vol. 203(1), pages 101-118, March.
    • Handle: RePEc:spr:annopr:v:203:y:2013:i:1:p:101-118:10.1007/s10479-013-1317-4
    DOI: 10.1007/s10479-013-1317-4
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    References listed on IDEAS

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    1. Zhe Liang & Wanpracha Art Chaovalitwongse, 2010. "Bounds of redundant multicast routing problem with SRLG-diverse constraints: edge, path and tree models," Journal of Global Optimization, Springer, vol. 48(2), pages 335-345, October.
    2. Marco E. Lübbecke & Jacques Desrosiers, 2005. "Selected Topics in Column Generation," Operations Research, INFORMS, vol. 53(6), pages 1007-1023, December.
    3. François Vanderbeck, 2005. "Implementing Mixed Integer Column Generation," Springer Books, in: Guy Desaulniers & Jacques Desrosiers & Marius M. Solomon (ed.), Column Generation, chapter 0, pages 331-358, Springer.
    4. Carlos A.S. Oliveira & Panos M. Pardalos & Tania M. Querido, 2005. "A combinatorial algorithm for message scheduling on controller area networks," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 1(1/2), pages 160-171.
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