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

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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.

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Acknowledgements

The first author is supported by the National Science Foundation of China [Grant 71201003], and the New Teachers’ Fund for Doctor Stations, Ministry of Education, China [Grant 20120001120113].

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Authors and Affiliations

  1. Department of Industrial Engineering & Management, Peking University, Haidian District, Chengfu Rd 298, Founder Building 608, Beijing, 100871, China

    Zhe Liang

  2. IT Convergence Technology Research Laboratory, ETRI, 218 Gajeongno, Yuseong-gu, Daejeon, 305-700, Republic of Korea

    Chungmok Lee

  3. Departments of Industrial & Systems Engineering and Radiology, University of Washington, Seattle, WA, 98195, USA

    W. Art Chaovalitwongse

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  1. Zhe Liang
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  2. Chungmok Lee
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  3. W. Art Chaovalitwongse
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Correspondence to W. Art Chaovalitwongse.

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Liang, Z., Lee, C. & Chaovalitwongse, W.A. Mathematical programming approaches for dual multicast routing problem with multilayer risk cost. Ann Oper Res 203, 101–118 (2013). https://doi.org/10.1007/s10479-013-1317-4

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