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Optimal multicast route packing

Author

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  • Kang, Jangha
  • Park, Kyungchul
  • Park, Sungsoo

Abstract

This paper considers the hop-constrained multicast route packing problem with a bandwidth reservation to build QoS-guaranteed multicast routing trees with a minimum installation cost. Given a set of multicast sessions, each of which has a hop limit constraint and a bandwidth requirement, the problem is to determine the set of multicast routing trees in an arc-capacitated network with the objective of minimizing the cost. For the problem, we propose a branch-and-cut-and-price algorithm, which can be viewed as a branch-and-bound method incorporating both the strong cutting plane algorithm and the column generation method. We implemented and tested the proposed algorithm on randomly generated problem instances with sizes up to 30 nodes, 570 arcs, and 10 multicast sessions. The test results show that the algorithm can obtain the optimal solution to practically sized problem instances within a reasonable time limit in most cases.

Suggested Citation

  • Kang, Jangha & Park, Kyungchul & Park, Sungsoo, 2009. "Optimal multicast route packing," European Journal of Operational Research, Elsevier, vol. 196(1), pages 351-359, July.
    • Handle: RePEc:eee:ejores:v:196:y:2009:i:1:p:351-359
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    References listed on IDEAS

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    1. Kyungchul Park & Seokhoon Kang & Sungsoo Park, 1996. "An Integer Programming Approach to the Bandwidth Packing Problem," Management Science, INFORMS, vol. 42(9), pages 1277-1291, September.
    2. Cynthia Barnhart & Christopher A. Hane & Pamela H. Vance, 2000. "Using Branch-and-Price-and-Cut to Solve Origin-Destination Integer Multicommodity Flow Problems," Operations Research, INFORMS, vol. 48(2), pages 318-326, April.
    3. Cynthia Barnhart & Ellis L. Johnson & George L. Nemhauser & Martin W. P. Savelsbergh & Pamela H. Vance, 1998. "Branch-and-Price: Column Generation for Solving Huge Integer Programs," Operations Research, INFORMS, vol. 46(3), pages 316-329, June.
    4. S. Voß, 1999. "The Steiner tree problem with hop constraints," Annals of Operations Research, Springer, vol. 86(0), pages 321-345, January.
    5. Kang, Jangha & Park, Kyungchul & Park, Sungsoo, 2004. "ATM VP-based network design," European Journal of Operational Research, Elsevier, vol. 158(3), pages 555-569, November.
    6. C S Sung & J M Hong, 1999. "Branch-and-price algorithm for a multicast routing problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(11), pages 1168-1175, November.
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