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On Solving the Rooted Delay- and Delay-Variation-Constrained Steiner Tree Problem

  • Mario Ruthmair
  • Günther R. Raidl
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7422)

Abstract

We present mixed integer programming approaches for optimally solving a combinatorial optimization problem arising in network design with additional quality of service constraints. The rooted delay- and delay-variation-constrained Steiner tree problem asks for a cost-minimal Steiner tree satisfying delay-constraints from source to terminals and a maximal variation-bound between particular terminal path-delays. Our MIP models are based on multi-commodity-flows and a layered graph transformation. For the latter model we propose some new sets of valid inequalities and an efficient separation method. Presented experimental results indicate that our layered graph approaches clearly outperform the flow-based model.

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References

  1. 1.
    Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network flows: theory, algorithms, and applications. Prentice Hall (1993)Google Scholar
  2. 2.
    Cherkassky, B.V., Goldberg, A.V.: On Implementing the Push-Relabel Method for the Maximum Flow Problem. Algorithmica 19(4), 390–410 (1997)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Gouveia, L.: Multicommodity flow models for spanning trees with hop constraints. European Journal of Operational Research 95(1), 178–190 (1996)MATHCrossRefGoogle Scholar
  4. 4.
    Gouveia, L., Paias, A., Sharma, D.: Modeling and solving the rooted distance-constrained minimum spanning tree problem. Computers & Operations Research 35(2), 600–613 (2008)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Gouveia, L., Simonetti, L.G., Uchoa, E.: Modeling hop-constrained and diameter-constrained minimum spanning tree problems as Steiner tree problems over layered graphs. Mathematical Programming 128(1), 123–148 (2011)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Haberman, B.K., Rouskas, G.N.: Cost, delay, and delay variation conscious multicast routing. Tech. rep., North Carolina State University (1996)Google Scholar
  7. 7.
    Koch, T., Martin, A.: Solving Steiner tree problems in graphs to optimality. Networks 32(3), 207–232 (1998)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Kun, Z., Heng, W., Feng-yu, L.: Distributed multicast routing for delay and delay variation-bounded Steiner tree using simulated annealing. Computer Communications 28(11), 1356–1370 (2005)CrossRefGoogle Scholar
  9. 9.
    Lee, H.-Y., Youn, C.-H.: Scalable multicast routing algorithm for delay-variation constrained minimum-cost tree. In: IEEE International Conference on Communications, vol. 3, pp. 1343–1347. IEEE Press (2000)Google Scholar
  10. 10.
    Ljubic, I., Weiskircher, R., Pferschy, U., Klau, G.W., Mutzel, P., Fischetti, M.: An algorithmic framework for the exact solution of the prize-collecting Steiner tree problem. Mathematical Programming 105(2), 427–449 (2006)MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    Low, C.P., Lee, Y.J.: Distributed multicast routing, with end-to-end delay and delay variation constraints. Computer Communications 23(9), 848–862 (2000)CrossRefGoogle Scholar
  12. 12.
    Rouskas, G.N., Baldine, I.: Multicast routing with end-to-end delay and delay variation constraints. IEEE Journal on Selected Areas in Communications 15(3), 346–356 (1997)CrossRefGoogle Scholar
  13. 13.
    Ruthmair, M., Raidl, G.R.: Variable Neighborhood Search and Ant Colony Optimization for the Rooted Delay-Constrained Minimum Spanning Tree Problem. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN XI, Part II. LNCS, vol. 6239, pp. 391–400. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  14. 14.
    Ruthmair, M., Raidl, G.R.: A Layered Graph Model and an Adaptive Layers Framework to Solve Delay-Constrained Minimum Tree Problems. In: Günlük, O., Woeginger, G.J. (eds.) IPCO 2011. LNCS, vol. 6655, pp. 376–388. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  15. 15.
    Sheu, P.-R., Chen, S.-T.: A fast and efficient heuristic algorithm for the delay- and delay variation-bounded multicast tree problem. Computer Communications 25(8), 825–833 (2002)CrossRefGoogle Scholar
  16. 16.
    Sheu, P.-R., Tsai, H.-Y., Chen, S.-C.: An Optimal MILP Formulation for the Delay- and Delay Variation-Bounded Multicast Tree Problem. Journal of Internet Technology 8(3), 321–328 (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Mario Ruthmair
    • 1
  • Günther R. Raidl
    • 1
  1. 1.Institute of Computer Graphics and AlgorithmsVienna University of TechnologyViennaAustria

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