Advertisement

Implementation of Approximation Algorithms for the Multicast Congestion Problem

  • Qiang Lu
  • Hu Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3503)

Abstract

We implement the approximation algorithm for the multicast congestion problem in communication networks in [14] based on the fast approximation algorithm for packing problems in [13]. We use an approximate minimum Steiner tree solver as an oracle in our implementation. Furthermore, we design some heuristics for our implementation such that both the quality of solution and the running time are improved significantly, while the correctness of the solution is preserved. We also present brief analysis of these heuristics. Numerical results are reported for large scale instances. We show that our implementation results are much better than the results of a theoretically good algorithm in [10].

Keywords

Approximation Algorithm Steiner Tree Online Algorithm Packing Problem Linear Programming Relaxation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Arora, S., Lund, C., Motwani, R., Sudan, M., Szegedy, M.: Proof verification and hardness of approximation problems. Journal of the ACM 45, 501–555 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Aspnes, J., Azar, Y., Fiat, A., Plotkin, S., Waarts, O.: On-line routing of virtual circuits with applications to load balancing and machine scheduling. Journal of the Association for Computing Machinery 44(3), 486–504 (1997)zbMATHMathSciNetGoogle Scholar
  3. 3.
    Baltz, A., Srivastav, A.: Fast approximation of multicast congestion (2001) (manuscript)Google Scholar
  4. 4.
    Baltz, A., Srivastav, A.: Fast approximation of minimum multicast congestion - implementation versus theory. In: Petreschi, R., Persiano, G., Silvestri, R. (eds.) CIAC 2003. LNCS, vol. 2653. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  5. 5.
    Bern, M., Plassmann, P.: The Steiner problem with edge lengths 1 and 2. Information Professing Letters 32, 171–176 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Carr, R., Vempala, S.: Randomized meta-rounding. In: Proceedings of the 32nd ACM Symposium on the Theory of Computing, STOC 2000, pp. 58–62 (2000)Google Scholar
  7. 7.
    Chen, S., Günlük, O., Yener, B.: The multicast packing problem. IEEE/ACM Transactions on Networking 8(3), 311–318 (2000)CrossRefGoogle Scholar
  8. 8.
    Chlebík, M., Chlebíková, J.: Approximation hardness of the Steiner tree problem. In: Penttonen, M., Schmidt, E.M. (eds.) SWAT 2002. LNCS, vol. 2368, pp. 170–179. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  9. 9.
    Floren, R.: A note on “A faster approximation algorithm for the Steiner problem in graphs”. Information Processing Letters 38, 177–178 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Garg, N., Könemann, J.: Fast and simpler algorithms for multicommodity flow and other fractional packing problems. In: Proceedings of the 39th IEEE Annual Symposium on Foundations of Computer Science, FOCS 1998, pp. 300–309 (1998)Google Scholar
  11. 11.
    Grigoriadis, M.D., Khachiyan, L.G.: Fast approximation schemes for convex programs with many blocks and coupling constraints. SIAM Journal on Optimization 4, 86–107 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Grigoriadis, M.D., Khachiyan, L.G.: Coordination complexity of parallel price-directive decomposition. Mathematics of Operations Research 2, 321–340 (1996)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Jansen, K., Zhang, H.: Approximation algorithms for general packing problems with modified logarithmic potential function. In: Proceedings of the 2nd IFIP International Conference on Theoretical Computer Science, TCS 2002, pp. 255–266 (2002)Google Scholar
  14. 14.
    Jansen, K., Zhang, H.: An approximation algorithm for the multicast congestion problem via minimum Steiner trees. In: Proceedings of the 3rd International Workshop on Approximation and Randomized Algorithms in Communication Networks, ARACNE 2002, pp. 77–90 (2002)Google Scholar
  15. 15.
    Karp, R.M.: Reducibility among combinatorial problems. In: Miller, R.E., Thatcher, J.W. (eds.) Complexity of Computer Computations, pp. 85–103. Plenum Press, NY (1972)Google Scholar
  16. 16.
    Klein, P., Plotkin, S., Stein, C., Tardos, E.: Faster approximation algorithms for the unit capacity concurrent flow problem with applications to routing and finding sparse cuts. SIAM Journal on Computing 23, 466–487 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Mehlhorn, K.: A faster approximation algorithm for the Steiner problem in graphs. Information Processing Letters 27, 125–128 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Oliveira, C.A.S., Pardolos, P.M.: A survey of combinatorial optimization problems in multicast routing. Computers and Operations Research 32, 1953–1981 (2005)zbMATHCrossRefGoogle Scholar
  19. 19.
    Raghavan, P.: Probabilistic construction of deterministic algorithms: Approximating packing integer programs. Journal of Computer and System Science 37, 130–143 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Raghavan, P., Thompson, C.: Randomized rounding: a technique for provably good algorithms and algorithmic proofs. Combinatorica 7, 365–374 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Robins, G., Zelikovsky, A.: Improved Steiner tree approximation in graphs. In: Proceedings of the 11th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2000, pp. 770–779 (2000)Google Scholar
  22. 22.
    Vempala, S., Vöcking, B.: Approximating multicast congestion. In: Aggarwal, A.K., Pandu Rangan, C. (eds.) ISAAC 1999. LNCS, vol. 1741, pp. 367–372. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  23. 23.
    Villavicencio, J., Grigoriadis, M.D.: Approximate structured optimization by cyclic block-coordinate descent. In: Fisher, H., et al. (eds.) Applied Mathematics and Parallel Computing, pp. 359–371. Physica Verlag, Heidelberg (1996)Google Scholar
  24. 24.
    Villavicencio, J., Grigoriadis, M.D.: Approximate Lagrangian decomposition with a modified Karmarkar logarithmic potential. In: Pardalos, P., Hearn, D.W., Hager, W.W. (eds.) Network Optimization. Lecture Notes in Economics and Mathematical Systems, vol. 450, pp. 471–485. Springer, Berlin (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Qiang Lu
    • 1
  • Hu Zhang
    • 2
  1. 1.College of Civil Engineering and ArchitectureZhejiang UniversityHangzhouChina
  2. 2.Department of Computing and SoftwareMcMaster UniversityHamiltonCanada

Personalised recommendations