Skip to main content

Multicast Routing and Design of Sparse Connectors

  • Chapter
Algorithmics of Large and Complex Networks

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5515))

  • 3704 Accesses

Abstract

In a multicast communication network, each sender communicates with multiple nodes which are in request of identical data. We summarize our studies of the minimum multicast congestion problem, which generalizes the well-known NP-hard multicommodity flow problem. Moreover, we describe efficient architectures for a network allowing n senders to connect to N receivers (n < N).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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, pp. 165–177. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  2. Baltz, A., Srivastav, A.: Fast approximation of minimum multicast congestion - implementation versus theory. Operations Research 38(4), 319–344 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  3. Baltz, A., Jäger, G., Srivastav, A.: Constructions of sparse asymmetric connectors with number theoretic methods. Networks 45(3), 119–124 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  4. 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)

    Chapter  Google Scholar 

  5. Carr, R.D., Vempala, S.: Randomized metarounding. Random Struct. Algorithms 20(3), 343–352 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  6. Shahrokhi, F., Matula, D.W.: The maximum concurrent flow problem. J. ACM 37(2), 318–334 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  7. Goldberg, A.V.: A natural randomization strategy for multicommodity flow and related algorithms. Inf. Process. Lett. 42(5), 249–256 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  8. Leighton, F.T., Makedon, F., Plotkin, S.A., Stein, C., Stein, É., Tragoudas, S.: Fast approximation algorithms for multicommodity flow problems. J. Comput. Syst. Sci. 50(2), 228–243 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  9. Klein, P.N., Plotkin, S.A., Stein, C., Tardos, É.: Faster approximation algorithms for the unit capacity concurrent flow problem with applications to routing and finding sparse cuts. SIAM J. Comput. 23(3), 466–487 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  10. Plotkin, S.A., Shmoys, D.B., Tardos, É.: Fast approximation algorithms for fractional packing and covering problems. In: FOCS, pp. 495–504. IEEE, Los Alamitos (1991)

    Google Scholar 

  11. Radzik, T.: Fast deterministic approximation for the multicommodity flow problem. Math. Program. 77, 43–58 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  12. Garg, N., Könemann, J.: Faster and simpler algorithms for multicommodity flow and other fractional packing problems. In: FOCS, pp. 300–309 (1998)

    Google Scholar 

  13. Grigoriadis, M.D., Khachiyan, L.G.: Approximate minimum-cost multicommodity flows in õ(epsilon\(^{\mbox{-2}}\)knm) time. Math. Program. 75, 477–482 (1996)

    MathSciNet  MATH  Google Scholar 

  14. Jansen, K., Zhang, H.: Approximation algorithms for general packing problems with modified logarithmic potential function. In: Baeza-Yates, R.A., Montanari, U., Santoro, N. (eds.) IFIP TCS. IFIP Conference Proceedings, vol. 223, pp. 255–266. Kluwer, Dordrecht (2002)

    Google Scholar 

  15. Aspnes, J., Azar, Y., Fiat, A., Plotkin, S.A., Waarts, O.: On-line routing of virtual circuits with applications to load balancing and machine scheduling. J. ACM 44(3), 486–504 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  16. Srivastav, A., Stangier, P.: On complexity, representation and approximation of integral multicommodity flows. Discrete Applied Mathematics 99(1-3), 183–208 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  17. Robins, G., Zelikovsky, A.: Improved steiner tree approximation in graphs. In: SODA, pp. 770–779 (2000)

    Google Scholar 

  18. Raghavan, P.: Probabilistic construction of deterministic algorithms: Approximating packing integer programs. J. Comput. Syst. Sci. 37(2), 130–143 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  19. Magun, J.: Greedy matching algorithms: An experimental study. ACM Journal of Experimental Algorithms 3, 6 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  20. Pippenger, N., Yao, A.C.C.C.: Rearrangeable networks with limited depth. SIAM Journal on Algebraic and Discrete Methods 3(4), 411–417 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  21. Pippenger, N.: On rearrangeable and non-blocking switching networks. J. Comput. Syst. Sci. 17(2), 145–162 (1978)

    Article  MATH  Google Scholar 

  22. Hwang, F., Richards, G.: A two-stage network with dual partial concentrators. j-networks (23), 53–58 (1992)

    Google Scholar 

  23. Oruç, A.Y.: A study of permutation networks: New designs and some generalizations. J. Parallel Distrib. Comput. 22(2), 359–366 (1994)

    Article  Google Scholar 

  24. Clos, C.: A study of non-blocking switching networks. Bell System Tech. J. 32, 406–424 (1953)

    Article  Google Scholar 

  25. Richards, G., Hwang, F.: A two-stage rearrangeable broadcast switching network. j-IEEE-com (33), 1025–1035 (1985)

    Google Scholar 

  26. Lev, V.F.: Restricted set addition in groups, ii. a generalization of the erdo”s-heilbronn conjecture. Electr. J. Comb. 7 (2000)

    Google Scholar 

  27. Diestel, R.: Graphentheorie, 2nd edn. Springer, New York (2000)

    Google Scholar 

  28. Ta-Shma, A., Umans, C., Zuckerman, D.: Loss-less condensers, unbalanced expanders, and extractors. In: STOC, pp. 143–152 (2001)

    Google Scholar 

  29. Raz, R., Reingold, O., Vadhan, S.P.: Extracting all the randomness and reducing the error in trevisan’s extractors. J. Comput. Syst. Sci. 65(1), 97–128 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  30. Wigderson, A., Zuckerman, D.: Expanders that beat the eigenvalue bound: Explicit construction and applications. Combinatorica 19(1), 125–138 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  31. Ahlswede, R., Aydinian, H.K.: Construction of asymmetric connectors of depth two. J. Comb. Theory, Ser. A 113(8), 1614–1620 (2006)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Baltz, A., Srivastav, A. (2009). Multicast Routing and Design of Sparse Connectors. In: Lerner, J., Wagner, D., Zweig, K.A. (eds) Algorithmics of Large and Complex Networks. Lecture Notes in Computer Science, vol 5515. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02094-0_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-02094-0_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02093-3

  • Online ISBN: 978-3-642-02094-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics