Skip to main content
SpringerLink
Log in

Second-Order Methods for Distributed Approximate Single- and Multicommodity Flow

  • Conference paper
  • First Online:
Randomization and Approximation Techniques in Computer Science (RANDOM 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1518))

Abstract

We study local-control algorithms for maximum flow and multicommodity flow problems in distributed networks. We propose a second-order method for accelerating the convergence of the “first-order” distributed algorithms recently proposed by Awerbuch and Leighton. Our experimental study shows that second-order methods are significantly faster than the first-order methods for approximate single- and multicommodity flow problems. Furthermore, our experimental study gives valuable insights into the diffusive processes that underly these local-control algorithms; this leads us to identify many open technical problems for theoretical study.

This work was done while the author was at Bell Labs.

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

Access this chapter

Log in via an institution
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. O. Axelsson. Iterative Solution Methods. Cambridge University Press, 1994.

    Google Scholar 

  2. B. Awerbuch, Y. Azar and Y. Bartal. Local multicast rate control with globally optimum throughput. Manuscript, 1997.

    Google Scholar 

  3. W. Aiello, B. Awerbuch, B. Maggs, and S. Rao. Approximate load balancing on dynamic and asynchronous networks. Proc. of 25th ACM Symp. on Theory of Computing, 632–641, 1993.

    Google Scholar 

  4. W. Aiello, E. Kushilevitz, R. Ostrovsky, and A. Rosen. Adaptive packet routing for bursty adversarial traffic. Proc. ACM STOC, 1998.

    Google Scholar 

  5. B. Awerbuch and T. Leighton. A simple local-control approximation algorithm for multicommodity flow. Proc. 34th IEEE FOCS, 459–468, 1993.

    Google Scholar 

  6. B. Awerbuch and T. Leighton. Improved approximation algorithms for the multicommodity flow problem and local competitive routing in dynamic networks. Proc. 26th ACM Symp. on Theory of Computing, 487–496, 1994.

    Google Scholar 

  7. B. Awerbuch, Y. Mansour and N. Shavit. End-to-end communication with polynomial overhead. Proc. 30th IEEE FOCS, 358–363, 1989.

    Google Scholar 

  8. R. Barrett, M. Berry, T. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine and H. van der Vorst. Templates for the solution of linear systems: Building blocks for iterative methods, SIAM, Philadelphia, Penn, 1993. http://netlib2.cs.utk.edu/linalg/html templates/Templates.html.

    MATH  Google Scholar 

  9. D. Bertsekas and R. Gallagher. Data Networks. Prentice-Hall Publ. 1991.

    Google Scholar 

  10. D. Bertsekas and J. Tsitsiklis. Parallel and Distributed Computation: NumericalMethods. Prentice Hall, 1989.

    Google Scholar 

  11. F. Chung. Spectral Graph Theory, Chapter 8, CBMS Regional conference series in Mathematics, 1997.

    Google Scholar 

  12. G. Cybenko. Dynamic load balancing for distributed memory multiprocessors. Journal of Parallel and Distributed Computing, 279–301, 1989.

    Google Scholar 

  13. R. Diekmann, S. Muthukrishnan and M. Nayakkankuppam. Engineering diffusive load balancing algorithms using experiments. Proc. IRREGULAR 97, LNCS Vol 1253, 111–122, 1997.

    Google Scholar 

  14. A. Goldberg and S. Rao. Beyond the Flow Decomposition Barrier. Proc. 38th IEEE FOCS, 1997.

    Google Scholar 

  15. A. Goldberg and R. Tarjan. A new approach to the maximum flow problem. Journal of the ACM, 1988, 921–940.

    Google Scholar 

  16. L. A. Hageman and D. M. Young. Applied Iterative Methods. Academic Press, New York, 1981.

    MATH  Google Scholar 

  17. D. Karger. Using random sampling to find maximum flows in uncapacitated undirected graphs. Proc. 30th ACM STOC, 1997.

    Google Scholar 

  18. T. Leighton, F. Makedon, S. Plotkin, C. Stein, E. Tardos and S. Tragoudas. Fast approximation algorithms for multicommodity flow problems. Proc. 24th ACM STOC, 101–111, 1991.

    Google Scholar 

  19. T. Leong, P. Shor and C. Stein. Implementation of a Combinatorial Multicommodity Flow Algorithm. First DIMACS Implementation Challenge: Network Flows and Matchings, 1993.

    Google Scholar 

  20. L. Lovasz and P. Winkler. Mixing of random walks and other diffusions on a graph. Technical Report, Yale University, 1995.

    Google Scholar 

  21. S. Muthukrishnan and R. Rajaraman. An adversarial model for distributed dynamic load balancing. Proc. 10th ACM SPAA, 1998.

    Google Scholar 

  22. S. Muthukrishnan, B. Ghosh, and M. Schultz. First-and second-order diffusive methods for rapid, coarse, distributed load balancing. To appear in Theory of Computing Systems, 1998. Special issue on ACM SPAA 96.

    Google Scholar 

  23. F. Shahrokhi and D. Matula. The maximum concurrent flow problem. Journal of the ACM, 37:318–334, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  24. A. Sinclair. Personal communication, 1998.

    Google Scholar 

  25. P. Vaidya. Speeding up linear programming using fast matrix multiplication. Proc. 30th IEEE FOCS, 332–337, 1989.

    Google Scholar 

  26. R. Varga. Matrix Iterative Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1962.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Bell Laboratories, 700 Mountain Avenue, Murray Hill, NJ, 07974

    S. Muthukrishnan

  2. Polytechnic University, Six MetroTech Center, Brooklyn, NY, 11201

    Torsten Suel

Authors
  1. S. Muthukrishnan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Torsten Suel
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. International Computer Science Institute, 1947 Center Street, Suite 600, Berkeley, CA, 94704-1198, USA

    Michael Luby

  2. Computer Science Department, University of Geneva, 24, rue Général Dufour, CH-1211, Geneva 4, Switzerland

    José D. P. Rolim

  3. University of Barcelona (UPC), Jordi Girona Salgado 1-3, E-08034, Barcelona, Spain

    Maria Serna

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Muthukrishnan, S., Suel, T. (1998). Second-Order Methods for Distributed Approximate Single- and Multicommodity Flow. In: Luby, M., Rolim, J.D.P., Serna, M. (eds) Randomization and Approximation Techniques in Computer Science. RANDOM 1998. Lecture Notes in Computer Science, vol 1518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49543-6_29

Download citation

  • DOI: https://doi.org/10.1007/3-540-49543-6_29

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65142-0

  • Online ISBN: 978-3-540-49543-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation