Advertisement

A Distributed Preflow-Push for the Maximum Flow Problem

  • Thuy Lien Pham
  • Marc Bui
  • Ivan Lavallee
  • Si Hoang Do
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3908)

Abstract

We present a new algorithm that solves the problem of distributively determining the maximum flow in an asynchronous network. This distributed algorithm is based on the preflow-push technique. Sequential processes, executing the same code over local data, exchange messages with neighbors to establish the max flow. This algorithm is derived to the case of multiple sources and/or sinks without modifications. For a network of n nodes and m arcs, the algorithm achieves O(n 2 m) message complexity and O(n 2 ) time complexity.

Keywords

Source Node Sink Node Message Complexity Algorithm Block Residual Network 
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.
    Goldberg, A.V.: Recent Developments in Maximum Flow Algorithms. Technical Report (April 1998)Google Scholar
  2. 2.
    Goldberg, A.V., Tarjan, R.E.: A New Approach to the Maximum Flow Problem. Journal of ACM 35(4), 921–940 (1988)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Gabow, H.N.: Scaling Algorithms for Network Problems. Journal of Computer and System Sciences 31(2), 148–168 (1985)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Goldberg, A.V., Rao, S.: Beyond the Flow Decomposition Barrier. Journal of ACM 45(5), 783–797 (1998)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Ford, L.R., Fulkerson, D.R.: Flows in networks. Princeton University Press, Princeton (1962)MATHGoogle Scholar
  6. 6.
    Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows – Theory, Algorithms and Applications. Prentice-Hall, Inc., USA (1993)MATHGoogle Scholar
  7. 7.
    Edmonds, J., Karp, R.M.: Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems. Journal of ACM 19(2), 248–264 (1972)CrossRefMATHGoogle Scholar
  8. 8.
    Dinic: Algorithm for Solution of a Problem in Networks with Power Estimation. Journal of ACM 19, 248–264 (1972)CrossRefGoogle Scholar
  9. 9.
    Karzanov: Determining the Maximum Flow in a Network by the Method of Preflows. Soviet Mathematics Doklady 15, 434–437 (1974)MATHGoogle Scholar
  10. 10.
    Cheriyan, J., Mehlhorn, K.: An analysis of the highest-level selection rule in the preflow-push max-flow algorithm. Information Processing Letters 69, 239–242 (1999)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Cherkassky, B.V., Goldberg, A.V.: On Implementing Push-Relabel Method for the Maximum Flow Problem. Algorithmica 19, 390–410 (1997)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Anderson, R.J., Setubal, J.C.: On the Parallel Implementation of Goldberg’s Maximum Flow Algorithm. In: Proc. of the 4th Annual ACM Symp. on Parallel Algorithms and Architectures, pp. 168–177 (1992)Google Scholar
  13. 13.
    Barbosa, V.C.: An introduction to distributed algorithms, ch. 7, pp. 200–216. The MIT Press, Cambridge (1996)Google Scholar
  14. 14.
    Takkula, T.: A preflow-push algorithm that handles online max flow problems in a static asynchronous network (Revision 1.18). Chalmers University of Technology, Gothenbourg, Sweden (2001)Google Scholar
  15. 15.
    Nagy, N., Akl, S.G.: The Maximum Flow Problem: A Real-Time Approach. Technical Report, Dept. of Computing and Information Sciences Queen’s Univ., Canada (2001)Google Scholar
  16. 16.
    Ahlswede, R., Cai, N., Li, S.-Y.R., Yeung, R.W.: Network information flow. IEEE Trans. on Information Theory 46, 1204–1216 (2000)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Thuy Lien Pham
    • 1
  • Marc Bui
    • 1
  • Ivan Lavallee
    • 1
  • Si Hoang Do
    • 1
  1. 1.Laboratoire de Recherche en Informatique AvancéeUniversité Paris 8France

Personalised recommendations