Towards Optimal Load Balancing Topologies

  • Thomas Decker
  • Burkhard Monien
  • Robert Preis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1900)


Many load balancing algorithms balance the load according to a certain topology. Its choice can significantly influence the performance of the algorithm. We consider a two phase balancing model. The first phase calculates a balancing flow with respect to a topology by applying a diffusion scheme. The second phase migrates the load according to the balancing flow. The cost functions of the phases depend on various properties of the topology; for the first phase these are the maximum node degree and the number of eigenvalues of the network topology, for the second phase these are a small flow volume and a small diameter of the topology. We compare and propose various network topologies with respect to these properties. Experiments on a Cray T3E and on a cluster of PCs confirm our cost functions for both balancing phases.


Load Balance Migration Time Dimension Exchange Diffusion Scheme Graph Class 
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.


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  1. [1]
    N. Biggs. Algebraic Graph Theory, Second Edition. Cambridge University Press, 1974/1993.Google Scholar
  2. [2]
    F. Comellas. (degree,diameter)-graphs.
  3. [3]
    D.M. Cvetkovic, M. Doob, and H. Sachs. Spectra of Graphs. Joh. Ambrosius Barth, 1995.Google Scholar
  4. [4]
    G. Cybenko. Load balancing for distributed memory multiprocessors. J. of Parallel and Distributed Computing, 7:279–301, 1989.CrossRefGoogle Scholar
  5. [5]
    T. Decker. Virtual Data Space-Load balancing for irregular applications. Parallel Computing, 2000. To appear.Google Scholar
  6. [6]
    R. Diekmann, A. Frommer, and B. Monien. Efficient schemes for nearest neighbor load balancing. Parallel Computing, 25(7):789–812, 1999.CrossRefMathSciNetGoogle Scholar
  7. [7]
    R. Elsasser, A. Frommer, B. Monien, and R. Preis. Optimal and alternating-direction load-balancing schemes. In EuroPar’99, LNCS 1685, pages 280–290, 1999.Google Scholar
  8. [8]
    G. Fertin, A. Raspaud, H. Schröder, O. Sykora, and I. Vrto. Diamater of Knödel graph. In Workshop on Graph-Theoretic Concepts in Computer Science ( WG), 2000. to appear.Google Scholar
  9. [9]
    B. Ghosh, S. Muthukrishnan, and M.H. Schultz. First and second order diffusive methods for rapid, coarse, distributed load balancing. In SPAA, pages 72–81, 1996.Google Scholar
  10. [10]
    M. C. Heydemann, N. Marlin, and S. Perennes. Cayley graphs with complete rotations. Technical Report 1155, L.R.I. Orsay, 1997.Google Scholar
  11. [11]
    Y.F. Hu and R.J. Blake. An improved diffusion algorithm for dynamic load balancing. Parallel Computing, 25(4):417–444, 1999.zbMATHCrossRefMathSciNetGoogle Scholar
  12. [12]
    Y.F. Hu, R.J. Blake, and D.R. Emerson. An optimal migration algorithm for dynamic load balancing. Concurrency: Prac. and Exp., 10(6):467–483, 1998.zbMATHCrossRefGoogle Scholar
  13. [13]
    W. Knodel. New gossips and telephones. Discrete Mathematics, 13:95, 1975.CrossRefMathSciNetGoogle Scholar
  14. [14]
    G. Royle. Cages of higher valency.
  15. [15]
    P. Sanders. Analysis of nearest neighbor load balancing algorithms for random loads. Parallel Computing, 25:1013–1033, 1999.zbMATHCrossRefMathSciNetGoogle Scholar
  16. [16]
    K. Schloegel, G. Karypis, and V. Kumar. Multilevel diffusion schemes for repartitioning of adaptive meshes. J. of Parallel and Distributed Computing, 47(2): 109–124, 1997.CrossRefGoogle Scholar
  17. [17]
    R.S. Varga. Matrix Iterative Analysis. Prentice-Hall, 1962.Google Scholar
  18. [18]
    C. Xu and F.C.M. Lau. Load Balancing in Parallel Computers. Kluwer, 1997.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Thomas Decker
    • 1
  • Burkhard Monien
    • 1
  • Robert Preis
    • 1
  1. 1.Department of Mathematics and Computer ScienceUniversity of PaderbornGermany

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