A Graphical Approach to Load Balancing and Sparse Matrix Vector Multiplication on the Hypercube

  • Geoffrey C. Fox
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 13)


We consider the implementation on a hypercube concurrent computer, of matrix vector multiplication y = Ax where A is a large sparse matrix. A good decomposition is crucial for the case when each column of A has on the average fewer non zero elements than there are nodes in the hypercube. We review simulated annealing and neural network methods for generating a hypercube decomposition for this problem. We introduce a new graphical method, orthogonal recursive bisection, which can be applied to general problems and is successful on this test case. The performance of the concurrent computer depends strongly on any correlations in the placement of non zero elements of A.


Simulated Annealing Neural Network Method Matrix Vector Multiplication Dynamic Load Balancer Bisection Algorithm 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    C 3 P-385, “A Review of Automatic Load Balancing and Decomposition Methods for the Hypercube,” G. C. Fox, November 1986Google Scholar
  2. 2.
    C 3 P-255, “Concurrent Computation and the Theory of Complex Systems”, G.C. Fox, S.W. Otto, March 3, 1986Google Scholar
  3. 3.
    C 3 P-292, “A Preprocessor for Irregular Finite Element Problems”, J.W. Flower, S.W. Otto, M.C. Salama, June 1986Google Scholar
  4. 4.
    C 3 P-363, “Load Balancing by a Neural Network,” G. C. Fox, W. Furmanski, September 1986Google Scholar
  5. 5.
    C 3 P-314, “Optimal Communication Algorithms on the Hypercube”, G.C. Fox, W. Furmanski, July 8, 1986Google Scholar
  6. 6.
    W. Furmanski, Private Communication, 1986Google Scholar
  7. 7.
    S. Kirkpatrick, C.D. Gelatt Jr., and M.P. Vecchi, Science 220, 671 (1983)MathSciNetMATHCrossRefGoogle Scholar
  8. 7a.
    S. Kirkpatrick, J. Stat Phys 34, 975 (1984)MathSciNetCrossRefGoogle Scholar
  9. 8.
    C 3 P-214, “Monte Carlo Physics on a Concurrent Processor”, G.C. Fox, S. W. Otto, E. A. Umland, November 6, 1985. Published in special issue of Journal of Statistical Physics, Vol. 43, 1209, Plenum Press, 1986Google Scholar
  10. 9.
    J. J. Hopfield and D. W. Tank, “Computing With Neural Circuits: A Model,” Science 233, 625 (1986)CrossRefGoogle Scholar
  11. 10.
    C 3 P-371 “Optimization by a Computational Neural Net,” R. D. Williams, October 10, 1986Google Scholar
  12. 11.
    C 3 P-328, “The Implementation of a Dynamic Load Balancer”, C. Fox, A. Kolawa, R. Williams, November 1986, submitted to 1986 Knoxville Hypercube Conference.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1988

Authors and Affiliations

  • Geoffrey C. Fox
    • 1
  1. 1.California Institute of TechnologyPasadenaUSA

Personalised recommendations