Abstract
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.
Work supported in part by DOE grant DE-FG03–85ER26009, Parsons and System Development Foundations, and the office of the program manager of the Joint Tactical Fusion Office.
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References
C 3 P-385, “A Review of Automatic Load Balancing and Decomposition Methods for the Hypercube,” G. C. Fox, November 1986
C 3 P-255, “Concurrent Computation and the Theory of Complex Systems”, G.C. Fox, S.W. Otto, March 3, 1986
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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.
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© 1988 Springer-Verlag New York Inc.
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Fox, G.C. (1988). A Graphical Approach to Load Balancing and Sparse Matrix Vector Multiplication on the Hypercube. In: Schultz, M. (eds) Numerical Algorithms for Modern Parallel Computer Architectures. The IMA Volumes in Mathematics and Its Applications, vol 13. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-6357-6_4
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DOI: https://doi.org/10.1007/978-1-4684-6357-6_4
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