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<p><b>Abstract</b>—In this paper, we address the issue of implementing matrix multiplication on heterogeneous platforms. We target two different classes of heterogeneous computing resources: heterogeneous networks of workstations and collections of heterogeneous clusters. Intuitively, the problem is to load balance the work with different speed resources while minimizing the communication volume. We formally state this problem in a geometric framework and prove its NP-completeness. Next, we introduce a (polynomial) column-based heuristic, which turns out to be very satisfactory: We derive a theoretical performance guarantee for the heuristic and we assess its practical usefulness through MPI experiments.</p>
Parallel algorithms, load balancing, communication volume, matrix multiplication, numerical linear algebra libraries, heterogeneous platforms, cluster computing, metacomputing.
Fabrice Rastello, Yves Robert, Vincent Boudet, Olivier Beaumont, "Matrix Multiplication on Heterogeneous Platforms", IEEE Transactions on Parallel & Distributed Systems, vol. 12, no. , pp. 1033-1051, October 2001, doi:10.1109/71.963416
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