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Proceedings of the 1999 ACM/IEEE conference on Supercomputing
Architecture-Cognizant Divide and Conquer Algorithms
Portland, Oregon, USA
November 13-November 18
ISBN: 1-58113-091-0
Kang Su Gatlin, University of California, San Diego
Larry Carter, University of California, San Diego
Divide and conquer programs can achieve good performance on parallel computers and computers with deep memory hierarchies. We introduce architecture-cognizant divide and conquer algorithms, and explore how they can achieve even better performance.
An architecture-cognizant algorithm has functionally-equivalent variants of the divide and/or combine functions, and a variant policy that specifies which variant to use at each level of recursion. An optimal variant policy is chosen for each target computer via experimentation. With h levels of recursion, an exhaustive search requires \theta(vh) experiments (where v is the number of variants). We present a method based on dynamic programming that reduces this to \theta(vc) (where c is typically a small constant) experiments for a class of architecture-cognizant programs.
We verify our technique on two kernels (matrix multiply and 2-D Point Jacobi) using three architectures. Our technique improves performance by up to a factor of two, compared to architecture-oblivious divide and conquer implementations. Further our dynamic programming approach succeeds in selecting the optimal variant policy.
Citation:
Kang Su Gatlin, Larry Carter, "Architecture-Cognizant Divide and Conquer Algorithms," sc, pp.25, Proceedings of the 1999 ACM/IEEE conference on Supercomputing, 1999
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