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Parallel Divide and Conquer on Meshes
October 1996 (vol. 7 no. 10)
pp. 1049-1058

Abstract—We address the problem of mapping divide-and-conquer programs to mesh connected multicomputers with wormhole or store-and-forward routing. We propose the binomial tree as an efficient model of parallel divide-and-conquer and present two mappings of the binomial tree to the 2D mesh. Our mappings exploit regularity in the communication structure of the divide-and-conquer computation and are also sensitive to the underlying flow control scheme of the target architecture. We evaluate these mappings using new metrics which are extensions of the classical notions of dilation and contention. We introduce the notion of communication slowdown as a measure of the total communication overhead incurred by a parallel computation. We conclude that significant performance gains can be realized when the mapping is sensitive to the flow control scheme of the target architecture.

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Index Terms:
Mapping, embedding, divide-and-conquer algorithms, binomial tree, mesh connected machines, routing, wormhole routing, store-and-forward routing, contention, dilation.
Virginia Lo, Sanjay Rajopadhye, Jan Arne Telle, Xiaoxiong Zhong, "Parallel Divide and Conquer on Meshes," IEEE Transactions on Parallel and Distributed Systems, vol. 7, no. 10, pp. 1049-1058, Oct. 1996, doi:10.1109/71.539736
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