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Solving Fundamental Problems on Sparse-Meshes
December 2000 (vol. 11 no. 12)
pp. 1324-1332

Abstract—A sparse-mesh, which has PUs on the diagonal of a two-dimensional grid only, is a cost effective distributed memory machine. Variants of this machine have been considered before, but none are as simple and pure as a sparse-mesh. Various fundamental problems (routing, sorting, list ranking) are analyzed, proving that sparse-meshes have great potential. It is shown that on a two-dimensional $n \times n$ sparse-mesh, which has $n$ PUs, for $h = \omega(n^\epsilon \cdot \log n)$, h-relations can be routed in $(h + o(h)) / \epsilon$ steps. The results are extended for higher dimensional sparse-meshes. On a $d$-dimensional $n \times \cdots \times n$ sparse-mesh, with $h = \omega(n^\epsilon \cdot \log n)$, h-relations are routed in $(6 \cdot (d - 1) / \epsilon - 4) \cdot (h + o(h))$ steps.

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Index Terms:
Theory of parallel computation, algorithms, networks, meshes, sorting, routing, list-ranking.
Jop F. Sibeyn, "Solving Fundamental Problems on Sparse-Meshes," IEEE Transactions on Parallel and Distributed Systems, vol. 11, no. 12, pp. 1324-1332, Dec. 2000, doi:10.1109/71.895796
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