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Issue No.12 - December (2000 vol.11)

pp: 1324-1332

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/71.895796

ABSTRACT

<p><b>Abstract</b>—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 <tmath>$n \times n$</tmath> sparse-mesh, which has <tmath>$n$</tmath> PUs, for <tmath>$h = \omega(n^\epsilon \cdot \log n)$</tmath>, <it>h</it>-relations can be routed in <tmath>$(h + o(h)) / \epsilon$</tmath> steps. The results are extended for higher dimensional sparse-meshes. On a <tmath>$d$</tmath>-dimensional <tmath>$n \times \cdots \times n$</tmath> sparse-mesh, with <tmath>$h = \omega(n^\epsilon \cdot \log n)$</tmath>, <it>h</it>-relations are routed in <tmath>$(6 \cdot (d - 1) / \epsilon - 4) \cdot (h + o(h))$</tmath> steps.</p>

INDEX TERMS

Theory of parallel computation, algorithms, networks, meshes, sorting, routing, list-ranking.

CITATION

Jop F. Sibeyn, "Solving Fundamental Problems on Sparse-Meshes",

*IEEE Transactions on Parallel & Distributed Systems*, vol.11, no. 12, pp. 1324-1332, December 2000, doi:10.1109/71.895796