Solving fundamental problems on sparse-meshes

Abstract

AbstractÐA 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  n sparse-mesh, which has n PUs, for h 3n Á log n, h-relations can be routed in h oha steps. The results are extended for higher dimensional sparse-meshes. On a d-dimensional n  Á Á Á  n sparse-mesh, with h 3n Á log n, h-relations are routed in T Á d À Ia À R Á h oh steps.

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