Solving fundamental problems on sparse-meshes

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×n sparse-mesh, which has n PUs, for h=ω(n^ε·log n), h-relations can be routed in (h+o(h))/ε steps. The results are extended for higher dimensional sparse-meshes. On a d-dimensional n x···x n sparse-mesh, with h=ω(n^ε ·log n), h-relations are routed in (6·(d-1)/ε-4)·(h+o(h)) steps