Abstract
We analyze the parallel time and speedup for processing divisible load on (1) a linear array with a corner initial processor, (2) a linear array with an interior initial processor, (3) a mesh with a corner initial processor, (4) a mesh with an interior initial processor, (5) a b-ary complete tree with the root as the initial processor, and (6) a pyramid with the apex as the initial processor. Due to communication overhead, and limited network connectivity, the speedup of parallel processing for divisible load is bounded from above by a quantity independent of the network size. It is shown that for the above six cases, as the network size becomes large, the asymptotic speedup is approximately, \(\sqrt \beta, 2\sqrt \beta, {\beta ^{3/4}}, 4{\beta ^{3/4}}, \left( {b - 1} \right)\beta,\) and 3β respectively, where β is the ratio of the time for computing a unit load to the time for communicating a unit load.
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