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Parallel Processing of Divisible Loads on Partitionable Static Interconnection Networks

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Abstract

We analyze the parallel time and speedup for processing a 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; (6) a pyramid with the apex as the initial processor. Due to communication overhead and limited network connectivity, the speedup of parallel processing for a divisible load on static interconnection networks with constant node degrees is bounded from above by a quantity independent of 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\(\sqrt \beta\), β3/4, 4β3/4, (b−1)β, and 3β, respectively, where β is the ratio of the time for computing a unit load to the time for communicating a unit load. We also investigate divisible load distribution on hypercubes. Our strategy takes advantage of the recursive structure of a hypercube. It is proven that linear speedup can be achieved as the communication cost becomes smaller and smaller.

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  1. Department of Computer Science, State University of New York, New Paltz, NY, 12561, USA

    Keqin Li

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  1. Keqin Li
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Li, K. Parallel Processing of Divisible Loads on Partitionable Static Interconnection Networks. Cluster Computing 6, 47–55 (2003). https://doi.org/10.1023/A:1020967017125

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