Regular Article
Designing Lower-Dimensional Regular Arrays for Algorithms with Uniform Dependencies

https://doi.org/10.1006/jpdc.1996.0021Get rights and content

Abstract

In this paper, we will propose a polynomial-time method to designm-dimensional regular arrays forn(nm+ 1) dimensional algorithms with uniform dependencies, regular algorithms. The proposed method has two steps: the first one is to transform an independently partitioned regular algorithm to a new one, which has an identity dependence matrix. We call this stepidentity transformation, which is an affine one. In the second step, we propose a spacetime mapping in a fixed form to map the new regular algorithm to a lower-dimensional regular array. Thus, anaffine spacetime mappingis constructed by combining the identity transformation and the fixed form's spacetime mapping together. With the proposed affine spacetime mapping, the original regular algorithm can be mapped to a lower-dimensional regular array in polynomial time, which depends only on the number of dimensions of the regular algorithm. Meanwhile, the designed regular array is asymptotically optimal in time and space.

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This work was supported by the National Science Council, Republic of China, under Contract NSC85-2213-E-009-103.s

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