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Design of Space-Optimal Regular Arrays for Algorithms with Linear Schedules
May 1995 (vol. 44 no. 5)
pp. 683-694

Abstract—The problem of designing space-optimal 2D regular N×N×N cubical mesh algorithms with linear schedule ai+bj+ck, 1 ≤abc, and N=nc, is studied. Three novel nonlinear processor allocation methods, each of which works by combining a partitioning technique (gcd-partition) with different nonlinear processor allocation procedures (traces), are proposed to handle different cases. In cases where a+bc, which are dealt with by the first processor allocation method, space-optimal designs can always be obtained in which the number of processing elements is equal to ${N^2\over c}$. For other cases where a+b > c and either a=b and b=c, two other optimal processor allocation methods are proposed. Besides, the closed form expressions for the optimal number of processing elements are derived for these cases.

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Index Terms:
Algorithm mapping, data dependency, linear schedule, matrix multiplication, optimizing compiler, space-optimal, systolic array.
Pen-Yuang Chang, Jong-Chuang Tsay, "Design of Space-Optimal Regular Arrays for Algorithms with Linear Schedules," IEEE Transactions on Computers, vol. 44, no. 5, pp. 683-694, May 1995, doi:10.1109/12.381953
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