2-D SIMD algorithms in the perfect shuffle networks

Authors:
Y. Ben-Asher;D. Egozi;A. Schuster
Affiliations:
The Hebrew University;The Hebrew University;The Hebrew University
Venue:
ISCA '89 Proceedings of the 16th annual international symposium on Computer architecture
Year:
1989

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Ultracomputers

ACM Transactions on Programming Languages and Systems (TOPLAS)
Upper and lower bounds on the performance of parallel algorithms

Upper and lower bounds on the performance of parallel algorithms

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Abstract

This paper studies a set of basic algorithms for SIMD Perfect Shuffle networks. These algorithms where studied in several papers, but for the 1-D case, where the size of the problem N is the same as the number of processors P. For the 2-D case of N = L * P, studied by [GK-80] and [Kr-81], we improve several algorithms, achieving run time &Ogr;(L + log P) rather than &Ogr;(L * log P), as N exceeds P. We give non-trivial algorithms for the following 2-D operations: Row-Reduction, Parallel-Prefix, Transpose, Smoothing and Cartesian-Product.