SIMD algorithms for matrix multiplication on the hypercube

Presents a new algorithm for n/spl times/n matrix multiplication on a hypercube of p processors, which outperforms, in terms of time complexity, the best algorithms known in the literature, due to Dekel, Nassimi and Sahni (1981). These authors presented algorithms of O/spl lsqb/n/sup /spl lambda/p/s...

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Bibliographic Details
Published inParallel Processing Symposium, 8th International (IPPS '94 pp. 492 - 496
Main Authors Alonso Sanches, C.A., Song, S.W.
Format Conference Proceeding
LanguageEnglish
Published IEEE Comput. Soc. Press 1994
Subjects
Algorithm design and analysis
Computer science
Hypercubes
Instruments
Parallel algorithms
Parallel architectures
Parallel processing
Visualization
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ISBN0818656026
9780818656026
DOI10.1109/IPPS.1994.288258

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Summary:Presents a new algorithm for n/spl times/n matrix multiplication on a hypercube of p processors, which outperforms, in terms of time complexity, the best algorithms known in the literature, due to Dekel, Nassimi and Sahni (1981). These authors presented algorithms of O/spl lsqb/n/sup /spl lambda/p/sup (/spl lambdaspl minus/12)/spl rsqb/, with 2/spl lesspl lambda/<3 and 1/spl les/p/spl les/n/sup 2/, and O/spl lsqb/log(p/n/sup 2/)+n/sup 3p/spl rsqb/, for n/sup 2spl les/p/spl les/n/sup 3/. The MMM/sub 1/ algorithm presented in this paper is O/spl lsqb/(n/sup 2p/sup 2/3/)log p + n/sup /spl lambda/p/sup /spl lambda3spl rsqb/, where 1/spl les/p/spl les/n/sup 3/. It can be shown that MMM/sub 1/ is better for 1/spl les/p/spl les/n/sup 3log/sup 3/n. The algorithm is derived by using the matricial visualization of the hypercube, suggested by Nassimi and Sahni (1982).< >
ISBN:0818656026
9780818656026
DOI:10.1109/IPPS.1994.288258