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Communication Efficient Basic Linear Algebra Computations on Hypercube Architectures
KTH, School of Computer Science and Communication (CSC), Centres, Centre for High Performance Computing, PDC. (Parallelldatorcentrum)
1987 (English)In: Journal of Parallel and Distributed Computing, ISSN 0743-7315, E-ISSN 1096-0848, Vol. 4, no 2, 133-179 p.Article in journal (Refereed) Published
Abstract [et]

This paper presents a few algorithms for embedding loops and multidimensional arrays in hypercubes with emphasis on proximity preserving embeddings. A proximity preserving embedding minimizes the need for communication bandwidth in computations requiring nearest neighbor communication. Two storage schemes for "large" problems on "small" machines are suggested and analyzed and algorithms for matrix transpose, multiplying matrices, factoring matrices,  and solving triangular linear systems are presented. A few complete binary tree embeddings are described and analyzed. The data movement in the matrix algorithms is analyzed and it is shown that in the majority of cases the directed routing paths intersect only at nodes of the hypercube allowing for a maximum degree of pipelining

Place, publisher, year, edition, pages
1987. Vol. 4, no 2, 133-179 p.
National Category
Computer and Information Science
Identifiers
URN: urn:nbn:se:kth:diva-91118OAI: oai:DiVA.org:kth-91118DiVA: diva2:508314
Note
NR 20140805Available from: 2012-03-08 Created: 2012-03-08 Last updated: 2017-12-07Bibliographically approved

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