Communication Efficient Basic Linear Algebra Computations on Hypercube Architectures

• 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

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NATURVETENSKAP  -- Data- och informationsvetenskap (hsv//swe)

NATURAL SCIENCES  -- Computer and Information Sciences (hsv//eng)

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