A Unified Approach to a Class of Data Movements on an Array Processor
IEEE Transactions on Computers
Communication effect basic linear algebra computations on hypercube architectures
Journal of Parallel and Distributed Computing
Expressing Boolean cube matrix algorithms in shared memory primitives
C3P Proceedings of the third conference on Hypercube concurrent computers and applications - Volume 2
Index Transformation Algorithms in a Linear Algebra Framework
IEEE Transactions on Parallel and Distributed Systems
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In this paper we present algorithms optimal within a small constant factor for stable dimension permutations on Boolean cubes. A stable dimension permutation is a permutation such that element (wm-1wm-2 … w0) is relocated to the location of element (w&dgr;(m-1)w&dgr;(m-2)…w&dgr;(0) after the permutation, or i → &dgr;(i), where &dgr;(·) is a permutation function on {0,1,…, m - 1}. Depending on communication capability, message size, cube size, data transfer rate, and communication start-up time, different algorithms must be chosen for a communication time optimal within a small constant factor. The bandwidth of the Boolean cube is fully explored by dividing the data set to be communicated between a pair of processors into subsets, one for each path between the pair of processors. The k-shuffle permutation, the bit-reversal permutation, and matrix transposition, are special cases of stable dimension permutations. Experimental results on the Intel iPSC are also provided.