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
Algorithms for matrix transposition on Boolean N-cube configured ensemble architecture
SIAM Journal on Matrix Analysis and Applications
Optimal algorithms for stable dimension permutations on Boolean cubes
C3P Proceedings of the third conference on Hypercube concurrent computers and applications: Architecture, software, computer systems, and general issues - Volume 1
Optimal matrix transposition of bit reversal on hypercubes: all-to-personalized communication
Journal of Parallel and Distributed Computing
Computational frameworks for the fast Fourier transform
Computational frameworks for the fast Fourier transform
Matrix computations (3rd ed.)
Array Permutation by Index-Digit Permutation
Journal of the ACM (JACM)
An optimal routing algorithm for mesh-connected Parallel computers
Journal of the ACM (JACM)
Structured permuting in place on parallel disk systems
Proceedings of the fourth workshop on I/O in parallel and distributed systems: part of the federated computing research conference
Embedding Hierarchical Hypercube Networks into the Hypercube
IEEE Transactions on Parallel and Distributed Systems
IEEE Transactions on Parallel and Distributed Systems
Performing BMMC Permutations in Two Passes through the Expanded Delta Network and MasPar MP-2
FRONTIERS '96 Proceedings of the 6th Symposium on the Frontiers of Massively Parallel Computation
Array organization in parallel memories
International Journal of Parallel Programming
Efficient parallel out-of-core matrix transposition
International Journal of High Performance Computing and Networking
Efficient Parallel I/O in Community Atmosphere Model (CAM)
International Journal of High Performance Computing Applications
Radix-4 FFT algorithms with ordered input and output data
DSP'09 Proceedings of the 16th international conference on Digital Signal Processing
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We present a linear algebraic formulation for a class of index transformations such asGray code encoding and decoding, matrix transpose, bit reversal, vector reversal,shuffles, and other index or dimension permutations. This formulation unifies, simplifies,and can be used to derive algorithms for hypercube multiprocessors. We show how all the widely known properties of Gray codes, and some not so well-known properties as well, can be derived using this framework. Using this framework, we relate hypercube communications algorithms to Gauss-Jordan elimination on a matrix of 0's and 1's.