Communication effect basic linear algebra computations on hypercube architectures
Journal of Parallel and Distributed Computing
Topological Properties of Hypercubes
IEEE Transactions on Computers
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Parallel permutation and sorting algorithms and a new generalized connection network
Journal of the ACM (JACM)
The cube-connected cycles: a versatile network for parallel computation
Communications of the ACM
IPPS '92 Proceedings of the 6th International Parallel Processing Symposium
Optimal All-to-Some Personalized Communication on Hypercubes
IPPS '98 Proceedings of the 12th. International Parallel Processing Symposium on International Parallel Processing Symposium
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Derives a simple lower bound for performing a 2/sup b/ permutation on an N-PE SIMDhypercube, proving that log N-b routing steps are needed even if one allows an arbitrarymapping of elements to processors. An algorithm for performing a 2/sup b/ permutationusing exactly log N-b full-duplex routing steps that is slightly more efficient thanpreviously known O(log N-b) algorithms, which perform the permutation as an Omega orOmega /sup -1/ mapping, is presented. The author has also identified a general class ofparallel computations called +or-2/sup b/ descend, which includes Batcher's odd-evenmerge and many other algorithms. An efficient algorithm for performing any computation in this class in O(log N) steps on an N-PE SIMD hypercube is given. A related class of parallel computations called +or-2/sup b/ ascend is also defined. This class appears to be more difficult than +or-2/sup b/ descend. A simple O(log/sup 2/ N/log log) N algorithm for this class on a SIMD hypercube, requiring Theta (log log N) space per processor is developed.