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Invariant Properties of the Shuffle-Exchange and a Simplified Cost-Effective Version of the Omega Network
May 1983 (vol. 32 no. 5)
pp. 444-450
| ASCII Text | x | ||
| D. Steinberg, "Invariant Properties of the Shuffle-Exchange and a Simplified Cost-Effective Version of the Omega Network," IEEE Transactions on Computers, vol. 32, no. 5, pp. 444-450, May, 1983. | |||
| BibTex | x | ||
| @article{ 10.1109/TC.1983.1676255, author = {D. Steinberg}, title = {Invariant Properties of the Shuffle-Exchange and a Simplified Cost-Effective Version of the Omega Network}, journal ={IEEE Transactions on Computers}, volume = {32}, number = {5}, issn = {0018-9340}, year = {1983}, pages = {444-450}, doi = {http://doi.ieeecomputersociety.org/10.1109/TC.1983.1676255}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - JOUR JO - IEEE Transactions on Computers TI - Invariant Properties of the Shuffle-Exchange and a Simplified Cost-Effective Version of the Omega Network IS - 5 SN - 0018-9340 SP444 EP450 EPD - 444-450 A1 - D. Steinberg, PY - 1983 KW - triangular permutation KW - Admissible permutation KW - invariance KW - linear permutation KW - lower triangular shuffle-exchange network KW - Omega network KW - parallel processing KW - permutation network KW - shuffle-exchange KW - SIMD array VL - 32 JA - IEEE Transactions on Computers ER - | |||
Let O denote the set of permutations performable by a pass through the Omega network (an n-stage shuffle-exchange network), and let p denote an arbitrary permutation of N = 2n elements. In this paper we characterize the sets {p|pO = O} (called left invariants) and {p|Op = O} (called right invariants). This characterization provides a useful criterion for determining whether or not the composition of two permutations belongs to O; it also allows a number of known results to be generalized and their derivations simplified.
Index Terms:
triangular permutation, Admissible permutation, invariance, linear permutation, lower triangular shuffle-exchange network, Omega network, parallel processing, permutation network, shuffle-exchange, SIMD array
Citation:
D. Steinberg, "Invariant Properties of the Shuffle-Exchange and a Simplified Cost-Effective Version of the Omega Network," IEEE Transactions on Computers, vol. 32, no. 5, pp. 444-450, May 1983, doi:10.1109/TC.1983.1676255
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