Issue No.03 - March (1980 vol.29)
D.S., Jr. Parker , Department of Computer Science, University of California
In this paper a number of properties of Shuffle/Exchange networks are analyzed. A set of algebraic tools is developed and is used to prove that Lawrie's inverse Omega network, Pease's indirect binary n-cube array, and a network related to the 3-stage rearrangeable switching network studied by Clos and Bene? have identical switching capabilities. The approach used leads to a number of insights on the structure of the fast Fourier transform (FFT) algorithm. The inherent permuting power, or "universality," of the networks when used iteratively is then probed, leading to some nonintuitive results which have implications on the optimal control of Shuffle/Exchange-type networks for realizing permutations and broadcast connections.
Shuffle/Exchange, Fast Fourier transform (FFT) algorithm, indirect binary n-cube, interconnection switches, Omega network, network universality, 3-stage rearrangeable switching network
D.S., Jr. Parker, "Notes on Shuffle/Exchange-Type Switching Networks", IEEE Transactions on Computers, vol.29, no. 3, pp. 213-222, March 1980, doi:10.1109/TC.1980.1675553