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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 31, Iss. 11 — Apr. 10, 1992
  • pp: 1709–1716

Transformation of three-dimensional shuffle patterns

Josef Gigimayr  »View Author Affiliations


Applied Optics, Vol. 31, Issue 11, pp. 1709-1716 (1992)
http://dx.doi.org/10.1364/AO.31.001709


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Abstract

Formulas are presented for the transformation of three-dimensional shuffle patterns into the two-dimensional domain. The results are applied to the transformation of the interstage patterns of three-dimensional multistage interconnection networks into their isomorphic two-dimensional patterns (and vice versa). This paper explains material in J. Giglmayr, “Classification scheme for 3-D shuffle interconnection patterns,” Appl. Opt. 28, 3120–3128 (1989) and corrects some algebraic results.

© 1992 Optical Society of America

History
Original Manuscript: September 26, 1990
Published: April 10, 1992

Citation
Josef Gigimayr, "Transformation of three-dimensional shuffle patterns," Appl. Opt. 31, 1709-1716 (1992)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-31-11-1709


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References

  1. T. J. Cloonan, F. B. McCormick, M. J. Herron, F. A. P. Tooley, G. W. Richards, E. Kerbis, J. L. Brubaker, A. L. Lentine, “A 3D crossover switching network based on S-SEED arrays,” in Photonics Switching II, K. Tada, H. S. Hinton, eds., Vol. 29 of Springer Series on Electronics and Photonics (Springer-Verlag, Berlin, 1990), pp. 196–199. [CrossRef]
  2. K. Padmanabhan, D. H. Lawrie, “A class of redundant multistage interconnection networks,” IEEE Trans. Comput. C-32, 1099–1108 (1983). [CrossRef]
  3. J. Giglmayr, “Classification scheme for 3-D shuffle interconnection patterns,” Appl. Opt. 28, 3120–3128 (1989). [CrossRef]
  4. M. Davio, “Kronecker products and shuffle algebra,” IEEE Trans. Comput. C-30, 116–125 (1981). [CrossRef]
  5. A. Graham, Kronecker Products and Matrix Calculus with Applications (Ellies Horwood, London, 1981), Chap. 1, pp. 24–25.
  6. M. C. Pease, “An adaption of the fast Fourier transform for parallel processing,” J. Assoc. Comput. Mach. 15, 252–264 (1968). [CrossRef]
  7. J. Giglmayr, “On the spatial extension of multistage interconnection networks,” in Technical Digest of the Topical Meeting on Photonic Switching (Optical Society of America, Washington, D.C., 1989), pp. 54–57.
  8. J. E. Eisele, R. M. Mason, Applied Matrix and Tensor Analysis (Wiley-Interscience, New York, 1970), Chap. 4, p. 216.
  9. J. Giglmayr, “Organization of k × k switches (k ≥ 4) interconnected by d-dimensional (d ≥ 2) regular optical patterns,” Appl. Opt. 30, 5119–5135.
  10. R. H. Bracewell, The Hartley Transform (Oxford U. Press, London, 1986), Chap. 7, p. 128 (German edition).

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