Abstract

We present a new design methodology for constructing three-dimensional space-invariant hypercube interconnection networks. The methodology is based on a graph bipartitioning technique and permits the construction of larger hypercube networks from smaller networks in a systematic and incremental fashion. Owing to their totally space-invariant nature, the resulting three-dimensional hypercube networks are amenable to optical implementations with simple optical hardware such as multiple imaging components and space-invariant holographic techniques.

© 1993 Optical Society of America

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References

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  1. Y. Sheng, Appl. Opt. 29, 1101 (1990).
    [Crossref] [PubMed]
  2. K. S. Huang, B. K. Jenkins, A. A. Sawchuk, Proc. Soc. Photo-Opt. Instrum. Eng. 829, 331 (1987).
  3. A. R. Johnston, L. Bergman, W. H. Wu, Proc. Soc. Photo-Opt. Instrum. Eng. 881, 186 (1988).
  4. G. E. Lohman, K. H. Brenner, Optik 89, 123 (1992).
  5. B. K. Jenkins, P. Chavel, R. Forchheimer, A. A. Sawchuk, T. C. Strand, Appl. Opt. 23, 3465 (1984).
    [Crossref] [PubMed]

1992 (1)

G. E. Lohman, K. H. Brenner, Optik 89, 123 (1992).

1990 (1)

1988 (1)

A. R. Johnston, L. Bergman, W. H. Wu, Proc. Soc. Photo-Opt. Instrum. Eng. 881, 186 (1988).

1987 (1)

K. S. Huang, B. K. Jenkins, A. A. Sawchuk, Proc. Soc. Photo-Opt. Instrum. Eng. 829, 331 (1987).

1984 (1)

Bergman, L.

A. R. Johnston, L. Bergman, W. H. Wu, Proc. Soc. Photo-Opt. Instrum. Eng. 881, 186 (1988).

Brenner, K. H.

G. E. Lohman, K. H. Brenner, Optik 89, 123 (1992).

Chavel, P.

Forchheimer, R.

Huang, K. S.

K. S. Huang, B. K. Jenkins, A. A. Sawchuk, Proc. Soc. Photo-Opt. Instrum. Eng. 829, 331 (1987).

Jenkins, B. K.

K. S. Huang, B. K. Jenkins, A. A. Sawchuk, Proc. Soc. Photo-Opt. Instrum. Eng. 829, 331 (1987).

B. K. Jenkins, P. Chavel, R. Forchheimer, A. A. Sawchuk, T. C. Strand, Appl. Opt. 23, 3465 (1984).
[Crossref] [PubMed]

Johnston, A. R.

A. R. Johnston, L. Bergman, W. H. Wu, Proc. Soc. Photo-Opt. Instrum. Eng. 881, 186 (1988).

Lohman, G. E.

G. E. Lohman, K. H. Brenner, Optik 89, 123 (1992).

Sawchuk, A. A.

K. S. Huang, B. K. Jenkins, A. A. Sawchuk, Proc. Soc. Photo-Opt. Instrum. Eng. 829, 331 (1987).

B. K. Jenkins, P. Chavel, R. Forchheimer, A. A. Sawchuk, T. C. Strand, Appl. Opt. 23, 3465 (1984).
[Crossref] [PubMed]

Sheng, Y.

Strand, T. C.

Wu, W. H.

A. R. Johnston, L. Bergman, W. H. Wu, Proc. Soc. Photo-Opt. Instrum. Eng. 881, 186 (1988).

Appl. Opt. (2)

Optik (1)

G. E. Lohman, K. H. Brenner, Optik 89, 123 (1992).

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

K. S. Huang, B. K. Jenkins, A. A. Sawchuk, Proc. Soc. Photo-Opt. Instrum. Eng. 829, 331 (1987).

A. R. Johnston, L. Bergman, W. H. Wu, Proc. Soc. Photo-Opt. Instrum. Eng. 881, 186 (1988).

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Figures (4)

Fig. 1
Fig. 1

Model for 3-D free-space optical interconnect architectures.

Fig. 2
Fig. 2

Realization of a 3-D space-invariant 5-cube network: (a) 32 nodes are bipartitioned; the binary number in the box represents the address of the corresponding node, (b) A conceptual optical realization; node addresses are shown by the decimal numbers. The connection rule represents the amount of row-wise or column-wise shifts that provide space-invariant connections for the 5-cube network.

Fig. 3
Fig. 3

3-D space-invariant hypercube networks of dimension n, where 2 ≤ n ≤ 5.

Fig. 4
Fig. 4

Construction of a 3-D space-invariant 6-cube network from a 3-D space-invariant 5-cube network. The node numbers at steps 2 and 3 are shown by decimal numbers.

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