Abstract

We present a novel algorithm for designing optimal cellular interconnects (OCI’s), which can significantly accelerate the communications among processors in single-instruction multiple-data machines with optoelectronic interconnections. We present the foundations of the OCI architecture and show that the optoelectronic OCI is the optimal topology for a space-invariant interconnect pattern. The OCI is optimal in achieving a minimum number of clock cycles per data shift for a given number of optoelectronic links. In addition, our algorithm for designing the OCI is deterministic, whereas previous designs required a trial-and-error procedure.

© 1998 Optical Society of America

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  1. K. Hwang, Advanced Computer Architecture: Parallelism, Scalability, Programmability (McGraw-Hill, New York, 1993).
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  3. H. J. Siegel, Interconnection Networks for Large-Scale Parallel Processing (McGraw-Hill, New York, 1990).
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    [CrossRef]
  5. H. N. Kim, M. J. Irwin, R. M. Owens, “Motion analysis on the micro grained array processor,” Real-time Imaging 3, 101–110 (1997).
    [CrossRef]
  6. D. G. Beetner, R. M. Arthur, “Generation of synthetic-focus images from pulse-echo ultrasound using difference-equations,” IEEE Trans. Med. Imaging 15, 665–672 (1996).
    [CrossRef] [PubMed]
  7. X. D. Wang, V. P. Roychowdhury, P. Balasingam, “Scaleable massively-parallel algorithms for computational nanoelectronics,” Parallel Computing 22, 1931–1963 (1997).
    [CrossRef]
  8. J. Brown, P. C. Hansen, J. Wasniewski, Z. Zlatev, “Comparing the performance of SIMD computers by running large air-pollution models,” Supercomputer 12, 21–35 (1996).
  9. C. B. Kuznia, “Cellular hypercube interconnections for optoelectronic smart pixel cellular arrays,” Ph.D. dissertation (University of Southern California, Los Angeles, California, 1994).
  10. P. Sweazey, “Limits of Performance of Backplane Buses,” in Digital Bus Handbook (McGraw-Hill, New York, 1990).
  11. A. Louri, H. Sung, “3D optical interconnects for high-speed interchip and interboard communications,” Computer 27, 27–37 (1994).
    [CrossRef]
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  13. A. A. Sawchuk, C. S. Raghavandra, B. K. Jenkins, A. Varma, “Optical crossbar networks,” IEEE Computer 20, 50–62 (1987).
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    [CrossRef]
  15. M. R. Feldman, C. C. Guest, T. J. Drabik, S. C. Esner, “Comparison between electrical and free space optical interconnects for fine grain processor arrays based on interconnect density capabilities,” Appl. Opt. 28, 3820–3829 (1989).
    [CrossRef] [PubMed]
  16. D. A. B. Miller, “Optics for low-energy communication inside digital processors: quantum detectors, sources, and modulators as efficient impedance converters,” Opt. Lett. 14, 146–148 (1989).
    [CrossRef] [PubMed]
  17. D. M. Chiarulli, S. P. Levitan, R. G. Mehlen, M. Bidnurkar, R. Ditmore, G. Gravenstreter, Z. Guo, C. Qiao, M. F. Sakr, J. P. Teza, “Optoelectronic buses for high-performance computing,” Proc. IEEE 82, 1701–1709 (1994).
    [CrossRef]
  18. F. E. Kiamilev, P. Marchand, A. V. Krishnamoorti, S. C. Esner, S. H. Lee, “Performance comparison between optoelectronic and VLSI multistage interconnection networks,” IEEE J. Lightwave Technol. 9, 1674–1692 (1991).
    [CrossRef]
  19. A. D. McAulay, Optical Computer Architectures: The Application of Optical Concepts to Next Generation Computers (Wiley, New York, 1991).
  20. B. K. Jenkins, P. Chavel, R. Forchheimer, A. A. Sawchuk, T. C. Strand, “Architectural implications of a digital optical processor,” Appl. Opt. 23, 3465–3474 (1984).
    [CrossRef] [PubMed]
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  22. A. Louri, H. Sung, “Efficient implementation methodology for three-dimensional space-invariant hypercube based optical interconnection networks,” Appl. Opt. 32, 7200–7209 (1993).
    [CrossRef] [PubMed]
  23. A. Louri, S. Furlonge, “Feasibility study of a scaleable optical interconnection network for massively parallel processing systems,” Appl. Opt. 35, 1296–1308 (1996).
    [CrossRef] [PubMed]
  24. J.-F. Lin, A. A. Sawchuk, “Optoelectronic communication speedup on mesh processors using reduced cellular hypercube interconnections,” in Optical Computing, Vol. 10 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 269–271.
  25. C. W. Stirk, J. Neff, “The cost of optical interconnects versus MCM’s,” in Digest of Topical Meeting on Optics in Computing ’97 (Optical Society of America, Washington, D.C., 1997, pp. 21–23.
  26. J. Jahns, M. M. Downs, M. E. Prise, “Damman gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
    [CrossRef]
  27. M. R. Feldman, C. C. Guest, “Holograms for optical interconnects for very large scale integrated circuits fabricated by electron-beam lithography,” Opt. Eng. 28, 915–921 (1989).
    [CrossRef]
  28. K.-S. Huang, C. B. Kuznia, B. K. Jenkins, A. A. Sawchuk, “Parallel architectures for digital optical cellular image processing,” Proc. IEEE 82, 1711–1723 (1994).
    [CrossRef]
  29. F. Sauer, J. Jahns, C. R. Nijander, “Refractive-diffractive micro-optics for permutation interconnects,” Opt. Eng. 33, 1550–1560 (1994).
    [CrossRef]
  30. C. B. Kuznia, A. A. Sawchuk, “Time multiplexing and control for optical cellular-hypercube arrays,” Appl. Opt. 35, 1836–1847 (1996).
    [CrossRef] [PubMed]

1997 (3)

X. D. Wang, V. P. Roychowdhury, P. Balasingam, “Scaleable massively-parallel algorithms for computational nanoelectronics,” Parallel Computing 22, 1931–1963 (1997).
[CrossRef]

H. C. Shi, G. X. Ritter, J. N. Wilson, “A fast general algorithm for extracting image features on SIMD mesh-connected computers,” Pattern Recogn. Lett. 30, 1205–1211 (1997).
[CrossRef]

H. N. Kim, M. J. Irwin, R. M. Owens, “Motion analysis on the micro grained array processor,” Real-time Imaging 3, 101–110 (1997).
[CrossRef]

1996 (4)

D. G. Beetner, R. M. Arthur, “Generation of synthetic-focus images from pulse-echo ultrasound using difference-equations,” IEEE Trans. Med. Imaging 15, 665–672 (1996).
[CrossRef] [PubMed]

J. Brown, P. C. Hansen, J. Wasniewski, Z. Zlatev, “Comparing the performance of SIMD computers by running large air-pollution models,” Supercomputer 12, 21–35 (1996).

A. Louri, S. Furlonge, “Feasibility study of a scaleable optical interconnection network for massively parallel processing systems,” Appl. Opt. 35, 1296–1308 (1996).
[CrossRef] [PubMed]

C. B. Kuznia, A. A. Sawchuk, “Time multiplexing and control for optical cellular-hypercube arrays,” Appl. Opt. 35, 1836–1847 (1996).
[CrossRef] [PubMed]

1994 (4)

K.-S. Huang, C. B. Kuznia, B. K. Jenkins, A. A. Sawchuk, “Parallel architectures for digital optical cellular image processing,” Proc. IEEE 82, 1711–1723 (1994).
[CrossRef]

F. Sauer, J. Jahns, C. R. Nijander, “Refractive-diffractive micro-optics for permutation interconnects,” Opt. Eng. 33, 1550–1560 (1994).
[CrossRef]

D. M. Chiarulli, S. P. Levitan, R. G. Mehlen, M. Bidnurkar, R. Ditmore, G. Gravenstreter, Z. Guo, C. Qiao, M. F. Sakr, J. P. Teza, “Optoelectronic buses for high-performance computing,” Proc. IEEE 82, 1701–1709 (1994).
[CrossRef]

A. Louri, H. Sung, “3D optical interconnects for high-speed interchip and interboard communications,” Computer 27, 27–37 (1994).
[CrossRef]

1993 (1)

1991 (2)

F. E. Kiamilev, P. Marchand, A. V. Krishnamoorti, S. C. Esner, S. H. Lee, “Performance comparison between optoelectronic and VLSI multistage interconnection networks,” IEEE J. Lightwave Technol. 9, 1674–1692 (1991).
[CrossRef]

H. S. Stone, J. Crocke, “Computer Architecture in the 1990s,” Computer 24, 30–38 (1991).
[CrossRef]

1990 (1)

1989 (5)

J. Jahns, M. M. Downs, M. E. Prise, “Damman gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[CrossRef]

M. R. Feldman, C. C. Guest, “Holograms for optical interconnects for very large scale integrated circuits fabricated by electron-beam lithography,” Opt. Eng. 28, 915–921 (1989).
[CrossRef]

P. B. Berra, A. Ghafoor, M. Guizani, S. J. Marcinkowski, P. A. Mitkas, “Optics and supercomputing,” Proc. IEEE 77, 1797–1815 (1989).
[CrossRef]

M. R. Feldman, C. C. Guest, T. J. Drabik, S. C. Esner, “Comparison between electrical and free space optical interconnects for fine grain processor arrays based on interconnect density capabilities,” Appl. Opt. 28, 3820–3829 (1989).
[CrossRef] [PubMed]

D. A. B. Miller, “Optics for low-energy communication inside digital processors: quantum detectors, sources, and modulators as efficient impedance converters,” Opt. Lett. 14, 146–148 (1989).
[CrossRef] [PubMed]

1987 (1)

A. A. Sawchuk, C. S. Raghavandra, B. K. Jenkins, A. Varma, “Optical crossbar networks,” IEEE Computer 20, 50–62 (1987).
[CrossRef]

1984 (2)

J. W. Goodman, F. J. Leonberg, S. Y. Kung, R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

B. K. Jenkins, P. Chavel, R. Forchheimer, A. A. Sawchuk, T. C. Strand, “Architectural implications of a digital optical processor,” Appl. Opt. 23, 3465–3474 (1984).
[CrossRef] [PubMed]

Arthur, R. M.

D. G. Beetner, R. M. Arthur, “Generation of synthetic-focus images from pulse-echo ultrasound using difference-equations,” IEEE Trans. Med. Imaging 15, 665–672 (1996).
[CrossRef] [PubMed]

Athale, R. A.

J. W. Goodman, F. J. Leonberg, S. Y. Kung, R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Balasingam, P.

X. D. Wang, V. P. Roychowdhury, P. Balasingam, “Scaleable massively-parallel algorithms for computational nanoelectronics,” Parallel Computing 22, 1931–1963 (1997).
[CrossRef]

Beetner, D. G.

D. G. Beetner, R. M. Arthur, “Generation of synthetic-focus images from pulse-echo ultrasound using difference-equations,” IEEE Trans. Med. Imaging 15, 665–672 (1996).
[CrossRef] [PubMed]

Berra, P. B.

P. B. Berra, A. Ghafoor, M. Guizani, S. J. Marcinkowski, P. A. Mitkas, “Optics and supercomputing,” Proc. IEEE 77, 1797–1815 (1989).
[CrossRef]

Bidnurkar, M.

D. M. Chiarulli, S. P. Levitan, R. G. Mehlen, M. Bidnurkar, R. Ditmore, G. Gravenstreter, Z. Guo, C. Qiao, M. F. Sakr, J. P. Teza, “Optoelectronic buses for high-performance computing,” Proc. IEEE 82, 1701–1709 (1994).
[CrossRef]

Brown, J.

J. Brown, P. C. Hansen, J. Wasniewski, Z. Zlatev, “Comparing the performance of SIMD computers by running large air-pollution models,” Supercomputer 12, 21–35 (1996).

Chavel, P.

Chiarulli, D. M.

D. M. Chiarulli, S. P. Levitan, R. G. Mehlen, M. Bidnurkar, R. Ditmore, G. Gravenstreter, Z. Guo, C. Qiao, M. F. Sakr, J. P. Teza, “Optoelectronic buses for high-performance computing,” Proc. IEEE 82, 1701–1709 (1994).
[CrossRef]

Crocke, J.

H. S. Stone, J. Crocke, “Computer Architecture in the 1990s,” Computer 24, 30–38 (1991).
[CrossRef]

Ditmore, R.

D. M. Chiarulli, S. P. Levitan, R. G. Mehlen, M. Bidnurkar, R. Ditmore, G. Gravenstreter, Z. Guo, C. Qiao, M. F. Sakr, J. P. Teza, “Optoelectronic buses for high-performance computing,” Proc. IEEE 82, 1701–1709 (1994).
[CrossRef]

Downs, M. M.

J. Jahns, M. M. Downs, M. E. Prise, “Damman gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[CrossRef]

Drabik, T. J.

Esner, S. C.

F. E. Kiamilev, P. Marchand, A. V. Krishnamoorti, S. C. Esner, S. H. Lee, “Performance comparison between optoelectronic and VLSI multistage interconnection networks,” IEEE J. Lightwave Technol. 9, 1674–1692 (1991).
[CrossRef]

M. R. Feldman, C. C. Guest, T. J. Drabik, S. C. Esner, “Comparison between electrical and free space optical interconnects for fine grain processor arrays based on interconnect density capabilities,” Appl. Opt. 28, 3820–3829 (1989).
[CrossRef] [PubMed]

Feldman, M. R.

M. R. Feldman, C. C. Guest, T. J. Drabik, S. C. Esner, “Comparison between electrical and free space optical interconnects for fine grain processor arrays based on interconnect density capabilities,” Appl. Opt. 28, 3820–3829 (1989).
[CrossRef] [PubMed]

M. R. Feldman, C. C. Guest, “Holograms for optical interconnects for very large scale integrated circuits fabricated by electron-beam lithography,” Opt. Eng. 28, 915–921 (1989).
[CrossRef]

Forchheimer, R.

Furlonge, S.

Ghafoor, A.

P. B. Berra, A. Ghafoor, M. Guizani, S. J. Marcinkowski, P. A. Mitkas, “Optics and supercomputing,” Proc. IEEE 77, 1797–1815 (1989).
[CrossRef]

Goodman, J. W.

J. W. Goodman, F. J. Leonberg, S. Y. Kung, R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Gravenstreter, G.

D. M. Chiarulli, S. P. Levitan, R. G. Mehlen, M. Bidnurkar, R. Ditmore, G. Gravenstreter, Z. Guo, C. Qiao, M. F. Sakr, J. P. Teza, “Optoelectronic buses for high-performance computing,” Proc. IEEE 82, 1701–1709 (1994).
[CrossRef]

Guest, C. C.

M. R. Feldman, C. C. Guest, T. J. Drabik, S. C. Esner, “Comparison between electrical and free space optical interconnects for fine grain processor arrays based on interconnect density capabilities,” Appl. Opt. 28, 3820–3829 (1989).
[CrossRef] [PubMed]

M. R. Feldman, C. C. Guest, “Holograms for optical interconnects for very large scale integrated circuits fabricated by electron-beam lithography,” Opt. Eng. 28, 915–921 (1989).
[CrossRef]

Guizani, M.

P. B. Berra, A. Ghafoor, M. Guizani, S. J. Marcinkowski, P. A. Mitkas, “Optics and supercomputing,” Proc. IEEE 77, 1797–1815 (1989).
[CrossRef]

Guo, Z.

D. M. Chiarulli, S. P. Levitan, R. G. Mehlen, M. Bidnurkar, R. Ditmore, G. Gravenstreter, Z. Guo, C. Qiao, M. F. Sakr, J. P. Teza, “Optoelectronic buses for high-performance computing,” Proc. IEEE 82, 1701–1709 (1994).
[CrossRef]

Hansen, P. C.

J. Brown, P. C. Hansen, J. Wasniewski, Z. Zlatev, “Comparing the performance of SIMD computers by running large air-pollution models,” Supercomputer 12, 21–35 (1996).

Huang, K.-S.

K.-S. Huang, C. B. Kuznia, B. K. Jenkins, A. A. Sawchuk, “Parallel architectures for digital optical cellular image processing,” Proc. IEEE 82, 1711–1723 (1994).
[CrossRef]

Hwang, K.

K. Hwang, Advanced Computer Architecture: Parallelism, Scalability, Programmability (McGraw-Hill, New York, 1993).

Irwin, M. J.

H. N. Kim, M. J. Irwin, R. M. Owens, “Motion analysis on the micro grained array processor,” Real-time Imaging 3, 101–110 (1997).
[CrossRef]

Jahns, J.

F. Sauer, J. Jahns, C. R. Nijander, “Refractive-diffractive micro-optics for permutation interconnects,” Opt. Eng. 33, 1550–1560 (1994).
[CrossRef]

J. Jahns, M. M. Downs, M. E. Prise, “Damman gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[CrossRef]

Jenkins, B. K.

K.-S. Huang, C. B. Kuznia, B. K. Jenkins, A. A. Sawchuk, “Parallel architectures for digital optical cellular image processing,” Proc. IEEE 82, 1711–1723 (1994).
[CrossRef]

A. A. Sawchuk, C. S. Raghavandra, B. K. Jenkins, A. Varma, “Optical crossbar networks,” IEEE Computer 20, 50–62 (1987).
[CrossRef]

B. K. Jenkins, P. Chavel, R. Forchheimer, A. A. Sawchuk, T. C. Strand, “Architectural implications of a digital optical processor,” Appl. Opt. 23, 3465–3474 (1984).
[CrossRef] [PubMed]

Kiamilev, F. E.

F. E. Kiamilev, P. Marchand, A. V. Krishnamoorti, S. C. Esner, S. H. Lee, “Performance comparison between optoelectronic and VLSI multistage interconnection networks,” IEEE J. Lightwave Technol. 9, 1674–1692 (1991).
[CrossRef]

Kim, H. N.

H. N. Kim, M. J. Irwin, R. M. Owens, “Motion analysis on the micro grained array processor,” Real-time Imaging 3, 101–110 (1997).
[CrossRef]

Krishnamoorti, A. V.

F. E. Kiamilev, P. Marchand, A. V. Krishnamoorti, S. C. Esner, S. H. Lee, “Performance comparison between optoelectronic and VLSI multistage interconnection networks,” IEEE J. Lightwave Technol. 9, 1674–1692 (1991).
[CrossRef]

Kung, S. Y.

J. W. Goodman, F. J. Leonberg, S. Y. Kung, R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Kuznia, C. B.

C. B. Kuznia, A. A. Sawchuk, “Time multiplexing and control for optical cellular-hypercube arrays,” Appl. Opt. 35, 1836–1847 (1996).
[CrossRef] [PubMed]

K.-S. Huang, C. B. Kuznia, B. K. Jenkins, A. A. Sawchuk, “Parallel architectures for digital optical cellular image processing,” Proc. IEEE 82, 1711–1723 (1994).
[CrossRef]

C. B. Kuznia, “Cellular hypercube interconnections for optoelectronic smart pixel cellular arrays,” Ph.D. dissertation (University of Southern California, Los Angeles, California, 1994).

Lee, S. H.

F. E. Kiamilev, P. Marchand, A. V. Krishnamoorti, S. C. Esner, S. H. Lee, “Performance comparison between optoelectronic and VLSI multistage interconnection networks,” IEEE J. Lightwave Technol. 9, 1674–1692 (1991).
[CrossRef]

Leonberg, F. J.

J. W. Goodman, F. J. Leonberg, S. Y. Kung, R. A. Athale, “Optical interconnections for VLSI systems,” Proc. IEEE 72, 850–866 (1984).
[CrossRef]

Levitan, S. P.

D. M. Chiarulli, S. P. Levitan, R. G. Mehlen, M. Bidnurkar, R. Ditmore, G. Gravenstreter, Z. Guo, C. Qiao, M. F. Sakr, J. P. Teza, “Optoelectronic buses for high-performance computing,” Proc. IEEE 82, 1701–1709 (1994).
[CrossRef]

Lin, J.-F.

J.-F. Lin, A. A. Sawchuk, “Optoelectronic communication speedup on mesh processors using reduced cellular hypercube interconnections,” in Optical Computing, Vol. 10 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 269–271.

Louri, A.

Marchand, P.

F. E. Kiamilev, P. Marchand, A. V. Krishnamoorti, S. C. Esner, S. H. Lee, “Performance comparison between optoelectronic and VLSI multistage interconnection networks,” IEEE J. Lightwave Technol. 9, 1674–1692 (1991).
[CrossRef]

Marcinkowski, S. J.

P. B. Berra, A. Ghafoor, M. Guizani, S. J. Marcinkowski, P. A. Mitkas, “Optics and supercomputing,” Proc. IEEE 77, 1797–1815 (1989).
[CrossRef]

McAulay, A. D.

A. D. McAulay, Optical Computer Architectures: The Application of Optical Concepts to Next Generation Computers (Wiley, New York, 1991).

Mehlen, R. G.

D. M. Chiarulli, S. P. Levitan, R. G. Mehlen, M. Bidnurkar, R. Ditmore, G. Gravenstreter, Z. Guo, C. Qiao, M. F. Sakr, J. P. Teza, “Optoelectronic buses for high-performance computing,” Proc. IEEE 82, 1701–1709 (1994).
[CrossRef]

Miller, D. A. B.

Mitkas, P. A.

P. B. Berra, A. Ghafoor, M. Guizani, S. J. Marcinkowski, P. A. Mitkas, “Optics and supercomputing,” Proc. IEEE 77, 1797–1815 (1989).
[CrossRef]

Neff, J.

C. W. Stirk, J. Neff, “The cost of optical interconnects versus MCM’s,” in Digest of Topical Meeting on Optics in Computing ’97 (Optical Society of America, Washington, D.C., 1997, pp. 21–23.

Nijander, C. R.

F. Sauer, J. Jahns, C. R. Nijander, “Refractive-diffractive micro-optics for permutation interconnects,” Opt. Eng. 33, 1550–1560 (1994).
[CrossRef]

Owens, R. M.

H. N. Kim, M. J. Irwin, R. M. Owens, “Motion analysis on the micro grained array processor,” Real-time Imaging 3, 101–110 (1997).
[CrossRef]

Prise, M. E.

J. Jahns, M. M. Downs, M. E. Prise, “Damman gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[CrossRef]

Qiao, C.

D. M. Chiarulli, S. P. Levitan, R. G. Mehlen, M. Bidnurkar, R. Ditmore, G. Gravenstreter, Z. Guo, C. Qiao, M. F. Sakr, J. P. Teza, “Optoelectronic buses for high-performance computing,” Proc. IEEE 82, 1701–1709 (1994).
[CrossRef]

Raghavandra, C. S.

A. A. Sawchuk, C. S. Raghavandra, B. K. Jenkins, A. Varma, “Optical crossbar networks,” IEEE Computer 20, 50–62 (1987).
[CrossRef]

Ritter, G. X.

H. C. Shi, G. X. Ritter, J. N. Wilson, “A fast general algorithm for extracting image features on SIMD mesh-connected computers,” Pattern Recogn. Lett. 30, 1205–1211 (1997).
[CrossRef]

Roychowdhury, V. P.

X. D. Wang, V. P. Roychowdhury, P. Balasingam, “Scaleable massively-parallel algorithms for computational nanoelectronics,” Parallel Computing 22, 1931–1963 (1997).
[CrossRef]

Sakr, M. F.

D. M. Chiarulli, S. P. Levitan, R. G. Mehlen, M. Bidnurkar, R. Ditmore, G. Gravenstreter, Z. Guo, C. Qiao, M. F. Sakr, J. P. Teza, “Optoelectronic buses for high-performance computing,” Proc. IEEE 82, 1701–1709 (1994).
[CrossRef]

Sauer, F.

F. Sauer, J. Jahns, C. R. Nijander, “Refractive-diffractive micro-optics for permutation interconnects,” Opt. Eng. 33, 1550–1560 (1994).
[CrossRef]

Sawchuk, A. A.

C. B. Kuznia, A. A. Sawchuk, “Time multiplexing and control for optical cellular-hypercube arrays,” Appl. Opt. 35, 1836–1847 (1996).
[CrossRef] [PubMed]

K.-S. Huang, C. B. Kuznia, B. K. Jenkins, A. A. Sawchuk, “Parallel architectures for digital optical cellular image processing,” Proc. IEEE 82, 1711–1723 (1994).
[CrossRef]

A. A. Sawchuk, C. S. Raghavandra, B. K. Jenkins, A. Varma, “Optical crossbar networks,” IEEE Computer 20, 50–62 (1987).
[CrossRef]

B. K. Jenkins, P. Chavel, R. Forchheimer, A. A. Sawchuk, T. C. Strand, “Architectural implications of a digital optical processor,” Appl. Opt. 23, 3465–3474 (1984).
[CrossRef] [PubMed]

J.-F. Lin, A. A. Sawchuk, “Optoelectronic communication speedup on mesh processors using reduced cellular hypercube interconnections,” in Optical Computing, Vol. 10 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 269–271.

Sheng, Y.

Shi, H. C.

H. C. Shi, G. X. Ritter, J. N. Wilson, “A fast general algorithm for extracting image features on SIMD mesh-connected computers,” Pattern Recogn. Lett. 30, 1205–1211 (1997).
[CrossRef]

Siegel, H. J.

H. J. Siegel, Interconnection Networks for Large-Scale Parallel Processing (McGraw-Hill, New York, 1990).

Stirk, C. W.

C. W. Stirk, J. Neff, “The cost of optical interconnects versus MCM’s,” in Digest of Topical Meeting on Optics in Computing ’97 (Optical Society of America, Washington, D.C., 1997, pp. 21–23.

Stone, H. S.

H. S. Stone, J. Crocke, “Computer Architecture in the 1990s,” Computer 24, 30–38 (1991).
[CrossRef]

Strand, T. C.

Sung, H.

Sweazey, P.

P. Sweazey, “Limits of Performance of Backplane Buses,” in Digital Bus Handbook (McGraw-Hill, New York, 1990).

Teza, J. P.

D. M. Chiarulli, S. P. Levitan, R. G. Mehlen, M. Bidnurkar, R. Ditmore, G. Gravenstreter, Z. Guo, C. Qiao, M. F. Sakr, J. P. Teza, “Optoelectronic buses for high-performance computing,” Proc. IEEE 82, 1701–1709 (1994).
[CrossRef]

Varma, A.

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Figures (10)

Fig. 1
Fig. 1

Implementation of the optical CH interconnect in a two-lens telecentric (4F) system.

Fig. 2
Fig. 2

Optical links and timing diagram for a 1-D CH. Here every 11th PE actively transmits data, and all the others receive data. (a) The connections are made to neighbors at distances of {±2, ±4, ±8, ±16}. Some connections fall outside the array, but no contention occurs. (b) Scheduling of the transmitting PE’s illustrating the time-slotted protocol for 11 consecutive time slots, after which the scheduling is repeated periodically.

Fig. 3
Fig. 3

Flow diagram for the algorithm for an OCI design: (a) symmetrical interconnect and (b) nonsymmetrical interconnect.

Fig. 4
Fig. 4

Number of clock cycles versus the maximum shift distance for an OCI of different fan-outs.

Fig. 5
Fig. 5

Two-dimensional interconnection pattern as the external product of two 1-D OCI patterns.

Fig. 6
Fig. 6

Histogram of the number of clock cycles per data shift in a 4096 processor array, with one data point for each shift distance from 1 to 4096. The OCI is optimized for a reduced number of clock cycles. The connection sets are as given in Table 1 for MRCH and OCI-N with K = 4.

Fig. 7
Fig. 7

Histogram of the number of clock cycles per data shift in a 4096 processor array, with one data point for each shift distance from 1 to 4096. The OCI is suboptimal with reduced fan-out. The connection sets are as given in Table 1 for an MRCH and an OCI-N with K = 3.

Fig. 8
Fig. 8

Histogram of the number of clock cycles per data shift in a 256 processor array, with one data point for each shift distance from 1 to 256. The OCI is optimized for reduced fan-out. The connection sets are as given in Table 2 for a MRCH, an OCI-S, and an OCI-N with K = 2.

Fig. 9
Fig. 9

Histogram of the number of clock cycles per data shift in a 256 processor array, with one data point for each shift distance from 1 to 256. OCI optimized for reduced number of clock cycles. The connection sets are as given in Table 2 for MRCH, OCI-S, and OCI-N with K = 3.

Fig. 10
Fig. 10

Optimal coverage of processor array with a given fan-out.

Tables (2)

Tables Icon

Table 1 Performance Comparison of OCI and MRCH for Arrays of 4096 PE’s

Tables Icon

Table 2 Performance Comparison of OCI and MRCH for Arrays of 256 PE’s

Equations (21)

Equations on this page are rendered with MathJax. Learn more.

X n + 1 = 4 X n - X n - 1 ,   n > 1 ,
X 0 = M ,
X 1 = M + 2 S + 1 .
X ( n ) = 1 2 3 { [ M ( 3 - 1 ) + 2 S + 1 ] ( 2 + 3 ) n + [ M ( 3 + 1 ) - 2 S - 1 ] ( 2 - 3 ) n } ,   n 0 .
D K = 3 X K - X K - 1 - 1 2 ,
X m ± X n = lM ,   l Z ,   m ,   n 1 ,   2 ,     K .
X m ± X n mod   M 0 ,   m ,   n 1 ,   2 ,     K ,
M 2 K + 1 .
M = 2 K + 1 .
t = P - X n mod   M .
X K + 1 = X K + 2 D K + 1 .
D K + 1 = X K + 1 + D K .
X K + 1 = 4 X K - X K - 1 .
X K = AR 1 K + BR 2 K ,
R i 2 - 4 R i + 1 = 0 ,     i = 1 ,   2 ,
A = 1 2 3 2 S + 1 + M 3 - 1 , B = 1 2 3 M 1 + 3 - 2 S - 1 ,
X ( K ) = 1 2 3 { [ M ( 3 - 1 ) + 2 S + 1 ] ( 2 + 3 ) K + [ M ( 3 + 1 ) - 2 S - 1 ) ( 2 - 3 ) K } ,   K 1 .
D ( K ) = X ( K + 1 ) - X ( K ) - 1 2 = 3 X ( K ) - X ( K - 1 ) - 1 2 = { [ ( 2 S + 1 ) ( 3 + 1 ) + 2 M ] ( 2 + 3 ) K + [ ( 2 S + 1 ) ( 3 - 1 ) - 2 M ] ( 2 - 3 ) K } 4 3 ,
X n + 1 = 4 X n - X n - 1 , n > 1 ,
X 0 = M ,   X 1 = M + 2 S + 1 ,
X ( n ) = 1 2 3 { [ M ( 3 - 1 ) + 2 S + 1 ] ( 2 + 3 ) n + [ M ( 3 + 1 ) - 2 S - 1 ] ( 2 - 3 ) n } , n 1 .

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