Abstract

Associative processing based on content-addressable memories has been argued to be the natural solution for nonnumerical information processing applications. Unfortunately, the implementation requirements of these architectures when one uses conventional electronic technology have been cost prohibitive; therefore associative processors have not been realized. Instead, software methods that emulate the behavior of associative processing have been promoted and mapped onto conventional location-addressable systems. However, this does not bring about the natural parallelism of associative processing, namely, the ability to access many data words simultaneously. Optics has the advantage over electronics of directly supporting associative processing by providing economic and efficient interconnects, massive parallelism, and high-speed processing. The principles of designing an optical content-addressable parallel processor (OCAPP) for the efficient support of parallel symbolic computing are presented. The architecture is designed to exploit optics advantages fully in interconnects and high-speed operations. Several parallel search-and-retrieval algorithms are mapped onto an OCAPP to illustrate its capability of supporting parallel symbolic computing. A theoretical performance analysis of these algorithms is presented. This analysis reveals that the execution times of the parallel algorithms presented are independent of the problem size, which makes the OCAPP suitable for applications in which the number of data sets to be operated on is high (e.g., massive parallel processing). A preliminary optical implementation of the architecture with currently available optical components is also presented.

© 1992 Optical Society of America

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    [CrossRef]
  44. A. A. Sawchuk, C. S. Raghavandra, B. K. Jenkins, A. Varma, “Optical cross-bar networks,” IEEE Computer 20(6), 50–62 (1987).
    [CrossRef]
  45. G. Gheen, “Optical matrix–matrix multiplier,” Appl. Opt. 29, 886–887 (1990).
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1991

A. Louri, “3-D optical architecture and data-parallel algorithms for massively parallel computing,” IEEE Micro 11(2), 24–68 (1991).
[CrossRef]

G. R. Olbright, R. P. Bryan, K. Lear, T. M. Brennan, G. Poirier, Y. H. Lee, J. L. Jewell, “Cascadable laser logic devices: Discrete integration of photoresistors will surface-emitting laser diodes,” Electron. Lett. 27, 216–218 (1991).
[CrossRef]

M. Prose, N. C. Craft, M. M. Downs, R. E. LaMarche, L. A. Asaro, L. Chirovsky, M. Murdocca, “Optical digital processor using arrays of symmetric self-electrooptic effect devices,” Appl. Opt. 30, 2287–2296 (1991).
[CrossRef]

1990

1989

N. Streibl, K. H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. Miller, M. Murdocca, M. E. Prise, T. Sizer, “Digital optics,” Proc. IEEE 77, 1954–1970 (1989).
[CrossRef]

W. T. Cathey, K. Wagner, W. J. Miceli, “Digital computing with optics,” Proc. IEEE 77, 1558–1572 (1989).
[CrossRef]

H. J. Caulfield, J. Kinser, S. K. Rogers, “Optical neural networks,” Proc. IEEE 77, 1573–1583 (1989).
[CrossRef]

Y. Li, D. H. Kim, A. Kostrzewski, G. Eichmann, “Content-addressable memory-based optical modified signed-digit arithmetic,” Opt. lett. 14, 1254–1256 (1989).
[CrossRef] [PubMed]

F. Kiamilev, S. C. Esner, R. Paturi, Y. Fainman, P. Mercier, C. C. Guest, S. H. Lee, “Programmable optoelectronic multiprocessors and their comparison with symbolic substitution for digital optical computing,” Opt. Eng. 28, 396–409 (1989).

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

K. Hwang, A. Louri, “Optical multiplication and division using modified signed-digit symbolic substitution,” Opt. Eng. 28, 364–373 (1989).

A. L. Lentine, H. S. Hinton, D. A. B. Miller, J. E. Henry, J. E. Cunningham, L. M. F. Chirovsky, “Symmetric self-electrooptic effect device: optical set–reset latch, differential logic gate, and differential modulator/detector,” IEEE J. Quantum Electron. 25, 1928–1936 (1989).
[CrossRef]

A. Hartmann, S. Redfield, “Design sketches for optical crossbar switches intended for large-scale parallel processing applications,” Opt. Eng. 28, 315–328 (1989).

1988

1987

A. A. Sawchuk, C. S. Raghavandra, B. K. Jenkins, A. Varma, “Optical cross-bar networks,” IEEE Computer 20(6), 50–62 (1987).
[CrossRef]

K. Wagner, D. Psaltis, “Multilayer optical learning networks,” Appl. Opt. 26, 5067–5076 (1987).
[CrossRef]

1986

R. Halstead, “Parallel symbolic computing,” Computer 19(8), 35–43 (1986).
[CrossRef]

R. M. Lea, “VLSI and WSI associative string processors for cost-effective parallel processing,” Computer J. 29, 486–494 (1986).
[CrossRef]

A. W. Lohmann, “What classical optics can do for the digital optical computer,” Appl. Opt. 25, 1543–1549 (1986).
[CrossRef] [PubMed]

1985

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, “The quantum well self-electro-optic effect device: optoelectronic bistability and oscillation, and self-linearized modulation,” IEEE J. Quantum Electron. QE-21, 1462–1476 (1985).
[CrossRef]

1984

S. D. Smith, J. G. H. Mathew, M. R. Taghizadeth, A. C. Walker, B. S. Wherret, A. Hendry, “Room temperature, visible wavelength optical bistability in ZnSe interference filters,” Opt. Commun. 51, 357–362 (1984).
[CrossRef]

J. L. Jewell, M. C. Rushford, H. M. Gibbs, “Use of a single nonlinear Fabry–Perot étalon as optical logic gate,” Appl. Phys. Lett. 44, 172–174 (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]

A. A. Sawchuk, T. C. Stand, “Digital optical computing,” Proc. IEEE 72, 758–779 (1984).
[CrossRef]

A. Huang, “Architectural considerations involved in the design of an optical digital computer,” Proc. IEEE 72, 780–787 (1984).
[CrossRef]

1982

D. A. B. Miller, D. S. Chemla, D. J. Eilenberger, P. W. Smith, A. C. Gossard, W. T. Tsang, “Large room-temperature optical nonlinearity in GaAs/Ga1−xAlxAs multiple quantum well structures,” Appl. Phys. Lett. 44, 821–823 (1982).

1975

R. M. Lea, “Information processing with an associative parallel processor,” Computer 8(11), 25–32 (1975).
[CrossRef]

1968

C. C. Foster, “Determination of priority in associative memories,” IEEE Trans. Comput. C-17, 788–789 (1968).
[CrossRef]

1964

C. Y. Lee, M. C. Paul, “A content addressable distributed logic memory with applications to information retrieval,” Proc. IEEE 51, 924–932 (1964).
[CrossRef]

Almasi, G. S.

G. S. Almasi, A. Gottlieb, Highly Parallel Computing (Addison-Wesley, Reading, Mass., 1989).

Asaro, L.

Asaro, L. A.

Athale, R. A.

J. A. Neff, R. A. Athale, S. H. Lee, “Two-dimensional spatial light modulators: a tutorial,” Proc. IEEE 78, 836–855 (1990).
[CrossRef]

R. A. Athale, “Optical matrix processors,” in Optical and Hybrid Computing, H. H. Szu, ed., Proc. Soc. Photo-Opt. Instrum. Eng.634, 96–111 (1986).
[CrossRef]

Berra, P. B.

P. B. Berra, K. H. Brenner, W. T. Cathey, H. J. Caulfield, S. H. Lee, H. Szu, “Optical database/knowledgebase machines,” Appl. Opt. 29, 195–205 (1990).
[CrossRef] [PubMed]

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

Brennan, T. M.

G. R. Olbright, R. P. Bryan, K. Lear, T. M. Brennan, G. Poirier, Y. H. Lee, J. L. Jewell, “Cascadable laser logic devices: Discrete integration of photoresistors will surface-emitting laser diodes,” Electron. Lett. 27, 216–218 (1991).
[CrossRef]

Brenner, K. H.

P. B. Berra, K. H. Brenner, W. T. Cathey, H. J. Caulfield, S. H. Lee, H. Szu, “Optical database/knowledgebase machines,” Appl. Opt. 29, 195–205 (1990).
[CrossRef] [PubMed]

N. Streibl, K. H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. Miller, M. Murdocca, M. E. Prise, T. Sizer, “Digital optics,” Proc. IEEE 77, 1954–1970 (1989).
[CrossRef]

Briggs, F.

K. Hwang, F. Briggs, Computer Architectures and Parallel Processing (McGraw-Hill, New York, 1984).

Bryan, R. P.

G. R. Olbright, R. P. Bryan, K. Lear, T. M. Brennan, G. Poirier, Y. H. Lee, J. L. Jewell, “Cascadable laser logic devices: Discrete integration of photoresistors will surface-emitting laser diodes,” Electron. Lett. 27, 216–218 (1991).
[CrossRef]

Burrus, C. A.

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, “The quantum well self-electro-optic effect device: optoelectronic bistability and oscillation, and self-linearized modulation,” IEEE J. Quantum Electron. QE-21, 1462–1476 (1985).
[CrossRef]

Cathey, W. T.

Caulfield, H. J.

Chavel, P.

Chemla, D. S.

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, “The quantum well self-electro-optic effect device: optoelectronic bistability and oscillation, and self-linearized modulation,” IEEE J. Quantum Electron. QE-21, 1462–1476 (1985).
[CrossRef]

D. A. B. Miller, D. S. Chemla, D. J. Eilenberger, P. W. Smith, A. C. Gossard, W. T. Tsang, “Large room-temperature optical nonlinearity in GaAs/Ga1−xAlxAs multiple quantum well structures,” Appl. Phys. Lett. 44, 821–823 (1982).

Chirovsky, L.

Chirovsky, L. M.

Chirovsky, L. M. F.

M. Prise, N. C. Craft, R. E. LaMarche, M. M. Downs, S. J. Walker, L. Asaro, L. M. F. Chirovsky, “Module for optical logic circuits using symmetric self-electrooptic effect devices,” Appl. Opt. 29, 2164–2170 (1990).
[CrossRef] [PubMed]

A. L. Lentine, H. S. Hinton, D. A. B. Miller, J. E. Henry, J. E. Cunningham, L. M. F. Chirovsky, “Symmetric self-electrooptic effect device: optical set–reset latch, differential logic gate, and differential modulator/detector,” IEEE J. Quantum Electron. 25, 1928–1936 (1989).
[CrossRef]

Craft, N. C.

Cunningham, J. E.

A. L. Lentine, D. A. Miller, J. E. Henry, J. E. Cunningham, L. M. Chirovsky, L. A. Asaro, “Optical logic using electrically connected quantum well PIN diode modulators and detectors,” Appl. Opt. 29, 2153–2163 (1990).
[CrossRef] [PubMed]

A. L. Lentine, H. S. Hinton, D. A. B. Miller, J. E. Henry, J. E. Cunningham, L. M. F. Chirovsky, “Symmetric self-electrooptic effect device: optical set–reset latch, differential logic gate, and differential modulator/detector,” IEEE J. Quantum Electron. 25, 1928–1936 (1989).
[CrossRef]

Damen, T. C.

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, “The quantum well self-electro-optic effect device: optoelectronic bistability and oscillation, and self-linearized modulation,” IEEE J. Quantum Electron. QE-21, 1462–1476 (1985).
[CrossRef]

Date, C. J.

C. J. Date, An Introduction to Database Systems (Addison-Wesley, Reading, Mass., 1986).

Degroot, D.

K. Hwang, D. Degroot, Parallel Processing for Supercomputers and Artificial Intelligence (McGraw-Hill, New York, 1988).

Devos, F.

Downs, M. M.

Eichmann, G.

Eilenberger, D. J.

D. A. B. Miller, D. S. Chemla, D. J. Eilenberger, P. W. Smith, A. C. Gossard, W. T. Tsang, “Large room-temperature optical nonlinearity in GaAs/Ga1−xAlxAs multiple quantum well structures,” Appl. Phys. Lett. 44, 821–823 (1982).

Esner, S. C.

F. Kiamilev, S. C. Esner, R. Paturi, Y. Fainman, P. Mercier, C. C. Guest, S. H. Lee, “Programmable optoelectronic multiprocessors and their comparison with symbolic substitution for digital optical computing,” Opt. Eng. 28, 396–409 (1989).

Fainman, Y.

F. Kiamilev, S. C. Esner, R. Paturi, Y. Fainman, P. Mercier, C. C. Guest, S. H. Lee, “Programmable optoelectronic multiprocessors and their comparison with symbolic substitution for digital optical computing,” Opt. Eng. 28, 396–409 (1989).

Fisher, A.

C. Warde, A. Fisher, “Spatial light modulators: applications and functional capabilities,” in Optical Signal Processing, J. Horner, ed. (Academic, New York, 1987), pp. 478–524.

Forchheimer, R.

Foster, C. C.

C. C. Foster, “Determination of priority in associative memories,” IEEE Trans. Comput. C-17, 788–789 (1968).
[CrossRef]

C. C. Foster, Content Addressable Parallel Processors (Reinhold, New York, 1976).

Garda, P.

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]

Gheen, G.

G. Gheen, “Optical matrix–matrix multiplier,” Appl. Opt. 29, 886–887 (1990).

Gibbs, H. M.

J. L. Jewell, M. C. Rushford, H. M. Gibbs, “Use of a single nonlinear Fabry–Perot étalon as optical logic gate,” Appl. Phys. Lett. 44, 172–174 (1984).
[CrossRef]

Gossard, A. C.

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, “The quantum well self-electro-optic effect device: optoelectronic bistability and oscillation, and self-linearized modulation,” IEEE J. Quantum Electron. QE-21, 1462–1476 (1985).
[CrossRef]

D. A. B. Miller, D. S. Chemla, D. J. Eilenberger, P. W. Smith, A. C. Gossard, W. T. Tsang, “Large room-temperature optical nonlinearity in GaAs/Ga1−xAlxAs multiple quantum well structures,” Appl. Phys. Lett. 44, 821–823 (1982).

Gottlieb, A.

G. S. Almasi, A. Gottlieb, Highly Parallel Computing (Addison-Wesley, Reading, Mass., 1989).

Guest, C. C.

F. Kiamilev, S. C. Esner, R. Paturi, Y. Fainman, P. Mercier, C. C. Guest, S. H. Lee, “Programmable optoelectronic multiprocessors and their comparison with symbolic substitution for digital optical computing,” Opt. Eng. 28, 396–409 (1989).

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]

Halstead, R.

R. Halstead, “Parallel symbolic computing,” Computer 19(8), 35–43 (1986).
[CrossRef]

Hartmann, A.

A. Hartmann, S. Redfield, “Design sketches for optical crossbar switches intended for large-scale parallel processing applications,” Opt. Eng. 28, 315–328 (1989).

Hendry, A.

S. D. Smith, J. G. H. Mathew, M. R. Taghizadeth, A. C. Walker, B. S. Wherret, A. Hendry, “Room temperature, visible wavelength optical bistability in ZnSe interference filters,” Opt. Commun. 51, 357–362 (1984).
[CrossRef]

Henry, J. E.

A. L. Lentine, D. A. Miller, J. E. Henry, J. E. Cunningham, L. M. Chirovsky, L. A. Asaro, “Optical logic using electrically connected quantum well PIN diode modulators and detectors,” Appl. Opt. 29, 2153–2163 (1990).
[CrossRef] [PubMed]

A. L. Lentine, H. S. Hinton, D. A. B. Miller, J. E. Henry, J. E. Cunningham, L. M. F. Chirovsky, “Symmetric self-electrooptic effect device: optical set–reset latch, differential logic gate, and differential modulator/detector,” IEEE J. Quantum Electron. 25, 1928–1936 (1989).
[CrossRef]

Hill, B.

B. Hill, “The current status of two-dimensional spatial light modulators,” in Optical Computing: Digital and Symbolic, R. Arrathoon, ed. (Dekker, New York, 1989), pp. 1–40.

Hinton, H. S.

A. L. Lentine, H. S. Hinton, D. A. B. Miller, J. E. Henry, J. E. Cunningham, L. M. F. Chirovsky, “Symmetric self-electrooptic effect device: optical set–reset latch, differential logic gate, and differential modulator/detector,” IEEE J. Quantum Electron. 25, 1928–1936 (1989).
[CrossRef]

Huang, A.

N. Streibl, K. H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. Miller, M. Murdocca, M. E. Prise, T. Sizer, “Digital optics,” Proc. IEEE 77, 1954–1970 (1989).
[CrossRef]

M. J. Murdocca, A. Huang, J. Jahns, N. Streibl, “Optical design of programmable logic arrays,” Appl. Opt. 27, 1651–1660 (1988).
[CrossRef] [PubMed]

A. Huang, “Architectural considerations involved in the design of an optical digital computer,” Proc. IEEE 72, 780–787 (1984).
[CrossRef]

Hwang, K.

K. Hwang, A. Louri, “Optical multiplication and division using modified signed-digit symbolic substitution,” Opt. Eng. 28, 364–373 (1989).

K. Hwang, D. Degroot, Parallel Processing for Supercomputers and Artificial Intelligence (McGraw-Hill, New York, 1988).

K. Hwang, F. Briggs, Computer Architectures and Parallel Processing (McGraw-Hill, New York, 1984).

A. Louri, K. Hwang, “A bit-plane architecture for optical computing with 2-d symbolic substitution algorithms,” in Proceedings of the 15th International Symposium on Computer Architecture (Institute of Electrical and Electronics Engineers, New York, 1988).

Jahns, J.

N. Streibl, K. H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. Miller, M. Murdocca, M. E. Prise, T. Sizer, “Digital optics,” Proc. IEEE 77, 1954–1970 (1989).
[CrossRef]

M. J. Murdocca, A. Huang, J. Jahns, N. Streibl, “Optical design of programmable logic arrays,” Appl. Opt. 27, 1651–1660 (1988).
[CrossRef] [PubMed]

Jenkins, B. K.

A. A. Sawchuk, C. S. Raghavandra, B. K. Jenkins, A. Varma, “Optical cross-bar networks,” IEEE Computer 20(6), 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]

A. A. Sawchuk, B. K. Jenkins, “Dynamic optical interconnections for optical processors,” in Optical Computing, J. Neff, ed., Proc. Soc. Photo-Opt. Instrum. Eng.625, 145–153 (1986).

Jewell, J.

N. Streibl, K. H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. Miller, M. Murdocca, M. E. Prise, T. Sizer, “Digital optics,” Proc. IEEE 77, 1954–1970 (1989).
[CrossRef]

Jewell, J. L.

G. R. Olbright, R. P. Bryan, K. Lear, T. M. Brennan, G. Poirier, Y. H. Lee, J. L. Jewell, “Cascadable laser logic devices: Discrete integration of photoresistors will surface-emitting laser diodes,” Electron. Lett. 27, 216–218 (1991).
[CrossRef]

J. L. Jewell, M. C. Rushford, H. M. Gibbs, “Use of a single nonlinear Fabry–Perot étalon as optical logic gate,” Appl. Phys. Lett. 44, 172–174 (1984).
[CrossRef]

Kiamilev, F.

F. Kiamilev, S. C. Esner, R. Paturi, Y. Fainman, P. Mercier, C. C. Guest, S. H. Lee, “Programmable optoelectronic multiprocessors and their comparison with symbolic substitution for digital optical computing,” Opt. Eng. 28, 396–409 (1989).

Kim, D. H.

Kinser, J.

H. J. Caulfield, J. Kinser, S. K. Rogers, “Optical neural networks,” Proc. IEEE 77, 1573–1583 (1989).
[CrossRef]

Kohonen, T.

T. Kohonen, Content-Addressable Memories (Springer-Verlag, New York, 1980).
[CrossRef]

Kostrzewski, A.

LaMarche, R. E.

Lea, R. M.

R. M. Lea, “VLSI and WSI associative string processors for cost-effective parallel processing,” Computer J. 29, 486–494 (1986).
[CrossRef]

R. M. Lea, “Information processing with an associative parallel processor,” Computer 8(11), 25–32 (1975).
[CrossRef]

Lear, K.

G. R. Olbright, R. P. Bryan, K. Lear, T. M. Brennan, G. Poirier, Y. H. Lee, J. L. Jewell, “Cascadable laser logic devices: Discrete integration of photoresistors will surface-emitting laser diodes,” Electron. Lett. 27, 216–218 (1991).
[CrossRef]

Lee, C. Y.

C. Y. Lee, M. C. Paul, “A content addressable distributed logic memory with applications to information retrieval,” Proc. IEEE 51, 924–932 (1964).
[CrossRef]

Lee, S. H.

P. B. Berra, K. H. Brenner, W. T. Cathey, H. J. Caulfield, S. H. Lee, H. Szu, “Optical database/knowledgebase machines,” Appl. Opt. 29, 195–205 (1990).
[CrossRef] [PubMed]

J. A. Neff, R. A. Athale, S. H. Lee, “Two-dimensional spatial light modulators: a tutorial,” Proc. IEEE 78, 836–855 (1990).
[CrossRef]

F. Kiamilev, S. C. Esner, R. Paturi, Y. Fainman, P. Mercier, C. C. Guest, S. H. Lee, “Programmable optoelectronic multiprocessors and their comparison with symbolic substitution for digital optical computing,” Opt. Eng. 28, 396–409 (1989).

Lee, Y. H.

G. R. Olbright, R. P. Bryan, K. Lear, T. M. Brennan, G. Poirier, Y. H. Lee, J. L. Jewell, “Cascadable laser logic devices: Discrete integration of photoresistors will surface-emitting laser diodes,” Electron. Lett. 27, 216–218 (1991).
[CrossRef]

Lentine, A. L.

A. L. Lentine, D. A. Miller, J. E. Henry, J. E. Cunningham, L. M. Chirovsky, L. A. Asaro, “Optical logic using electrically connected quantum well PIN diode modulators and detectors,” Appl. Opt. 29, 2153–2163 (1990).
[CrossRef] [PubMed]

A. L. Lentine, H. S. Hinton, D. A. B. Miller, J. E. Henry, J. E. Cunningham, L. M. F. Chirovsky, “Symmetric self-electrooptic effect device: optical set–reset latch, differential logic gate, and differential modulator/detector,” IEEE J. Quantum Electron. 25, 1928–1936 (1989).
[CrossRef]

Li, Y.

Lohmann, A. W.

N. Streibl, K. H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. Miller, M. Murdocca, M. E. Prise, T. Sizer, “Digital optics,” Proc. IEEE 77, 1954–1970 (1989).
[CrossRef]

A. W. Lohmann, “What classical optics can do for the digital optical computer,” Appl. Opt. 25, 1543–1549 (1986).
[CrossRef] [PubMed]

Louri, A.

A. Louri, “3-D optical architecture and data-parallel algorithms for massively parallel computing,” IEEE Micro 11(2), 24–68 (1991).
[CrossRef]

K. Hwang, A. Louri, “Optical multiplication and division using modified signed-digit symbolic substitution,” Opt. Eng. 28, 364–373 (1989).

A. Louri, K. Hwang, “A bit-plane architecture for optical computing with 2-d symbolic substitution algorithms,” in Proceedings of the 15th International Symposium on Computer Architecture (Institute of Electrical and Electronics Engineers, New York, 1988).

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]

Mathew, J. G. H.

S. D. Smith, J. G. H. Mathew, M. R. Taghizadeth, A. C. Walker, B. S. Wherret, A. Hendry, “Room temperature, visible wavelength optical bistability in ZnSe interference filters,” Opt. Commun. 51, 357–362 (1984).
[CrossRef]

McAulay, A. D.

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

Mercier, P.

F. Kiamilev, S. C. Esner, R. Paturi, Y. Fainman, P. Mercier, C. C. Guest, S. H. Lee, “Programmable optoelectronic multiprocessors and their comparison with symbolic substitution for digital optical computing,” Opt. Eng. 28, 396–409 (1989).

Miceli, W. J.

W. T. Cathey, K. Wagner, W. J. Miceli, “Digital computing with optics,” Proc. IEEE 77, 1558–1572 (1989).
[CrossRef]

Miller, D.

N. Streibl, K. H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. Miller, M. Murdocca, M. E. Prise, T. Sizer, “Digital optics,” Proc. IEEE 77, 1954–1970 (1989).
[CrossRef]

Miller, D. A.

Miller, D. A. B.

A. L. Lentine, H. S. Hinton, D. A. B. Miller, J. E. Henry, J. E. Cunningham, L. M. F. Chirovsky, “Symmetric self-electrooptic effect device: optical set–reset latch, differential logic gate, and differential modulator/detector,” IEEE J. Quantum Electron. 25, 1928–1936 (1989).
[CrossRef]

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, “The quantum well self-electro-optic effect device: optoelectronic bistability and oscillation, and self-linearized modulation,” IEEE J. Quantum Electron. QE-21, 1462–1476 (1985).
[CrossRef]

D. A. B. Miller, D. S. Chemla, D. J. Eilenberger, P. W. Smith, A. C. Gossard, W. T. Tsang, “Large room-temperature optical nonlinearity in GaAs/Ga1−xAlxAs multiple quantum well structures,” Appl. Phys. Lett. 44, 821–823 (1982).

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]

Murdocca, M.

M. Prose, N. C. Craft, M. M. Downs, R. E. LaMarche, L. A. Asaro, L. Chirovsky, M. Murdocca, “Optical digital processor using arrays of symmetric self-electrooptic effect devices,” Appl. Opt. 30, 2287–2296 (1991).
[CrossRef]

N. Streibl, K. H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. Miller, M. Murdocca, M. E. Prise, T. Sizer, “Digital optics,” Proc. IEEE 77, 1954–1970 (1989).
[CrossRef]

Murdocca, M. J.

Neff, J. A.

J. A. Neff, R. A. Athale, S. H. Lee, “Two-dimensional spatial light modulators: a tutorial,” Proc. IEEE 78, 836–855 (1990).
[CrossRef]

Olbright, G. R.

G. R. Olbright, R. P. Bryan, K. Lear, T. M. Brennan, G. Poirier, Y. H. Lee, J. L. Jewell, “Cascadable laser logic devices: Discrete integration of photoresistors will surface-emitting laser diodes,” Electron. Lett. 27, 216–218 (1991).
[CrossRef]

Paturi, R.

F. Kiamilev, S. C. Esner, R. Paturi, Y. Fainman, P. Mercier, C. C. Guest, S. H. Lee, “Programmable optoelectronic multiprocessors and their comparison with symbolic substitution for digital optical computing,” Opt. Eng. 28, 396–409 (1989).

Paul, M. C.

C. Y. Lee, M. C. Paul, “A content addressable distributed logic memory with applications to information retrieval,” Proc. IEEE 51, 924–932 (1964).
[CrossRef]

Poirier, G.

G. R. Olbright, R. P. Bryan, K. Lear, T. M. Brennan, G. Poirier, Y. H. Lee, J. L. Jewell, “Cascadable laser logic devices: Discrete integration of photoresistors will surface-emitting laser diodes,” Electron. Lett. 27, 216–218 (1991).
[CrossRef]

Prise, M.

Prise, M. E.

N. Streibl, K. H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. Miller, M. Murdocca, M. E. Prise, T. Sizer, “Digital optics,” Proc. IEEE 77, 1954–1970 (1989).
[CrossRef]

Prose, M.

Psaltis, D.

K. Wagner, D. Psaltis, “Multilayer optical learning networks,” Appl. Opt. 26, 5067–5076 (1987).
[CrossRef]

Raghavandra, C. S.

A. A. Sawchuk, C. S. Raghavandra, B. K. Jenkins, A. Varma, “Optical cross-bar networks,” IEEE Computer 20(6), 50–62 (1987).
[CrossRef]

Redfield, S.

A. Hartmann, S. Redfield, “Design sketches for optical crossbar switches intended for large-scale parallel processing applications,” Opt. Eng. 28, 315–328 (1989).

Rogers, S. K.

H. J. Caulfield, J. Kinser, S. K. Rogers, “Optical neural networks,” Proc. IEEE 77, 1573–1583 (1989).
[CrossRef]

Rushford, M. C.

J. L. Jewell, M. C. Rushford, H. M. Gibbs, “Use of a single nonlinear Fabry–Perot étalon as optical logic gate,” Appl. Phys. Lett. 44, 172–174 (1984).
[CrossRef]

Sawchuk, A. A.

A. A. Sawchuk, C. S. Raghavandra, B. K. Jenkins, A. Varma, “Optical cross-bar networks,” IEEE Computer 20(6), 50–62 (1987).
[CrossRef]

A. A. Sawchuk, T. C. Stand, “Digital optical computing,” Proc. IEEE 72, 758–779 (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]

A. A. Sawchuk, B. K. Jenkins, “Dynamic optical interconnections for optical processors,” in Optical Computing, J. Neff, ed., Proc. Soc. Photo-Opt. Instrum. Eng.625, 145–153 (1986).

Sizer, T.

N. Streibl, K. H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. Miller, M. Murdocca, M. E. Prise, T. Sizer, “Digital optics,” Proc. IEEE 77, 1954–1970 (1989).
[CrossRef]

Smith, P. W.

D. A. B. Miller, D. S. Chemla, D. J. Eilenberger, P. W. Smith, A. C. Gossard, W. T. Tsang, “Large room-temperature optical nonlinearity in GaAs/Ga1−xAlxAs multiple quantum well structures,” Appl. Phys. Lett. 44, 821–823 (1982).

Smith, S. D.

S. D. Smith, J. G. H. Mathew, M. R. Taghizadeth, A. C. Walker, B. S. Wherret, A. Hendry, “Room temperature, visible wavelength optical bistability in ZnSe interference filters,” Opt. Commun. 51, 357–362 (1984).
[CrossRef]

Stand, T. C.

A. A. Sawchuk, T. C. Stand, “Digital optical computing,” Proc. IEEE 72, 758–779 (1984).
[CrossRef]

Strand, T. C.

Streibl, N.

N. Streibl, K. H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. Miller, M. Murdocca, M. E. Prise, T. Sizer, “Digital optics,” Proc. IEEE 77, 1954–1970 (1989).
[CrossRef]

M. J. Murdocca, A. Huang, J. Jahns, N. Streibl, “Optical design of programmable logic arrays,” Appl. Opt. 27, 1651–1660 (1988).
[CrossRef] [PubMed]

Szu, H.

Taboury, J.

Taghizadeth, M. R.

S. D. Smith, J. G. H. Mathew, M. R. Taghizadeth, A. C. Walker, B. S. Wherret, A. Hendry, “Room temperature, visible wavelength optical bistability in ZnSe interference filters,” Opt. Commun. 51, 357–362 (1984).
[CrossRef]

Tsang, W. T.

D. A. B. Miller, D. S. Chemla, D. J. Eilenberger, P. W. Smith, A. C. Gossard, W. T. Tsang, “Large room-temperature optical nonlinearity in GaAs/Ga1−xAlxAs multiple quantum well structures,” Appl. Phys. Lett. 44, 821–823 (1982).

Varma, A.

A. A. Sawchuk, C. S. Raghavandra, B. K. Jenkins, A. Varma, “Optical cross-bar networks,” IEEE Computer 20(6), 50–62 (1987).
[CrossRef]

Wagner, K.

W. T. Cathey, K. Wagner, W. J. Miceli, “Digital computing with optics,” Proc. IEEE 77, 1558–1572 (1989).
[CrossRef]

K. Wagner, D. Psaltis, “Multilayer optical learning networks,” Appl. Opt. 26, 5067–5076 (1987).
[CrossRef]

Walker, A. C.

S. D. Smith, J. G. H. Mathew, M. R. Taghizadeth, A. C. Walker, B. S. Wherret, A. Hendry, “Room temperature, visible wavelength optical bistability in ZnSe interference filters,” Opt. Commun. 51, 357–362 (1984).
[CrossRef]

Walker, S. J.

Wang, J. M.

Warde, C.

C. Warde, A. Fisher, “Spatial light modulators: applications and functional capabilities,” in Optical Signal Processing, J. Horner, ed. (Academic, New York, 1987), pp. 478–524.

Wherret, B. S.

S. D. Smith, J. G. H. Mathew, M. R. Taghizadeth, A. C. Walker, B. S. Wherret, A. Hendry, “Room temperature, visible wavelength optical bistability in ZnSe interference filters,” Opt. Commun. 51, 357–362 (1984).
[CrossRef]

Wiegmann, W.

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, “The quantum well self-electro-optic effect device: optoelectronic bistability and oscillation, and self-linearized modulation,” IEEE J. Quantum Electron. QE-21, 1462–1476 (1985).
[CrossRef]

Wood, T. H.

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, “The quantum well self-electro-optic effect device: optoelectronic bistability and oscillation, and self-linearized modulation,” IEEE J. Quantum Electron. QE-21, 1462–1476 (1985).
[CrossRef]

Appl. Opt.

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]

K. Wagner, D. Psaltis, “Multilayer optical learning networks,” Appl. Opt. 26, 5067–5076 (1987).
[CrossRef]

P. B. Berra, K. H. Brenner, W. T. Cathey, H. J. Caulfield, S. H. Lee, H. Szu, “Optical database/knowledgebase machines,” Appl. Opt. 29, 195–205 (1990).
[CrossRef] [PubMed]

A. W. Lohmann, “What classical optics can do for the digital optical computer,” Appl. Opt. 25, 1543–1549 (1986).
[CrossRef] [PubMed]

J. Taboury, J. M. Wang, P. Chavel, F. Devos, P. Garda, “Optical cellular logic architecture 1: Principles,” Appl. Opt. 27, 1643–1650 (1988).
[CrossRef] [PubMed]

M. Prise, N. C. Craft, R. E. LaMarche, M. M. Downs, S. J. Walker, L. Asaro, L. M. F. Chirovsky, “Module for optical logic circuits using symmetric self-electrooptic effect devices,” Appl. Opt. 29, 2164–2170 (1990).
[CrossRef] [PubMed]

M. Prose, N. C. Craft, M. M. Downs, R. E. LaMarche, L. A. Asaro, L. Chirovsky, M. Murdocca, “Optical digital processor using arrays of symmetric self-electrooptic effect devices,” Appl. Opt. 30, 2287–2296 (1991).
[CrossRef]

A. L. Lentine, D. A. Miller, J. E. Henry, J. E. Cunningham, L. M. Chirovsky, L. A. Asaro, “Optical logic using electrically connected quantum well PIN diode modulators and detectors,” Appl. Opt. 29, 2153–2163 (1990).
[CrossRef] [PubMed]

M. J. Murdocca, A. Huang, J. Jahns, N. Streibl, “Optical design of programmable logic arrays,” Appl. Opt. 27, 1651–1660 (1988).
[CrossRef] [PubMed]

G. Gheen, “Optical matrix–matrix multiplier,” Appl. Opt. 29, 886–887 (1990).

Appl. Phys. Lett.

J. L. Jewell, M. C. Rushford, H. M. Gibbs, “Use of a single nonlinear Fabry–Perot étalon as optical logic gate,” Appl. Phys. Lett. 44, 172–174 (1984).
[CrossRef]

D. A. B. Miller, D. S. Chemla, D. J. Eilenberger, P. W. Smith, A. C. Gossard, W. T. Tsang, “Large room-temperature optical nonlinearity in GaAs/Ga1−xAlxAs multiple quantum well structures,” Appl. Phys. Lett. 44, 821–823 (1982).

Computer

R. Halstead, “Parallel symbolic computing,” Computer 19(8), 35–43 (1986).
[CrossRef]

R. M. Lea, “Information processing with an associative parallel processor,” Computer 8(11), 25–32 (1975).
[CrossRef]

Computer J.

R. M. Lea, “VLSI and WSI associative string processors for cost-effective parallel processing,” Computer J. 29, 486–494 (1986).
[CrossRef]

Electron. Lett.

G. R. Olbright, R. P. Bryan, K. Lear, T. M. Brennan, G. Poirier, Y. H. Lee, J. L. Jewell, “Cascadable laser logic devices: Discrete integration of photoresistors will surface-emitting laser diodes,” Electron. Lett. 27, 216–218 (1991).
[CrossRef]

IEEE Computer

A. A. Sawchuk, C. S. Raghavandra, B. K. Jenkins, A. Varma, “Optical cross-bar networks,” IEEE Computer 20(6), 50–62 (1987).
[CrossRef]

IEEE J. Quantum Electron.

D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, C. A. Burrus, “The quantum well self-electro-optic effect device: optoelectronic bistability and oscillation, and self-linearized modulation,” IEEE J. Quantum Electron. QE-21, 1462–1476 (1985).
[CrossRef]

A. L. Lentine, H. S. Hinton, D. A. B. Miller, J. E. Henry, J. E. Cunningham, L. M. F. Chirovsky, “Symmetric self-electrooptic effect device: optical set–reset latch, differential logic gate, and differential modulator/detector,” IEEE J. Quantum Electron. 25, 1928–1936 (1989).
[CrossRef]

IEEE Micro

A. Louri, “3-D optical architecture and data-parallel algorithms for massively parallel computing,” IEEE Micro 11(2), 24–68 (1991).
[CrossRef]

IEEE Trans. Comput.

C. C. Foster, “Determination of priority in associative memories,” IEEE Trans. Comput. C-17, 788–789 (1968).
[CrossRef]

Opt. Commun.

S. D. Smith, J. G. H. Mathew, M. R. Taghizadeth, A. C. Walker, B. S. Wherret, A. Hendry, “Room temperature, visible wavelength optical bistability in ZnSe interference filters,” Opt. Commun. 51, 357–362 (1984).
[CrossRef]

Opt. Eng.

K. Hwang, A. Louri, “Optical multiplication and division using modified signed-digit symbolic substitution,” Opt. Eng. 28, 364–373 (1989).

F. Kiamilev, S. C. Esner, R. Paturi, Y. Fainman, P. Mercier, C. C. Guest, S. H. Lee, “Programmable optoelectronic multiprocessors and their comparison with symbolic substitution for digital optical computing,” Opt. Eng. 28, 396–409 (1989).

A. Hartmann, S. Redfield, “Design sketches for optical crossbar switches intended for large-scale parallel processing applications,” Opt. Eng. 28, 315–328 (1989).

Opt. lett.

Proc. IEEE

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

A. A. Sawchuk, T. C. Stand, “Digital optical computing,” Proc. IEEE 72, 758–779 (1984).
[CrossRef]

A. Huang, “Architectural considerations involved in the design of an optical digital computer,” Proc. IEEE 72, 780–787 (1984).
[CrossRef]

W. T. Cathey, K. Wagner, W. J. Miceli, “Digital computing with optics,” Proc. IEEE 77, 1558–1572 (1989).
[CrossRef]

C. Y. Lee, M. C. Paul, “A content addressable distributed logic memory with applications to information retrieval,” Proc. IEEE 51, 924–932 (1964).
[CrossRef]

J. A. Neff, R. A. Athale, S. H. Lee, “Two-dimensional spatial light modulators: a tutorial,” Proc. IEEE 78, 836–855 (1990).
[CrossRef]

N. Streibl, K. H. Brenner, A. Huang, J. Jahns, J. Jewell, A. W. Lohmann, D. Miller, M. Murdocca, M. E. Prise, T. Sizer, “Digital optics,” Proc. IEEE 77, 1954–1970 (1989).
[CrossRef]

H. J. Caulfield, J. Kinser, S. K. Rogers, “Optical neural networks,” Proc. IEEE 77, 1573–1583 (1989).
[CrossRef]

Other

A. Louri, K. Hwang, “A bit-plane architecture for optical computing with 2-d symbolic substitution algorithms,” in Proceedings of the 15th International Symposium on Computer Architecture (Institute of Electrical and Electronics Engineers, New York, 1988).

C. Warde, A. Fisher, “Spatial light modulators: applications and functional capabilities,” in Optical Signal Processing, J. Horner, ed. (Academic, New York, 1987), pp. 478–524.

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

A. A. Sawchuk, B. K. Jenkins, “Dynamic optical interconnections for optical processors,” in Optical Computing, J. Neff, ed., Proc. Soc. Photo-Opt. Instrum. Eng.625, 145–153 (1986).

K. Hwang, F. Briggs, Computer Architectures and Parallel Processing (McGraw-Hill, New York, 1984).

G. S. Almasi, A. Gottlieb, Highly Parallel Computing (Addison-Wesley, Reading, Mass., 1989).

C. C. Foster, Content Addressable Parallel Processors (Reinhold, New York, 1976).

T. Kohonen, Content-Addressable Memories (Springer-Verlag, New York, 1980).
[CrossRef]

C. J. Date, An Introduction to Database Systems (Addison-Wesley, Reading, Mass., 1986).

K. Hwang, D. Degroot, Parallel Processing for Supercomputers and Artificial Intelligence (McGraw-Hill, New York, 1988).

B. Hill, “The current status of two-dimensional spatial light modulators,” in Optical Computing: Digital and Symbolic, R. Arrathoon, ed. (Dekker, New York, 1989), pp. 1–40.

R. A. Athale, “Optical matrix processors,” in Optical and Hybrid Computing, H. H. Szu, ed., Proc. Soc. Photo-Opt. Instrum. Eng.634, 96–111 (1986).
[CrossRef]

M. J. Murdocca, A Digital Design Methodology for Optical Computing (MIT, Cambridge, Mass., 1990).

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Figures (9)

Fig. 1
Fig. 1

Basic architecture of an associative memory processor.

Fig. 2
Fig. 2

Schematic organization of the optical content-addressable parallel processor.

Fig. 3
Fig. 3

Organization of the selection unit.

Fig. 4
Fig. 4

Organization of the match–compare unit.

Fig. 5
Fig. 5

S-SEED device operating as a clocked S-R latch: (a) schematic diagram, (b) timing diagram. MQW, multiple quantum well.

Fig. 6
Fig. 6

Optical implementation of the selection unit.

Fig. 7
Fig. 7

Optical implementation of match–compare unit.

Fig. 8
Fig. 8

Optical implementation of a multiple match–compare unit. The interrogation and the response registers of Fig. 7 are replaced by two-dimensional arrays of search arguments and response registers, respectively. Register R1 indicates the match or mismatch of memory words with interrogation register I1 (for i = 1, …, k).

Fig. 9
Fig. 9

Optical implementation of the output unit: (a) single word output, (b) parallel readout of multiple words.

Tables (4)

Tables Icon

Table I Formulation of Interrogation Register I

Tables Icon

Table II Example of Threshold Search Algorithms

Tables Icon

Table III Example of Maximum Search Algorithm

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Table IV Estimated Execution Time of the Parallel Algorithms on an Optical Content-Addressable Parallel Processor

Equations (22)

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b i j ¯ = ( I j w i j ¯ ) ( I j ¯ w i j ) ,
M i = j = 1 j = m b i j ¯ = b i m ¯ b i m - 1 ¯ b i 1 ¯ ,
R i = M i ¯ = ( I 1 w i 1 ¯ ) ( I 1 ¯ w i 1 ) ( I m w i m ¯ ) ( I m ¯ w i m ) ¯ .
R i = I 1 w i 1 ¯ ¯ I 1 ¯ w i 1 ¯ I m w i m ¯ ¯ I m ¯ w i m ¯ ¯ ,
G i = I j ¯ w i j             ( word W i > I ) ,
L i = I j w i j ¯             ( word W i < I ) .
R i = M i ¯ E R i ¯ ¯             for all i = 1 , , n .
R i = M i ¯ ( I 0 E R i ¯ I 0 ¯ E R i ) ¯             for all i = 1 , , n .
R i = I 0 E R i ¯ ¯ I 0 ¯ E R i ¯ I 1 w i 1 ¯ ¯ I 1 ¯ w i 1 ¯ I m w i m ¯ ¯ I m ¯ w i m ¯ ¯ .
O j ¯ = P 1 w 1 j P 2 w 2 j P n w n j ¯             for j = 1 , , m .
O j ¯ = P 1 ¯ w 1 j ¯ ¯ P 2 ¯ w 2 j ¯ ¯ P n ¯ w n j ¯ ¯ .
O j = P 1 ¯ w 1 j ¯ P 2 ¯ w 2 j ¯ P n ¯ w n j ¯ ¯ .
T proc = T resp + T p 1 + T resp 2 + T p + T resp 3 = 3 T resp + 2 T p .
T tresh = T resp + T p 1 + T resp 2 + T p + T resp 3 + T resp 4 ,
T tresh = m ( T resp + T p 1 + T resp 2 + T p + T resp 3 + T resp 4 + T p + 2 T resp 5 ) .
T extrem = m ( 6 T resp + 3 T p ) .
T double = 4 T resp + 2 T p 1 + T p + 2 T resp 2 + T i 3 + 4 T resp + 2 T p 4 ,
T double = m ( 6 T resp + 3 T p ) 1 + T p + 2 T resp 2 + T i 3 + m ( 6 T resp + 3 T p ) 4 .
T adjac = 4 T resp + 2 T p 1 + T p + 2 T resp 2 + m ( 6 T resp + 3 T p ) 3 ,
T adjac = m ( 6 T resp + 3 T p ) + T p + 2 T resp + m ( 6 T resp + 3 T p ) .
T sort = n [ m ( 6 T resp + 3 T p ) + 2 T p + 2 T resp ] ,
T sort = n [ m ( 6 T resp + 3 T p ) 1 + T p 2 + log 2 n ( T p + T resp ) 3 + T p + 4 3 ( T resp + T p ) 5 ] .

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