Abstract

Database management is considered as an application of optical array logic. To generalize the problem, a systematic procedure for massively parallel data processing that consists of pattern expansion, template matching, magnitude comparison, and sorting is presented. With this procedure, a method for implementing basic operations for relational database models is developed. Basic operations are described by parallel programs in optical array logic. Developed programs are evaluated by their performance. To improve the performance, the development of specialized optical functional modules is needed.

© 1993 Optical Society of America

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References

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  1. A. D. McAulay, Optical Computing Architectures: the Application of Optical Concepts to Next Generation Computers (Wiley, New York, 1991), Chaps. 6–15.
  2. J. Tanida, Y. Ichioka, “A paradigm for digital optical computing based on coded pattern processing,” Int. J. Opt. Comput. 1, 113–128 (1990).
  3. M. Iwata, J. Tanida, Y. Ichioka, “Inference engine using optical array logic,” Jpn. J. Appl. Phys. 29, L1259–L1261 (1990).
    [CrossRef]
  4. M. Iwata, J. Tanida, Y. Ichioka, “Inference engine for expert system by using optical array logic,” Appl. Opt. 31, 5604–5613 (1992).
    [CrossRef] [PubMed]
  5. P. B. Berra, A. Ghafoor, P. A. Mitkas, S. J. Marcinkowski, M. Guizani, “The impact of optics on data and knowledge base systems,” IEEE Trans. Knowledge Data Eng. 1, 111–132 (1989).
    [CrossRef]
  6. 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]
  7. S. G. Akl, Parallel Sorting Algorithms (Academic, London, 1985), Chap. 3.
  8. E. F. Codd, “A Relational model of data for large shared data banks,” Commun. ACM 13, 377–387 (1970).
    [CrossRef]
  9. In Sections 4 and 5 we gave the term Attribute a specific meaning for the database concept to avoid confusion with the same term that is used in OAL.
  10. M. Fukui, K. Kitayama, “Image logic algebra and its optical implementations,” Appl. Opt. 31, 581–591 (1992).
    [CrossRef] [PubMed]
  11. M. Iwata, J. Tanida, Y. Ichioka, “Two dimensional virtual storage mechanism for optical parallel digital computing systems,” submitted to Kogaku (Jpn. J. Opt.).

1992 (2)

1990 (3)

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. Tanida, Y. Ichioka, “A paradigm for digital optical computing based on coded pattern processing,” Int. J. Opt. Comput. 1, 113–128 (1990).

M. Iwata, J. Tanida, Y. Ichioka, “Inference engine using optical array logic,” Jpn. J. Appl. Phys. 29, L1259–L1261 (1990).
[CrossRef]

1989 (1)

P. B. Berra, A. Ghafoor, P. A. Mitkas, S. J. Marcinkowski, M. Guizani, “The impact of optics on data and knowledge base systems,” IEEE Trans. Knowledge Data Eng. 1, 111–132 (1989).
[CrossRef]

1970 (1)

E. F. Codd, “A Relational model of data for large shared data banks,” Commun. ACM 13, 377–387 (1970).
[CrossRef]

Akl, S. G.

S. G. Akl, Parallel Sorting Algorithms (Academic, London, 1985), Chap. 3.

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, P. A. Mitkas, S. J. Marcinkowski, M. Guizani, “The impact of optics on data and knowledge base systems,” IEEE Trans. Knowledge Data Eng. 1, 111–132 (1989).
[CrossRef]

Brenner, K.-H.

Cathey, W. T.

Caulfield, H. J.

Codd, E. F.

E. F. Codd, “A Relational model of data for large shared data banks,” Commun. ACM 13, 377–387 (1970).
[CrossRef]

Fukui, M.

Ghafoor, A.

P. B. Berra, A. Ghafoor, P. A. Mitkas, S. J. Marcinkowski, M. Guizani, “The impact of optics on data and knowledge base systems,” IEEE Trans. Knowledge Data Eng. 1, 111–132 (1989).
[CrossRef]

Guizani, M.

P. B. Berra, A. Ghafoor, P. A. Mitkas, S. J. Marcinkowski, M. Guizani, “The impact of optics on data and knowledge base systems,” IEEE Trans. Knowledge Data Eng. 1, 111–132 (1989).
[CrossRef]

Ichioka, Y.

M. Iwata, J. Tanida, Y. Ichioka, “Inference engine for expert system by using optical array logic,” Appl. Opt. 31, 5604–5613 (1992).
[CrossRef] [PubMed]

M. Iwata, J. Tanida, Y. Ichioka, “Inference engine using optical array logic,” Jpn. J. Appl. Phys. 29, L1259–L1261 (1990).
[CrossRef]

J. Tanida, Y. Ichioka, “A paradigm for digital optical computing based on coded pattern processing,” Int. J. Opt. Comput. 1, 113–128 (1990).

M. Iwata, J. Tanida, Y. Ichioka, “Two dimensional virtual storage mechanism for optical parallel digital computing systems,” submitted to Kogaku (Jpn. J. Opt.).

Iwata, M.

M. Iwata, J. Tanida, Y. Ichioka, “Inference engine for expert system by using optical array logic,” Appl. Opt. 31, 5604–5613 (1992).
[CrossRef] [PubMed]

M. Iwata, J. Tanida, Y. Ichioka, “Inference engine using optical array logic,” Jpn. J. Appl. Phys. 29, L1259–L1261 (1990).
[CrossRef]

M. Iwata, J. Tanida, Y. Ichioka, “Two dimensional virtual storage mechanism for optical parallel digital computing systems,” submitted to Kogaku (Jpn. J. Opt.).

Kitayama, K.

Lee, S. H.

Marcinkowski, S. J.

P. B. Berra, A. Ghafoor, P. A. Mitkas, S. J. Marcinkowski, M. Guizani, “The impact of optics on data and knowledge base systems,” IEEE Trans. Knowledge Data Eng. 1, 111–132 (1989).
[CrossRef]

McAulay, A. D.

A. D. McAulay, Optical Computing Architectures: the Application of Optical Concepts to Next Generation Computers (Wiley, New York, 1991), Chaps. 6–15.

Mitkas, P. A.

P. B. Berra, A. Ghafoor, P. A. Mitkas, S. J. Marcinkowski, M. Guizani, “The impact of optics on data and knowledge base systems,” IEEE Trans. Knowledge Data Eng. 1, 111–132 (1989).
[CrossRef]

Szu, H.

Tanida, J.

M. Iwata, J. Tanida, Y. Ichioka, “Inference engine for expert system by using optical array logic,” Appl. Opt. 31, 5604–5613 (1992).
[CrossRef] [PubMed]

J. Tanida, Y. Ichioka, “A paradigm for digital optical computing based on coded pattern processing,” Int. J. Opt. Comput. 1, 113–128 (1990).

M. Iwata, J. Tanida, Y. Ichioka, “Inference engine using optical array logic,” Jpn. J. Appl. Phys. 29, L1259–L1261 (1990).
[CrossRef]

M. Iwata, J. Tanida, Y. Ichioka, “Two dimensional virtual storage mechanism for optical parallel digital computing systems,” submitted to Kogaku (Jpn. J. Opt.).

Appl. Opt. (3)

Commun. ACM (1)

E. F. Codd, “A Relational model of data for large shared data banks,” Commun. ACM 13, 377–387 (1970).
[CrossRef]

IEEE Trans. Knowledge Data Eng. (1)

P. B. Berra, A. Ghafoor, P. A. Mitkas, S. J. Marcinkowski, M. Guizani, “The impact of optics on data and knowledge base systems,” IEEE Trans. Knowledge Data Eng. 1, 111–132 (1989).
[CrossRef]

Int. J. Opt. Comput. (1)

J. Tanida, Y. Ichioka, “A paradigm for digital optical computing based on coded pattern processing,” Int. J. Opt. Comput. 1, 113–128 (1990).

Jpn. J. Appl. Phys. (1)

M. Iwata, J. Tanida, Y. Ichioka, “Inference engine using optical array logic,” Jpn. J. Appl. Phys. 29, L1259–L1261 (1990).
[CrossRef]

Other (4)

In Sections 4 and 5 we gave the term Attribute a specific meaning for the database concept to avoid confusion with the same term that is used in OAL.

S. G. Akl, Parallel Sorting Algorithms (Academic, London, 1985), Chap. 3.

M. Iwata, J. Tanida, Y. Ichioka, “Two dimensional virtual storage mechanism for optical parallel digital computing systems,” submitted to Kogaku (Jpn. J. Opt.).

A. D. McAulay, Optical Computing Architectures: the Application of Optical Concepts to Next Generation Computers (Wiley, New York, 1991), Chaps. 6–15.

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Figures (13)

Fig. 1
Fig. 1

Processing procedure of OAL.

Fig. 2
Fig. 2

Processing procedure of pattern expansion.

Fig. 3
Fig. 3

Processing procedure of template matching.

Fig. 4
Fig. 4

Processing flow of magnitude comparison for two images: (a) data arrangement on processed images and (b) processing example of detecting data greater than five from image Input B.

Fig. 5
Fig. 5

Processing flow of magnitude comparison for one image: (a) data arrangement on processed images and (b) processing example.

Fig. 6
Fig. 6

Sorting diagram of an odd–even transposition sorting.

Fig. 7
Fig. 7

Processing flow of sorting: (a) magnitude comparison, (b) exchange procedure, (c) input image B for the second stage.

Fig. 8
Fig. 8

Basic operations of relational database.

Fig. 9
Fig. 9

Relation of an image: (a) example of a relation and (b) coded relation.

Fig. 10
Fig. 10

Processing flow of the selection operation.

Fig. 11
Fig. 11

Processing flow of the projection operation.

Fig. 12
Fig. 12

Simulation results of the projection operation: (a) image representing the relation in Table 2, (b) image representing the condition area, (c) result of the projection operation.

Fig. 13
Fig. 13

Optical system of the pattern expansion module.

Tables (4)

Tables Icon

Table 1 Symbolic Notation of OAL

Tables Icon

Table 2 Examples of Relations

Tables Icon

Table 3 Performance Estimations of the Basic Relational Operations

Tables Icon

Table 4 Performance Estimations of the Basic Relational Operations with Specialized Optical Functional Modules

Equations (20)

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[ 10 0. _ ] + [ 1. _ .0 ] 0 , 1 ,
c 0 , 0 = a 0 , - 1 b ¯ 0 , - 1 a ¯ 0 , 0 + a 0 , 1 b ¯ 1 , 1 ,
( i , j ) T . area [ 1. ] i , j ,
( i , j ) T . area [ 0. ] i , j ,
i = 0 n - 1 [ UU ] 0 , i .
z i = x i y i             ( i = 0 , 1 , , s - 1 ) ,
r = z s - 1 y s - 1 + j = 0 s - 2 z j y j ( i = j + 1 s - 1 z ¯ i ) ,
[ UU ] ,
[ 11 ] + j = 1 s - 1 [ 11 ] 0 , j i = 0 j - 1 [ 0. ] 0 , i .
p i = x i y ¯ i             ( i = 0 , , s - 1 ) ,
q i = x ¯ i y i             ( i = 0 , , s - 1 ) ,
r = p ¯ s - 1 q s - 1 + j = 1 s - 2 p ¯ j q j ( i = 1 s - 1 p ¯ i q ¯ i ) .
[ .1 _ .0 ] ,             [ .1 .0 _ ] ,
[ 1. _ 0. ] [ .1 _ .0 ] = [ 11 _ 00 ] ,
[ 0. 1. _ ] [ .1 .0 _ ] = [ 01 10 _ ] .
[ 11 _ 00 ] + [ 01 10 _ ] .
[ 0. _ 1. ] [ .1 _ .0 ] + j = 1 s - 1 ( [ 0. _ 1. ] [ .1 _ .0 ] ) 0 , j i = 0 j - 1 ( [ 0. _ 0. ] [ .1 _ .0 ] ) 0 , i = [ 01 _ 10 ] + j = 1 s - 1 [ 01 _ 10 ] 0 , j i = 0 j - 1 [ 01 _ 00 ] 0 , i .
[ 1. .. _ ] [ .1 .0 _ ] + [ .. _ 1. ] [ .1 _ .0 ] + [ .. 1. _ ] [ .0 .0 _ ] + [ 1. _ .. ] [ .0 _ .0 ] = [ 11 .0 _ ] + [ .1 _ 10 ] + [ .0 10 _ ] + [ 10 _ .0 ] .
X 2 k - 1 = X 2 k R k + X 2 k - 1 R ¯ k
X 2 k = X 2 k - 1 R k + X 2 k R ¯ k

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