BIT Numerical Mathematics

, Volume 27, Issue 1, pp 25–43 | Cite as

Array processing machines: An abstract model

  • J. van Leeuwen
  • J. Wiedermann
Part I Computer Science
Received:
Revised:

Abstract

We present a new model of parallel computation called the “array processing machine” or APM (for short). The APM was designed to closely model the architecture of existing vector- and array processors, and to provide a suitable unifying framework for the complexity theory of parallel combinatorial and numerical algorithms. It is shown that every problem that is solvable in polynomial space on an ordinary, sequential random access machine can be solved in parallel polynomial time on an APM (and vice versa). The relationship to other models of parallel computation is discussed.

CR categories

F.2.0 C.1.2 
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. V. Aho, J. E. Hopcroft and J. D. Ullman,The Design and Analysis of Computer Algorithms, Addison-Wesley Publ. Comp., Reading, Mass., 1974.Google Scholar
  2. 2.
    A. K. Chandra, D. C. Kozen and L. J. Stockmeyer,Alternation, J. ACM 28 (1981), 114–133.CrossRefGoogle Scholar
  3. 3.
    S. A. Cook,Towards a complexity theory of synchronous parallel computation, Enseign. Math. 27 (1981), 99–124.Google Scholar
  4. 4.
    S. A. Cook,The classification of problems which have fast parallel algorithms, Proc. FCT'83, Springer Lecture Notes in Comput. Sci. 158 (1983), 78–93; revised and extended version in: Inf. & Control 64 (1985), 2–22.Google Scholar
  5. 5.
    S. A. Cook and R. A. Reckhow,Time-bounded random access machines, J. Comput. Syst. Sci. 7 (1973), 354–375.Google Scholar
  6. 6.
    E. Engeler,Introduction to the Theory of Computation, Acad. Press, New York, NY, 1973.Google Scholar
  7. 7.
    M. J. Flynn,Some computer organisations and their effectiveness, IEEE Trans. Comput. C-21 (1972), 948–960.Google Scholar
  8. 8.
    S. Fortune and J. Wyllie,Parallelism in random access machines, Proc. 10th ACM Sympos. Theory of Comput., San Diego, 1978, pp. 89–94.Google Scholar
  9. 9.
    L. M. Goldschlager,A universal interconnection pattern for parallel computers, J. ACM 29 (1982), 1073–1086.CrossRefGoogle Scholar
  10. 10.
    J. Hartmanis and J. Simon,On power of multiplication in random access machines, Proc. 15th Ann. IEEE Sympos. Switching and Automata Theor., New Orleans, 1974, pp. 13–23.Google Scholar
  11. 11.
    R. W. Hockney and C. R. Jesshope,Parallel Computers, Hilger, Bristol, 1981.Google Scholar
  12. 12.
    K. Hwang, S. P. Su and L. M. Ni,Vector computer architecture and processing techniques, in: M. C. Yovits (ed.),Advances in Computers, Vol. 20, Acad. Press, New York, NY, 1981, pp. 115–197.Google Scholar
  13. 13.
    D. E. Knuth,The Art of Computer Programming, Vol. 3: Sorting and Searching, Addison-Wesley Publ. Comp., Reading, Mass., 1975.Google Scholar
  14. 14.
    V. R. Pratt, and L. J. Stockmeyer,A characterization of the power of vector machines, J. Comput. Syst. Sci. 12 (1976), 198–221.Google Scholar
  15. 15.
    W. L. Ruzzo,On uniform circuit complexity, J. Comput. Syst. Sci. 22 (1981), 365–383.CrossRefGoogle Scholar
  16. 16.
    W. J. Savitch,Parallel random access machines with powerful instruction sets, Math. Syst. Theor. 15 (1982), 191–210.CrossRefGoogle Scholar
  17. 17.
    W. J. Savitch and M. J. Stimson,Time-bounded random access machines with parallel processing. J. ACM 26 (1979), 103–118.CrossRefGoogle Scholar
  18. 18.
    L. J. Stockmeyer and U. Vishkin,Simulation of parallel random access machines by circuits, SIAM J. Comput. 13 (1984), 409–422.CrossRefGoogle Scholar
  19. 19.
    H. S. Stone,Parallel processing with the perfect shuffle, IEEE Trans. Comput. 3–20 (1971), 153–161.Google Scholar
  20. 20.
    H. S. Stone,An efficient parallel algorithm for the solution of a tridiagonal linear system of equations, J. ACM 20 (1973), 27–38.CrossRefGoogle Scholar
  21. 21.
    P. van Emde Boas,The second machine class: models of parallelism, in: J. van Leeuwen and J. K. Lenstra, (eds.),Parallel Computers and Computations, CWI Syll. 9, Centre for Mathematics and Computer Science, Amsterdam, 1985, pp. 133–161.Google Scholar
  22. 22.
    P. van Emde Boas,The second machine class 2: an encyclopedic view of the parallel computation thesis, Rep. 85-24, Dept. of Mathematics, University of Amsterdam, Amsterdam, 1985.Google Scholar
  23. 23.
    J. van Leeuwen,Parallel computers and algorithms, Techn. Rep. RUU-CS-83-13, Dept. of Computer Science, University of Utrecht, 1983; also in: J. van Leeuwen and J. K. Lenstra (eds.),Parallel Computers and Computations, CWI Syll. 9, Centre for Mathematics and Computer Science, Amsterdam, 1985, pp, 1–32.Google Scholar
  24. 24.
    J. van Leeuwen and H. A. G. Wijshoff,Data mappings in large parallel computers, in: I. Kupka (ed.), GI-13 Jahrestagung, Informatik Fb 73, Springer Verlag, Berlin, 1983, pp. 8–20.Google Scholar
  25. 25.
    J. van Leeuwen and J. Wiedermann,Array processing machines, Techn. Rep. RUU-CS-84-13, Dept. of Computer Science, University of Utrecht, Utrecht, 1984. Extended abstract in: L. Budach (ed.),Fundamentals of Computation Theory, Proceedings, Lecture Notes in Computer Science, Vol. 199, Springer-Verlag, Berlin, 1985, pp. 257–268.Google Scholar
  26. 26.
    J. Wiedermann,Parallel Turing machines, Techn. Rep. RUU-CS-84-11, Dept. of Computer Science, University of Utrecht, Utrecht, 1984.Google Scholar

Copyright information

© BIT Foundations 1987

Authors and Affiliations

  • J. van Leeuwen
    • 1
    • 2
  • J. Wiedermann
    • 1
    • 2
  1. 1.Department of Computer ScienceUniversity of UtrechtUtrechtthe Netherlands
  2. 2.VUSEI-ARBratislavaCzechoslovakia

Personalised recommendations