Complexity of Boolean functions on PRAMs - Lower bound techniques

  • Mirosław Kutyłowski
Parallel and Distributed Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 594)

Abstract

Determining time necessary for computing important functions on parallel machines is one of the most important problems in complexity theory for parallel algorithms. Recently, a substantial progress has been made in this area. In this survey paper, we discuss the results that have been obtained for three types of parallel random access machines (PRAMs): CREW, ROBUST and EREW.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    P. Beame and J. Hastad. Optimal bounds for decision problems on the CRCW PRAM. J. ACM, 36 (1989), 643–670.CrossRefGoogle Scholar
  2. [2]
    P. Beame, M. Kik and M. Kutylowski. Information broadcasting by Exclusive Read PRAMs. Submitted.Google Scholar
  3. [3]
    S. J. Bellantoni. Parallel random access machines with bounded memory wordsize. Inform. and Comput., 91 (1991), 259–273.CrossRefGoogle Scholar
  4. [4]
    S. Cook, C. Dwork, and R. Reischuk. Upper and lower time bounds for parallel random access machines without simultaneous writes. SIAM J. Comput., 15 (1986), 87–97.CrossRefGoogle Scholar
  5. [5]
    M. Dietzfelbinger, M. Kutyłowski and R. Reischuk. Exact time bounds for computing Boolean functions on PRAMs without simultaneous writes. In Proc. 2nd ACM Symposium on Parallel Algorithms and Architectures (Heraklion), Association for Computing Machinery, 1990, 125–135.Google Scholar
  6. [6]
    M. Dietzfelbinger, M. Kutyłowski and R. Reischuk. Exact lower bounds for computing Boolean functions on CREW PRAMs. A journal version of the first part of [5], submitted.Google Scholar
  7. [7]
    M. Dietzfelbinger, M. Kutyłowski and R. Reischuk. Realistic time-optimal algorithms for Boolean functions on Exclusive-Write PRAMs. A journal version of the second part of [5].Google Scholar
  8. [8]
    F. E. Fich, R. Impagliazzo, B. Kapron and V. King. Limits on the power of parallel random access machines with weak forms of write conflict resolution. Preliminary draft, 1991.Google Scholar
  9. [9]
    F. E. Fich, and P. Ragde. Personal communication.Google Scholar
  10. [10]
    F. E. Fich and A. Wigderson. Towards understanding exclusive write. In Proc. 1st ACM Symposium on Parallel Algorithms and Architectures (Santa Fe), Association for Computing Machinery, 1989, 76–82.Google Scholar
  11. [11]
    E. Gafni, J. Naor and P. Ragde. On separating the EREW and CROW models. To appear in Theoret. Comput. Sci. Google Scholar
  12. [12]
    T. Hagerup. Personal communication.Google Scholar
  13. [13]
    T. Hagerup and M. Kutylowski. Fast merging on the EREW PRAM. Submitted.Google Scholar
  14. [14]
    T. Hagerup and M. Nowak. Parallel retrieval of scattered information. In Proc. International Congress on Automata Languages and Programming (Stresa), European Association for Theoretical Computer Science, 1989, 439–450.Google Scholar
  15. [15]
    T. Hagerup and T. Radzik. Every ROBUST CRCW PRAM can efficiently simulate a PRIORITY PRAM. In Proc. 2nd ACM Symposium on Parallel Algorithms and Architectures (Crete), Association for Computing Machinery, 1990, 125–135.Google Scholar
  16. [16]
    M. Kowaluk and K. Lorys. Personal communication.Google Scholar
  17. [17]
    M. Kutyłowski. Time complexity of Boolean functions on CREW PRAMs. SIAM J. Comput. 20 (1991).Google Scholar
  18. [18]
    M. Kutyłowski. Lower time bounds for computing Boolean functions on ROBUST PRAMs. Preliminary draft, 1991.Google Scholar
  19. [19]
    N. Nisan. CREW PRAMs and decision trees. In Proc. 21st ACM Symposium on Theory of Computing (Seattle), Association for Computing Machinery, 1989, pp. 327–335.Google Scholar
  20. [20]
    I. Parberry and P. Y. Yan. Improved upper and lower time bounds for parallel random access machines without simultaneous writes. SIAM J. Comput., 20 (1991), 88–99.CrossRefGoogle Scholar
  21. [21]
    M. Szegedy. Algebraic methods in lower bounds for computational models with limited communication. Ph. D. dissertation, University of Chicago, Chicago, Illinois, 1989.Google Scholar
  22. [22]
    M. Snir. On parallel searching. SIAM J. Comput., 14 (1985), 688–708.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Mirosław Kutyłowski
    • 1
  1. 1.Fachbereich Mathematik-InformatikUniversität-GH PaderbornPaderbornGermany

Personalised recommendations