Limitations of the QRQW and EREW PRAM models

  • Mirosław Kutyłowski
  • Krzysztof LoryŚ
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1180)

Abstract

We consider parallel random access machines (PRAMs) with restricted access to the shared memory resulting from handling congestion of memory requests. We study the (SIMD) QRQW PRAM model where multiple requests are queued and serviced one at a time. We also consider exclusive read exclusive write (EREW) PRAM and its modification obtained by adding a single bus.

For the QRQW PRAMs we investigate the case when the machine can measure the duration of a single step. Even for such a (powerful) QRQW PRAM PARITY of n bits (PARITYn) requires Ω(log n) time while OR of n bits can be computed deterministically in a constant time. On randomized QRQW PRAM the function PARITYn is still difficult. We prove a lower time bound Ω(√ log n/log log n) for algorithms that succeed with probability 0.5+∃ (∃>0). These bounds show that implementing concurrent writes may degradate runtime of a CRCW PRAM algorithm.

The simple 2-compaction problem is known to be hard for EREW PRAM. The same time bound Ω(√log n) for this problem has been proved for both deterministic and randomized EREW PRAM. We show that this is not a coincidence since the time complexity of this problem is the same for deterministic and randomized case. The technique which we apply is quite general and may be used to obtain similar results for any problem where the number of input configurations is small.

We also show that improving time bound Ω(√ log n) for 2-compaction on EREW PRAM requires novel and more sophisticated techniques.

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References

  1. 1.
    D. Angluin, L.G. Valiant, Fast probabilistic algorithms for Hamiltonian circuits and matchings, J. Comput. System Sci. 18 (1979) 155–193.Google Scholar
  2. 2.
    P. Beame, J. Håstad, Optimal bounds for decision problems on the CRCW PRAM, JACM, 36(3) (1989) 643–670.Google Scholar
  3. 3.
    C. Berge: Graphs and Hypergraphs. North-Holland, Amsterdam, 1976.Google Scholar
  4. 4.
    S. Cook, C. Dwork, R. Reischuk, Upper and lower time bounds for parallel random access machines without simultaneous writes, SIAM J. Comput. 15(1) (1986) 87–97.Google Scholar
  5. 5.
    M. Dietzfelbinger, M. Kutyłowski, R. Reischuk, Exact lower time bounds for computing Boolean functions on CREW PRAMs, JCSS 48(2) (1994) 231–253.Google Scholar
  6. 6.
    F.E. Fich, The complexity of computation on the Parallel Random Access Machine, in Synthesis of Parallel Algorithms, J.H. Reif (ed.) (Morgan Kaufmann, San Mateo, 1993) 843–899.Google Scholar
  7. 7.
    F. Fich, M. Kowaluk, M.Kutyłowski, K. LoryŚ, P. Ragde, Retrieval of scattered information by EREW, CREW and CRCW PRAMs, Comput. Complexity 5 (1995) 113–131.Google Scholar
  8. 8.
    P. Gibbons, Y. Matias, V. Ramachandran, Efficient low-contention parallel algorithms, in Proc. 6th ACM Symp. on Parallel Algorithms and Architectures, (ACM Press, New York, 1994) 236–247.Google Scholar
  9. 9.
    P. Gibbons, Y. Matias, V. Ramachandran, The QRQW PRAM: accounting for contention in parallel algorithms, in Proc. 5th ACM Symp. on Discrete Algorithms, (ACM Press, New York, 1994) 638–648.Google Scholar
  10. 10.
    P. D. MacKenzie, Lower bounds for randomized exclusive write PRAMs, in Proc. 7th ACM Symp. on Parallel Algorithms and Architectures, (ACM Press, New York, 1995) 254–263.Google Scholar
  11. 11.
    R. Motwani, P. Raghavan: Randomized Algorithms, Cambridge University Press, Cambridge 1995.Google Scholar
  12. 12.
    H. Robbins, A remark on Stirling formula, American Mathematical Monthly 62 (1955) 26–29.Google Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Mirosław Kutyłowski
    • 1
  • Krzysztof LoryŚ
    • 2
    • 3
  1. 1.Heinz Nixdorf Institute and Dept. of Mathematics & Computer ScienceUniversity of PaderbornPaderbornGermany
  2. 2.Institute of Computer ScienceUniversity of WrocławPoland
  3. 3.Dept. of Computer ScienceUniversity of TrierTrierGermany

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