Fast and optimal simulations between CRCW PRAMs

  • Torben Hagerup
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 577)

Abstract

We describe new simulations between different variants of the CRCW PRAM. On a Minimum PRAM, the minimum value is written in the event of a write conflict, whereas concurrent writing to the same cell is without effect on a Tolerant PRAM. Compared to other variants of the CRCW PRAM, the Minimum PRAM is very strong, and the Tolerant PRAM is very weak. In fact, the two variants are near opposite ends of the spectrum of CRCW PRAM variants commonly considered. We show that one step of a (randomized) Minimum PRAM with n processors can be simulated with high probability in O((log*n)3) time on a randomized Tolerant PRAM with O(n/(log*n)3) processors. The simulation is optimal, in the sense that the product of its slowdown and the number of simulating processors is within a constant factor of the number of simulated processors. It subsumes most previous work on randomized simulations between n-processor CRCW PRAMs with infinite memories.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bast, H., and Hagerup, T. (1991), Fast and Reliable Parallel Hashing, manuscript. A preliminary version appears in Proc. 3rd Annual ACM Symposium on Parallel Algorithms and Architectures, pp. 50–61.Google Scholar
  2. Berkman, O., and Vishkin, U. (1989), Recursive *-Tree Parallel Data-Structure, in Proc. 30th Annual Symposium on Foundations of Computer Science, pp. 196–202.Google Scholar
  3. Bhatt, P. C. P., Diks, K., Hagerup, T., Prasad, V. C., Radzik, T., and Saxena, S. (1991), Improved Deterministic Parallel Integer Sorting, Inform. and Comput.94, pp. 29–47.Google Scholar
  4. Boppana, R. B. (1989), Optimal Separations between Concurrent-Write Parallel Machines, in Proc. 21st Annual ACM Symposium on Theory of Computing, pp. 320–326.Google Scholar
  5. Chlebus, B. S., Diks, K., Hagerup, T., and Radzik, T. (1988), Efficient Simulations between Concurrent-Read Concurrent-Write PRAM Models, in Proc. 13th Symposium on Mathematical Foundations of Computer Science, Springer Lecture Notes in Computer Science, Vol. 324, pp. 231–239.Google Scholar
  6. Chlebus, B. S., Diks, K., Hagerup, T., and Radzik, T. (1989), New Simulations between CRCW PRAMs, in Proc. 7th International Conference on Fundamentals of Computation Theory, Springer Lecture Notes in Computer Science, Vol. 380, pp. 95–104.Google Scholar
  7. Cole, R., and Vishkin, U. (1986), Deterministic Coin Tossing and Accelerating Cascades: Micro and Macro Techniques for Designing Parallel Algorithms, in Proc. 18th Annual ACM Symposium on Theory of Computing, pp. 206–219.Google Scholar
  8. Cole, R., and Vishkin, U. (1989), Faster Optimal Parallel Prefix Sums and List Ranking, Inform. and Comput.81, pp. 334–352.Google Scholar
  9. Fich, F. E., Ragde, P., and Wigderson, A. (1988a), Simulations Among Concurrent-Write PRAMs, Algorithmica3, pp. 43–51.Google Scholar
  10. Fich, F. E., Ragde, P., and Wigderson, A. (1988b), Relations Between Concurrent-Write Models of Parallel Computation, SIAM J. Comput.17, pp. 606–627.Google Scholar
  11. Gil, J. (1990), Lower Bounds and Algorithms for Hashing and Parallel Processing, Ph.D. Thesis, The Hebrew University, Jerusalem.Google Scholar
  12. Gil, J., Matias, Y., and Vishkin, U. (1991), Towards a Theory of Nearly Constant Time Parallel Algorithms, in Proc. 32nd Annual Symposium on Foundations of Computer Science, pp. 698–710.Google Scholar
  13. Goldschlager, L. M. (1982), A Universal Interconnection Pattern for Parallel Computers, J. ACM29, pp. 1073–1086.Google Scholar
  14. Gottlieb, A., Grishman, R., Kruskal, C. P., McAuliffe, K.P., Rudolph, L., and Snir, M. (1983), The NYU Ultracomputer — Designing an MIMD Shared Memory Parallel Computer, IEEE Trans. Comp.32, pp. 175–189.Google Scholar
  15. Grolmusz, V., and Ragde, P. (1987), Incomparability in Parallel Computation, in Proc. 28th Annual Symposium on Foundations of Computer Science, pp. 89–98.Google Scholar
  16. Hagerup, T. (1990), Optimal Parallel Algorithms on Planar Graphs, Inform. and Comput.84, pp. 71–96.Google Scholar
  17. Hagerup, T. (1991a), Fast Parallel Space Allocation, Estimation and Integer Sorting, Tech. Rep. no. MPI-I-91-106, Max-Planck-Institut für Informatik, Saarbrücken.Google Scholar
  18. Hagerup, T. (1991b), Fast Parallel Generation of Random Permutations, in Proc. 18th International Colloquium on Automata, Languages and Programming, Springer Lecture Notes in Computer Science, Vol. 510, pp. 405–416.Google Scholar
  19. Hagerup, T. (1992), The Log-Star Revolution, these proceedings.Google Scholar
  20. Hagerup, T., and Radzik, T. (1990), Every Robust CRCW PRAM Can Efficiently Simulate a Priority PRAM, in Proc. 2nd Annual ACM Symposium on Parallel Algorithms and Architectures, pp. 117–124.Google Scholar
  21. Hagerup, T., and Rüb, C. (1990), A Guided Tour of Chernoff Bounds, Inform. Proc. Lett.33, pp. 305–308.Google Scholar
  22. Kučera, L. (1982), Parallel Computation and Conflicts in Memory Access, Inform. Proc. Lett.14, pp. 93–96.Google Scholar
  23. Kucera, L. (1983), Erratum and Addendum to: Parallel Computation and Conflicts in Memory Access, Inform. Proc. Lett.17, p. 107.Google Scholar
  24. Martel, C. U., and Gusfield, D. (1989), A Fast Parallel Quicksort Algorithm, Inform. Proc. Lett.30, pp. 97–102.Google Scholar
  25. Matias, Y., and Vishkin, U. (1990a), On Parallel Hashing and Integer Sorting, in Proc. 17th International Colloquium on Automata, Languages and Programming, Springer Lecture Notes in Computer Science, Vol. 443, pp. 729–743.Google Scholar
  26. Matias, Y., and Vishkin, U. (1990b), On Parallel Hashing and Integer Sorting, Tech. Rep. no. UMIACS-TR-90-13.1 (revised version), University of Maryland, College Park.Google Scholar
  27. Matias, Y., and Vishkin, U. (1991), Converting High Probability into Nearly-Constant Time — with Applications to Parallel Hashing, in Proc. 23rd Annual ACM Symposium on Theory of Computing, pp. 307–316.Google Scholar
  28. McDiarmid, C. (1989), On the Method of Bounded Differences, in Surveys in Combinatorics, 1989, ed. J. Siemons, London Math. Soc. Lecture Note Series 141, Cambridge University Press, pp. 148–188.Google Scholar
  29. Ragde, P. (1989), Processor-Time Tradeoffs in PRAM Simulations, J. Comp. Sys. Sci., to appear.Google Scholar
  30. Ragde, P. (1990), The Parallel Simplicity of Compaction and Chaining, in Proc. 17th International Colloquium on Automata, Languages and Programming, Springer Lecture Notes in Computer Science, Vol. 443, pp. 744–751.Google Scholar
  31. Reischuk, R. (1985), Probabilistic Parallel Algorithms for Sorting and Selection, SIAM J. Comput.14, pp. 396–409.Google Scholar
  32. Shiloach, Y., and Vishkin, U. (1981), Finding the Maximum, Merging, and Sorting in a Parallel Computation Model, J. Alg.2, pp. 88–102.Google Scholar
  33. Shiloach, Y., and Vishkin, U. (1982), An O(log n) Parallel Connectivity Algorithm, J. Alg.3, pp. 57–67.Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Torben Hagerup
    • 1
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany

Personalised recommendations