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.
Supported in part by the Deutsche Forschungsgemeinschaft, SFB 124, TP B2, VLSI Entwurfsmethoden und Parallelität, and in part by the ESPRIT II Basic Research Actions Program of the EC under contract No. 3075 (project ALCOM).
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References
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.
Berkman, O., and Vishkin, U. (1989), Recursive *-Tree Parallel Data-Structure, in Proc. 30th Annual Symposium on Foundations of Computer Science, pp. 196–202.
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.
Boppana, R. B. (1989), Optimal Separations between Concurrent-Write Parallel Machines, in Proc. 21st Annual ACM Symposium on Theory of Computing, pp. 320–326.
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.
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.
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.
Cole, R., and Vishkin, U. (1989), Faster Optimal Parallel Prefix Sums and List Ranking, Inform. and Comput.81, pp. 334–352.
Fich, F. E., Ragde, P., and Wigderson, A. (1988a), Simulations Among Concurrent-Write PRAMs, Algorithmica3, pp. 43–51.
Fich, F. E., Ragde, P., and Wigderson, A. (1988b), Relations Between Concurrent-Write Models of Parallel Computation, SIAM J. Comput.17, pp. 606–627.
Gil, J. (1990), Lower Bounds and Algorithms for Hashing and Parallel Processing, Ph.D. Thesis, The Hebrew University, Jerusalem.
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.
Goldschlager, L. M. (1982), A Universal Interconnection Pattern for Parallel Computers, J. ACM29, pp. 1073–1086.
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.
Grolmusz, V., and Ragde, P. (1987), Incomparability in Parallel Computation, in Proc. 28th Annual Symposium on Foundations of Computer Science, pp. 89–98.
Hagerup, T. (1990), Optimal Parallel Algorithms on Planar Graphs, Inform. and Comput.84, pp. 71–96.
Hagerup, T. (1991a), Fast Parallel Space Allocation, Estimation and Integer Sorting, Tech. Rep. no. MPI-I-91-106, Max-Planck-Institut für Informatik, Saarbrücken.
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.
Hagerup, T. (1992), The Log-Star Revolution, these proceedings.
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.
Hagerup, T., and Rüb, C. (1990), A Guided Tour of Chernoff Bounds, Inform. Proc. Lett.33, pp. 305–308.
Kučera, L. (1982), Parallel Computation and Conflicts in Memory Access, Inform. Proc. Lett.14, pp. 93–96.
Kucera, L. (1983), Erratum and Addendum to: Parallel Computation and Conflicts in Memory Access, Inform. Proc. Lett.17, p. 107.
Martel, C. U., and Gusfield, D. (1989), A Fast Parallel Quicksort Algorithm, Inform. Proc. Lett.30, pp. 97–102.
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.
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.
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.
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.
Ragde, P. (1989), Processor-Time Tradeoffs in PRAM Simulations, J. Comp. Sys. Sci., to appear.
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.
Reischuk, R. (1985), Probabilistic Parallel Algorithms for Sorting and Selection, SIAM J. Comput.14, pp. 396–409.
Shiloach, Y., and Vishkin, U. (1981), Finding the Maximum, Merging, and Sorting in a Parallel Computation Model, J. Alg.2, pp. 88–102.
Shiloach, Y., and Vishkin, U. (1982), An O(log n) Parallel Connectivity Algorithm, J. Alg.3, pp. 57–67.
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© 1992 Springer-Verlag Berlin Heidelberg
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Hagerup, T. (1992). Fast and optimal simulations between CRCW PRAMs. In: Finkel, A., Jantzen, M. (eds) STACS 92. STACS 1992. Lecture Notes in Computer Science, vol 577. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55210-3_172
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DOI: https://doi.org/10.1007/3-540-55210-3_172
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