Abstract
This paper presents and analyses efficient implementations of a so-called direct process on distributed memory machines (DMMs) that yields
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a simulation of an n-processor PRAM on an n-processor optical crossbar DMM with delay O(log log n),
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a simulation of an n-processor PRAM on an n-processor arbitrary DMM with delay O(log log n/log log log n),
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an implementation of a static dictionary on an n-processor arbitrary DMM with parallel access time of O(log* n).
We further prove a lower bound for executing the above process, showing that our implementations are optimal.
Supported in part by DFG-Forschergruppe “Effiziente Nutzung massiv paralleler Systeme, Teilprojekt 4”, by Volkswagen Foundation and by the Esprit Basic Research Action Nr 7141 (ALCOM II)
Supported by the DFG-grant Me 872/6-1 (Leibniz Preis)
Supported by the DFG-Graduiertenkolleg “Parallele Rechnernetzwerke in der Produktionstechnik”, ME 872/4-1
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References
R.J. Anderson and G.L. Miller. Optical Communication for Pointer Based Algorithms, Technical Report CRI 88-14, Computer Science Department, University of Southern Carolina, Los Angeles, CA 90089-0782 USA, 1988.
H. Bast and T. Hagerup. Fast and reliable parallel hashing. In Proc. of the 3rd Ann. ACM Symp. on Parallel Algorithms and Architectures, pp. 50–61, 1991.
M. Dietzfelbinger, F. Meyer auf der Heide. How to distribute a hash table in a complete network. In Proc. of the 22nd Ann. ACM Symp. on Theory of Computing, pp. 117–127, 1990.
M. Dietzfelbinger and F. Meyer auf der Heide. Simple efficient shared memory simulations. In Proceedings of the 5th Ann. ACM Symposium on Parallel Algorithms and Architectures, pp. 110–119, 1993.
M. Geréb-Graus and T. Tsantilas. Efficient Optical Communication in Parallel Computers. In Proceedings of the 4th ACM Symposium on Parallel Algorithms and Architectures, pp. 41–48, 1992.
L. A. Goldberg and M. Jerrum and T. Leighton. A doubly logarithmic communication algorithm for the completely connected optical communication parallel computer. In Proceedings of the 5th Ann. ACM Symposium on Parallel Algorithms and Architectures, pp. 300–309, 1993.
L.A. Goldberg, Y. Matias, S. Rao. An optical simulation of shared memory. Technical Report, 1994.
J. Gil, Y. Matias, U. Vishkin. Towards a theory of nearly constant time parallel algorithms. In Proc. of the 32nd Ann. IEEE Symp. on Foundations of Computer Science, pp. 698–710, 1991.
R. Karp, M. Luby and F. Meyer auf der Heide. Efficient PRAM simulation on distributed memory machine. In Proc. of the 24th Ann. ACM Symp. on Theory of Computing, pp. 318–326, 1992.
F. Meyer auf der Heide. Hashing strategies for simulating shared memory on distributed memory machines. In Proc. of the 1st Heinz Nixdorf Symposium “Parallel Architectures and Their Efficient Use”, F. Meyer auf der Heide, B. Monien, A.L. Rosenberg, eds., pp. 20–29, 1992.
P.D. MacKenzie, C.G. Plaxton, R. Rajamaran. On contention resolution protocols and associated phenomena. University of Texas at Austin, Technical Report 94-06, 1994.
A. Siegel. On universal classes of fast high performance hash functions, their time-space tradeoff, and their applications. In Proc. of the 30th IEEE Ann. Symp. on Foundations of Computer Science, pp. 20–25, 1989.
E. Upfal, A. Wigderson. How to share memory in a distributed system. J. Assoc. Comput. Mach. 34, pp. 116–127, 1987.
L. Valiant. Parallelism in comparison problems. In SIAM J. Comp. 4(3), pp. 348–355, 1975.
L. Valiant. General Purpose Parallel Architectures, Chapter 18 of Handbook of Theoretical Computer Science. Edited by J. van Leeuwen, Elsevier 1990.
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Meyer, F., Scheideier, C., Stemann, V. (1995). Exploiting storage redundancy to speed up randomized shared memory simulations. In: Mayr, E.W., Puech, C. (eds) STACS 95. STACS 1995. Lecture Notes in Computer Science, vol 900. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59042-0_79
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DOI: https://doi.org/10.1007/3-540-59042-0_79
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