Abstract
We study the Distributed Memory Machine (DMM) with faults in memory. The DMM consists of n synchronized processors together with n memory units (MUs). A MU can be accessed by at most one processor at a time. The total number of memory faults is assumed to be at most a fixed fraction of the total number of words.
We develop two fast randomized simulations of the PRAM on such a faulty DMM. A simulation consists of two phases: the preprocessing is followed by the simulation proper done in a step-by-step fashion. One simulation is of an n·log n-processor PRAM and it operates with the optimal expected slowdown O(log n), the other is of a PRAM with n /log n processors and has the slowdown O (log log n).
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References
R.J. Anderson, and G.L. Miller, Optical Communication for Pointer Based Algorithms, Tech. Rep. CRI 88-14, Comp. Sci. Dpt., USC, Los Angeles, 1988.
B.S. Chlebus, A. Gambin, and P. Indyk, PRAM Computations Resilient to Memory Faults, in Proceedings of the 2nd Annual European Symposium on Algorithms, 1994, LNCS 855, pp. 401–412.
B.S. Chlebus, L. G⇓sieniec, and A. Pelc, Fast Deterministic Simulation of Computations on Faulty Parallel Machines, in Proceedings of the 3rd Annual European Symposium on Algorithms, 1995, LNCS 979, pp. 89–101.
A. Czumaj, F. Meyer auf der Heide, and V. Stemann, Shared Memory Simulations with Triple-Logarithmic Delay, in Proceedings of the 3rd Annual European Symposium on Algorithms, 1995, LNCS 979, pp. 46–59.
M. Dietzfelbinger, and F. Meyer auf der Heide, Simple, Efficient Shared Memory Simulations, in Proceedings of the 5th Annual ACM Symposium on Parallel Algorithms and Architectures, 1993, pp. 110–119.
P. Indyk, On Word-Level Parallelism in Fault-Tolerant Computing, in Proceedings of the 13th Annual Symposium on Theoretical Aspects of Computer Science, 1996.
P.C. Kanellakis, and A.A. Shvartsman, Efficient Parallel Algorithms Can Be Made Robust, Distributed Computing, 5 (1992) 201–217.
R. Karp, M. Luby, and F. Meyer auf der Heide, Efficient PRAM Simulations on Distributed Memory Machine, in Proceedings of the 24-th Annual ACM Symposium on Theory of Computing, 1992, pp. 318–326.
Z. M. Kedem, K. V. Palem, A. Raghunathan, and P. Spirakis, Combining Tentative and Definite Executions for Very Fast Dependable Parallel Computing, in Proceedings of the 23rd Annual ACM Symposium on Theory of Computing, 1991, pp. 381–390.
Z. M. Kedem, K. V. Palem, and P. Spirakis, Efficient Robust Parallel Computations, in Proceedings of the 22nd Annual ACM Symposium on Theory of Computing, 1990, pp. 138–148.
T. Leighton, and G. Plaxton, A (Fairly) Simple Circuit That (Usually) Sorts, in Proceedings of the 31st Annual Symposium on Foundations in Computer Science, 1990, pp. 264–274.
C. Martel, A. Park, and R. Subramonian, Work-Optimal Asynchronous Algorithms for Shared Memory Parallel Computers, SIAM J. Comput (1992) 1070–1099.
K. Mehlhorn, and U. Vishkin, Randomized and Deterministic Simulations of PRAMs by Parallel Machines with Restricted Granularity of Parallel Memories, Acta Informatica 21 (1984) 339–374.
F. Meyer auf der Heide, Hashing Strategies for Simulating Shared Memory on Distributed Memory Machines, in Proceedings of the 1st Heinz Nixdorf Symposium “Parallel Architectures and their Efficient Use,” 1992, LNCS 678, pp. 20–29.
F. Meyer auf der Heide, C. Scheideier, and V. Stemann, Exploiting Storage Redundancy to Speed Up Randomized Shared Memory Simulations, in Proceedings, 12th Annual Symposium on Theoretical Aspects of Computer Science, 1995, LNCS 900, pp. 267–278.
A. Siegel, On Universal Classes of Fast High Performance Hash Functions, Their Time-Space Tradeoff, and Their Applications, in Proceedings of the 30th Annual Symposium on Foundations of Computer Science, 1989, pp. 20–25.
L.G. Valiant, General Purpose Parallel Architectures, in “Handbook of Theoretical Computer Science,” J. van Leeuwen (Ed.), Eisevier, 1990, vol. A, pp. 869–941.
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© 1996 Springer-Verlag Berlin Heidelberg
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Chlebus, B.S., Gambin, A., Indyk, P. (1996). Shared-memory simulations on a faulty-memory DMM. In: Meyer, F., Monien, B. (eds) Automata, Languages and Programming. ICALP 1996. Lecture Notes in Computer Science, vol 1099. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61440-0_161
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DOI: https://doi.org/10.1007/3-540-61440-0_161
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