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Simulations between different models of parallel computers

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Fundamentals of Computation Theory (FCT 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 710))

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Abstract

We discuss simulations of parallel computers with shared memory (PRAMs) on distributed memory machines (DMMs). Such simulations are an important step in realizing algorithms written for the theoretical PRAM model. In all simulations considered here, the shared memory is distributed over the memory modules of the DMM by means of a hash function chosen at random from a suitable universal class. We discuss universal classes of hash functions, internal organization of memory modules, and a series of classical and novel simulation results.

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References

  1. F. Abolhassan, J. Keller, and W.J. Paul. On the cost-effectiveness of PRAMs. In Proc. of the 3rd IEEE Symp. on Parallel and Distributed Processing, pp. 2–9, 1991.

    Google Scholar 

  2. F. Abolhassan, R. Drefenstedt, J. Keller, W.J. Paul, and D. Scheerer. On the physical design of PRAMs. In J. Buchmann, H. Ganzinger, and W. J. Paul, Eds., Informatik — Festschrift zum 60. Geburtstag von Günter Hotz, pp. 1–19, Teubner Verlag, 1992.

    Google Scholar 

  3. R. J. Anderson, G. L. Miller. Optical communication for pointer based algorithms. Tech. Rep. CRI 88-14, Comp. Sci. Dept., Univ. of Southern California, Los Angeles, 1988.

    Google Scholar 

  4. 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.

    Google Scholar 

  5. J. L. Carter and M. N. Wegman. Universal classes of hash functions. J. Comput. Syst. Sci., 18:143–154, 1979.

    Article  Google Scholar 

  6. B. S. Chlebus, K. Diks, T. Hagerup, and T. Radzik. Efficient simulations between concurrent-read concurrent-write PRAM models. In Proc. 13th Symp. on Mathematical Foundations of Computer Science, LNCS 324, pp. 231–239, Springer, 1988.

    Google Scholar 

  7. B. S. Chlebus, K. Diks, T. Hagerup, and T. Radzik. New simulations between CRCW PRAMs. In Proc. 7th Int. Conf. on Fundamentals of Computation Theory, LNCS 380, pp. 95–104, Springer, 1989.

    Google Scholar 

  8. R. Cole. Parallel merge sort. SIAM J. Comp. 17(4):770–785, 1988.

    Article  Google Scholar 

  9. M. Dietzfelbinger, J. Gil, Y. Matias, and N. Pippenger. Polynomial hash functions are reliable. In W. Kuich, editor, Proceedings of 19th ICALP, LNCS 623, pp. 235–246, Springer, 1992.

    Google Scholar 

  10. M. Dietzfelbinger, A. Karlin, K. Mehlhorn, F. Meyer auf der Heide, H. Rohnert, R E. Tarjan. Dynamic perfect hashing: Upper and lower bounds. In Proc. of the 29th IEEE Ann. Symp. on Foundations of Computer Science, pp. 524–531, 1988. (Revised Version to appear in SIAM J. Comput.)

    Google Scholar 

  11. M. Dietzfelbinger and F. Meyer auf der Heide. How to distribute a dictionary in a complete network. In Proc. of the 22nd Ann. ACM Symp. on Theory of Computing, pp. 117–127, 1990.

    Google Scholar 

  12. M. Dietzfelbinger and F. Meyer auf der Heide. A new universal class of hash functions and dynamic hashing in real time. In M. S. Paterson, editor, Proceedings of 17th ICALP, LNCS 443, pp. 6–19, Springer, 1990. Revised Version in J. Buchmann, H. Ganzinger, and W. J. Paul, Eds., Informatik — Festschrift zum 60. Geburtstag von Günter Hotz, pp. 95–119, Teubner Verlag, 1992.

    Google Scholar 

  13. M. Dietzfelbinger and F. Meyer auf der Heide. Simple, efficient shared memory simulations. To appear in Proc. of the 5th Ann. ACM Symp. on Parallel Algorithms and Architectures, 1993.

    Google Scholar 

  14. C. Engelmann and J. Keller. Comparison of hash functions for emulated shared memory. Manuscript, 1992.

    Google Scholar 

  15. F. Fich, P. Ragde, and A. Wigderson. Simulations among concurrent-write models of parallel computation. Algorithmica, 3:43–51, 1988.

    Article  Google Scholar 

  16. M. Geréb-Graus and T. Tsantilas. Efficient optical communication in parallel computers. In Proc. of the 4th Ann. ACM Symp. on Parallel Algorithms and Architectures, pp. 41–48, 1992.

    Google Scholar 

  17. J. Gil, Y. Matias, and U. Vishkin. Towards a theory of nearly constant time parallel algorithms. In Proc. of the 32nd IEEE Ann. Symp. on Foundations of Computer Science, pp. 698–710, 1991.

    Google Scholar 

  18. G. H. Gonnet. Expected length of the longest probe sequence in hash code searching. J. Assoc. Comput. Mach., 28:289–304, 1981.

    Google Scholar 

  19. T. Hagerup. The log-star revolution. In Proc. 9th STACS, LNCS 577, pp. 259–280, Springer, 1992.

    Google Scholar 

  20. T. Hagerup. Fast and optimal simulations between CRCW PRAMs. In Proc. 9th STACS, LNCS 577, pp. 46–56, Springer, 1992.

    Google Scholar 

  21. Y. Han. An optimal linked list prefix algorithm on a local memory computer. IEEE Trans. on Computers, 40:1149–1153, 1991.

    Article  Google Scholar 

  22. A. Karlin and E. Upfal. Parallel hashing — an efficient implementation of shared memory. In Proc. of the 18th Ann. ACM Symp. on Theory of Computing, pp. 160–168, 1986.

    Google Scholar 

  23. R. Karp, M. Luby, 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.

    Google Scholar 

  24. R. M. Karp and V. Ramachandran. Parallel algorithms for shared-memory machines. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, Vol. A: Algorithms and Complexity, chapter 17, pp. 869–941. Elsevier, Amsterdam, 1990.

    Google Scholar 

  25. C. P. Kruskal, T. Madej, and L. Rudolph, Parallel prefix on fully connected direct connection machines. In Proc. Int. Conf. on Parallel Processing, pp. 278–283, 1986.

    Google Scholar 

  26. C. P. Kruskal, L. Rudolph, and M. Snir. A complexity theory of efficient parallel algorithms. Theoret. Comput. Sci., 71:95–132, 1990.

    Article  Google Scholar 

  27. F. T. Leighton. Introduction to parallel algorithms and architectures: arrays, trees, hypercubes. Morgan Kaufmann Publishers, San Mateo, 1992.

    Google Scholar 

  28. F. T. Leighton. Methods for packet routing in parallel machines. In Proc. of the 24th Ann. ACM Symp. on Theory of Computing, pp. 77–96, 1992.

    Google Scholar 

  29. Y. Matias and U. Vishkin. Converting high probability into nearly-constant time — with applications to parallel hashing. In Proc. of the 23rd Ann. ACM Symp. on Theory of Computing, pp. 307–316, 1991.

    Google Scholar 

  30. K. Mehlhorn and U. Vishkin. Randomized and deterministic simulations of PRAMs by parallel machines with restricted granularity of parallel memories. Acta Informatica, 21:339–374, 1984.

    Article  Google Scholar 

  31. F. Meyer auf der Heide. Hashing strategies for simulating shared memory on distributed memory machines. In Proc. of the 1st Heinz Nixdorf Symposium “Parallel Algorithms and their Efficient Use”, Paderborn, Germany, November 1992, LNCS, Springer Verlag, to appear.

    Google Scholar 

  32. A. G. Ranade. How to emulate shared memory. J. Comput. Syst. Sci., 42:307–326, 1991.

    MathSciNet  Google Scholar 

  33. A. G. Ranade, S. N. Bhatt, and S. L. Johnsson. The fluent abstract machine. In Proc. of the 5th MIT Conference on Advanced Research in VLSI. pp. 71–93, 1988.

    Google Scholar 

  34. 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. Revised Version.

    Google Scholar 

  35. E. Upfal. Efficient schemes for parallel communication. J. Assoc. Comput. Mach., 31(3):507–517, 1984.

    MathSciNet  Google Scholar 

  36. L. G. Valiant. General purpose parallel architectures. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, Vol. A: Algorithms and Complexity, chapter 18, pp. 943–971. Elsevier, Amsterdam, 1990.

    Google Scholar 

  37. L. Valiant. A bridging model for parallel computation. Communications of the ACM, 33(8), pp. 103–111, 1990.

    Article  Google Scholar 

  38. L. G. Valiant. A combining mechanism for parallel computers. Technical Report TR-24-92, Aiken Computation Laboratory, Harvard University, 1992.

    Google Scholar 

  39. E. Upfal, A. Wigderson. How to share memory in a distributed system. J. Assoc. Comput. Mach., 34:116–127, 1987.

    Google Scholar 

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Authors and Affiliations

  1. Fachbereich Informatik, Lehrstuhl II, Universität Dortmund, 44221, Dortmund, Germany

    Martin Dietzfelbinger

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  1. Martin Dietzfelbinger
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Zoltán Ésik

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© 1993 Springer-Verlag Berlin Heidelberg

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Dietzfelbinger, M. (1993). Simulations between different models of parallel computers. In: Ésik, Z. (eds) Fundamentals of Computation Theory. FCT 1993. Lecture Notes in Computer Science, vol 710. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57163-9_2

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  • DOI: https://doi.org/10.1007/3-540-57163-9_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57163-6

  • Online ISBN: 978-3-540-47923-9

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