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The complexity of deterministic PRAM simulation on distributed memory machines

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Abstract

In this paper we present lower and upper bounds for the deterministic simulation of a Parallel Random Access Machine (PRAM) withn processors andm variables on a Distributed Memory Machine (DMM) withp ≤n processors. The bounds are expressed as a function of the redundancyr of the scheme (i.e., the number of copies used to represent each PRAM variable in the DMM), and become tight for anym polynomial inn andr=Θ(1).

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References

  1. H. Alt, T. Hagerup, K. Mehlhorn, and F. P. Preparata. Deterministic simulation of idealized parallel computers on more realistic ones.SIAM Journal on Computing, 16(5):808–835, 1987.

    Article  MathSciNet  MATH  Google Scholar 

  2. G. Baudet and D. Stevenson. Optimal sorting algorithms for parallel computers.IEEE Transactions on Computers, 27(1):84–87, January 1978.

    Article  MathSciNet  MATH  Google Scholar 

  3. A. Czumaj, F. Meyer auf der Heide, and V. Stemann. Shared memory simulations with triple-logarithmic delay.Proceedings of the 3rd European Symposium on Algorithms, Corfu, September 1995. LNCS, volume 979, pages 46–59, 1995.

  4. K.T. Herley. Representing shared data on distributed-memory parallel computers.Mathematical Systems Theory, 29:111–156, 1996.

    MathSciNet  MATH  Google Scholar 

  5. K. Herley and G. Bilardi. Deterministic simulations of PRAMs on bounded-degree networks.SIAM Journal on Computing, 23(2):276–292, April 1994.

    Article  MathSciNet  MATH  Google Scholar 

  6. K. Herley, A. Pietracaprina, and G. Pucci. Implementing shared memory on multi-dimensional meshes and on the fat-tree.Proceedings of the 3rd European Symposium on Algorithms, Corfu, September 1995. LNCS, volume 979, pages 60–74, 1995.

  7. A.R. Karlin and E. Upfal. Parallel hashing: An efficient implementation of shared memory.Journal of the ACM, 35(4):876–892, October 1988.

    Article  MathSciNet  MATH  Google Scholar 

  8. F. T. Leighton. Tight bounds on the complexity of parallel sorting.IEEE Transactions on Computers, 34(4):344–354, April 1985.

    Article  MathSciNet  MATH  Google Scholar 

  9. F. Luccio, A. Pietracaprina, and G. Pucci. A new scheme for the deterministic simulation of PRAMs in VLSI.Algorithmica, 5(4):529–544, 1990.

    Article  MathSciNet  MATH  Google Scholar 

  10. 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  MathSciNet  MATH  Google Scholar 

  11. D. Peleg and E. Upfal. The token distribution problem.SIAM Journal on Computing, 18(2):229–243, April 1989.

    Article  MathSciNet  MATH  Google Scholar 

  12. A. Pietracaprina and F. P. Preparata. AnO(√n)-worst-case-time solution to the granularity problem.Proceedings of the 10th Symposium on Theoretical Aspects of Computer Science, Würzburg, February 1993. LNCS, volume 665, pages 110–119.

  13. A. Pietracaprina and F. P. Preparata. A practical constructive scheme for deterministic shared-memory access.Proceedings of the 5th ACM Symposium on Parallel Algorithms and Architectures, Velen, July 1993, pages 100–109.

  14. A. Pietracaprina and G. Pucci. Tight bounds on deterministic PRAM emulations with constant redundancy.Proceedings of the 2nd European Symposium on Algorithms, Papendal, September 1994. LNCS, volume 855, pages 391–400.

  15. A. Pietracaprina and G. Pucci. Improved deterministic PRAM simulation on the mesh.Proceedings of the 22nd International Colloquium on Automata, Languages and Programming, Szeged, July 1995. LNCS, volume 944, pages 372–383.

  16. A. Pietracaprina, G. Pucci, and J. Sibeyn. Constructive deterministic PRAM simulation on a mesh-connected computer.Proceedings of the 6th ACM Symposium on Parallel Algorithms and Architectures, Cape May, NJ, June 1994, pages 248–256.

  17. E. Upfal and A. Wigderson. How to share memory in a distributed system.Journal of the ACM, 34(1):116–127, 1987.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Matematica Pura e Applicata, Università di Padova, 135131, Padova, Italy

    A. Pietracaprina

  2. Dipartimento di Elettronica e Informatica, Università di Padova, 135131, Padova, Italy

    G. Pucci

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  1. A. Pietracaprina
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  2. G. Pucci
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Additional information

A preliminary version of this work was presented at the 2nd European Symposium on Algorithms, Papendal, September 1994 [14]. This research was supported in part by MURST of Italy and by the ESPRIT III Basic Research Programme of the EC under Contract No. 9072 (Project GEPPCOM).

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Pietracaprina, A., Pucci, G. The complexity of deterministic PRAM simulation on distributed memory machines. Theory of Computing Systems 30, 231–247 (1997). https://doi.org/10.1007/BF02679461

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