Advertisement

Introduction to the Complexity of Parallel Algorithms

  • Michel Cosnard
Part of the Applied Optimization book series (APOP, volume 67)

Abstract

We present an introduction to the general theory of complexity of parallel algorithms. We first recall the main results of sequential complexity, then introduce models for parallel computation and compare them to sequential models. We show that some of these models are not reasonable and explain the parallel computation thesis for reasonable models. Finally we study the PRAM model and give basic complexity results for parallel algorithms.

Keywords

Complexity parallel algorithms PRAM 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    G.M. Amdahl, Validity of a single processor approach of achieving large scale computing capabilities. AFIPS Conf. Proc. 30, 483–485, 1967.Google Scholar
  2. [2]
    J.L. Balcazar, J. Diaz and J. Gabarro, Structural Complexity 1. Springer 1995.zbMATHCrossRefGoogle Scholar
  3. [3]
    R.P. Brent, The parallel evaluation of general arithmetic expressions. Journal of ACM, 21(2):201 206, 1974.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    S. Cook, The complexity of theorem proving procedures. 3rd. ACM Symp. on Theory of Computing, 151–158, 1971.Google Scholar
  5. [5]
    M. Cosnard and A. Ferreira, On the real power of loosely coupled parallel architectures. Parallel Processing Letters 1(2):103–112, 1991.MathSciNetCrossRefGoogle Scholar
  6. [6]
    M. Cosnard and D. Trystram, Parallel Algorithms and Architectures. Thomson Computer Press, 1995.Google Scholar
  7. [7]
    M.R. Garey and D.S. Johnson, Computers and Intractability — A guide to the theory of NP-completeness. Freeman and Co. 1979.zbMATHGoogle Scholar
  8. [8]
    A. Gibbons and W. Rytter, Eficient parallel algorithms. Cambridge University Press, 1988.Google Scholar
  9. [9]
    J.L. Gustafson, Reevaluating Amdahl’s law. Communications of ACM 31,5:532–533, 1988.CrossRefGoogle Scholar
  10. [10]
    R.M. Karp, Reducibility among combinatorial problems. in Complexity of Computer Computations (R. Miller and J. Thatcher eds.), 85–104, Plenum Press New York, 1972.CrossRefGoogle Scholar
  11. [11]
    I. Munro and M. Paterson, Optimal algorithms for parallel polynomial evaluation. Journal Comput. System Sci. 189–198, 1973.Google Scholar
  12. [12]
    D. Nassimi and S. Sahni, Data broadcasting in SIMD computers. IEEE Transactions on Computers, 30:101–106, 1981.MathSciNetCrossRefGoogle Scholar
  13. [13]
    N. Pippenger, On simultaneous resource bounds. 20th. IEEE Symp. on Foundations of Computer Science, 307–311, 1979.Google Scholar
  14. [14]
    W.J. Savitch, Relationships between nondeterministic and deterministic tape complexities. Journal Comput. System Sci., 4:177–192, 1970.MathSciNetzbMATHCrossRefGoogle Scholar
  15. [15]
    M.J. Serna, The parallel approximability of P-complete problems. PhD Thesis, Universitat Politechnica de Catalunya, 1990.Google Scholar
  16. [16]
    M. Snir, On parallel searching. SIAM Journal of Computing, 14(3):688–708, 1985.MathSciNetzbMATHCrossRefGoogle Scholar
  17. [17]
    U. Vishkin, Implementation of simultaneaous memory address access in models that forbids it. Journal of Algorithms, 4:45–50, 1983.MathSciNetzbMATHCrossRefGoogle Scholar
  18. [18]
    H. Vollmer, The gap-language-technique revisited. Proc. Computer Science and Logic 91, LNCS, Springer-Verlag, 1991.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Michel Cosnard
    • 1
  1. 1.LORIA - INRIAVillers Les NancyFrance

Personalised recommendations