Skip to main content

Advertisement

Springer Nature Link
Log in

K-Dimensional Optimal Parallel Algorithm for the solution of a general class of recurrence equations

  • Regular Papers
  • Published:
Journal of Computer Science and Technology Aims and scope Submit manuscript

Abstract

This paper proposes a parallel algorithm, called KDOP (K-Dimensional Optimal Parallel algorithm), to solve a general class of recurrence equations efficiently. The KDOP algorithm partitions the computation into a series of subcomputations, each of which is executed in the fashion that all the processors work simultaneously with each one executing an optimal sequential algorithm to solve a subcomputation task. The algorithm solves the equations inO(N/p) steps in EREW PRAM model (Exculsive Read Exclusive Write Parallel Random Access Machine model) usingp≤N 1-∈ processors, whereN is the size of the problem, and ∈ is a given constant. This is an optimal algorithm (its speedup isO(p)) in the case ofp≤N 1-∈. Such an optimal speedup for this problem was previously achieved only in the case ofp≤N 0.5. The algorithm can be implemented on machines with multiple processing elements or pipelined vector machines with parallel memory systems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Kogge P M, Stone H S. A parallel algorithm for the efficient solution of a general class of recurrence equations.IEEE Trans. on Computers, 1973, C-22(8): 786–792.

    Article  MATH  MathSciNet  Google Scholar 

  2. Kogge P M. Parallel solution of recurrence problems.IBM J. Res. Develop., 1974, 18: 138–148.

    Article  MATH  MathSciNet  Google Scholar 

  3. Gao Qingshi. Another parallel algorithm for the efficient solution of a class of recursive computation.Computer Application and Applied Mathematics, 1974, 1(8).

  4. Chen S C, Kuck D J. Time and parallel processor bounds for linear recurrence systems.IEEE Trans. on Computers, 1975, C-24(7).

  5. Kuck D J. Parallel processing of ordinary programs. InAdvances in Computers, Vol. 15. Academic Press, New York, 1976, pp.119–179.

    Google Scholar 

  6. Sameh A H, Brent R P. Solving triangular systems on a parallel computer.SIAM J. Numerical Analysis, 1977, 14(6): 1101–1113.

    Article  MATH  MathSciNet  Google Scholar 

  7. Chen S C, Kuck D J, Sameh A H. Practical parallel band triangular system solvers.ACM Trans. Math. Software, 1978, 4(3): 270–277.

    Article  MATH  MathSciNet  Google Scholar 

  8. Gajski D D. An algorithm for solving linear recurrence systems on parallel and pipelined machines.IEEE Trans. on Computers, 1981, C-30(3): 190–206.

    Article  MATH  MathSciNet  Google Scholar 

  9. Gao Qingshi. Super Vector Computer. Science Press, Beijing, China, 1984, pp.153–165.

    Google Scholar 

  10. Carlson D A, Sugla B. Time and processor efficient parallel algorithms for recurrence equations and related problems. InProc. 1984Int’l Conf. Parallel Processing, San Charles, U.S.A., Aug. 1984, pp.310–314.

  11. Kruskal C P, Rudolph L, Snir M. The power of parallel prefix.IEEE Trans. on Computers, 1985, C-34(10): 965–968.

    Google Scholar 

  12. Snir M. Depth-size trade-offs for parallel prefix computation.Journal of Algorithms, 1986, 7: 185–201.

    Article  MATH  MathSciNet  Google Scholar 

  13. Meyer G G L, Podrazik L J. A parallel first-order linear recurrence solver.Journal of Parallel and Distributed Computing, 1987, 4: 117–132.

    Article  Google Scholar 

  14. Gao Qingshi. The Chinese remainder theorem and the prime memory system. InProc. of the 20th Int’l Symp. Computer Architecture, San Diego, U.S.A., 1993.

  15. Jaja J. An Introduction to Parallel Algorithms. Addison-Wesley Publishing Company, Reading, Massachusetts, U.S.A., 1992.

    MATH  Google Scholar 

  16. Hwang K, Briggs F A. Computer Architecture and Parallel Processing. McGraw-Hill Book Company, New York, U.S.A., 1987.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The Institute of Intelligence, Language and Computer Science, Beijing University of Science and Technology, 100083, Beijing

    Gao Qingshi

  2. Institute of Computing Technology, The Chinese Academy of Sciences, 100080, Beijing

    Liu Zhiyong

Authors
  1. Gao Qingshi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Liu Zhiyong
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Project supported in part by the High Tech Research and Development Programme of China

For the biography ofGao Qingshi, please see p.475 of this issue

For the biography ofLiu Zhiyong, please see p.309 of Vol.10, No.4

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gao, Q., Liu, Z. K-Dimensional Optimal Parallel Algorithm for the solution of a general class of recurrence equations. J. of Comput. Sci. & Technol. 10, 417–424 (1995). https://doi.org/10.1007/BF02948337

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02948337

Keywords

Search

Navigation