Advertisement

Parallel implementation of the algebraic path problem

  • Yves Robert
  • Denis Trystram
Nonnumerical Algorithms (Session 2.2)
Part of the Lecture Notes in Computer Science book series (LNCS, volume 237)

Abstract

The Algebraic Path Problem is a general framework which unifies several algorithms arising from various fields of computer science. Rote [11] introduces a general algorithm to solve any instance of the APP, as well as a hexagonal systolic array of (n+1)2 elementary processors which can solve the problem in 7n-2 time steps. We propose a new algorithm to solve the APP, and demonstrate its equivalence with Rote's algorithm. The new algorithm is more suitable to parallelization: we propose an orthogonal systolic array of n(n+1) processors which solves the APP within only 5n-2 steps. Finally, we give some experiments on the implementation of our new algorithm in the parallel environment developped by IBM at ECSEC in Roma.

Keywords

Virtual Machine Shared Memory Transitive Closure Matrix Inversion Systolic Array 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    E. CLEMENTI, Progress report on our experimentation with parallel supercomputers ICAP1 and ICAP2, Conf. "Le Calcul ... Demain", P. Chenin et al. eds, Masson 1985Google Scholar
  2. [2]
    P. DI CHIO, V. ZECCA, IBM ECSEC facilities: user's guide, IBM ECSEC Report, Roma 1985Google Scholar
  3. [3]
    L.J. GUIBAS, H.T. KUNG, C.D. THOMPSON, Direct VLSI implementation of combinatorial algorithms, Proc. Caltech Conf. on VLSI, California Inst. Technology, Pasadena 1979, 509–525Google Scholar
  4. [4]
    K. HWANG et F. BRIGGS, Parallel processing and computer architecture, Mc Graw Hill, 1984Google Scholar
  5. [5]
    H.T. KUNG, Why systolic architectures, Computer 15, 1 (1982), 37–46Google Scholar
  6. [6]
    H.T. KUNG, C.E. LEISERSON, Systolic arrays for (VLSI), Proc. of the Symposium on Sparse Matrices Computations, I.S. Duff and G.W. Stewart eds, Knoxville, Tenn. (1978), 256–282Google Scholar
  7. [7]
    R.E. LORD, J.S. KOWALIK, S.P. KUMAR, Solving linear algebraic equations on an MIMD computer, J. ACM 30 (1), (1983), p 103–117CrossRefGoogle Scholar
  8. [8]
    J.G. NASH, S. HANSEN, G.R. NUDD, VLSI processor arrays for matrix manipulation, VLSI Systems & Computations, H.T.Kung et al. eds, Computer Science Press (1981), 367–378Google Scholar
  9. [9]
    Y. ROBERT, Block LU decomposition of a band matrix on a systolic array, Int. J. Computer Math. 17 (1985), 295–315Google Scholar
  10. [10]
    Y. ROBERT, D. TRYSTRAM, Un réseau systolique pour le problème du chemin algébrique, C.R.A.S. Paris 302, I, 6 (1986), 241–244Google Scholar
  11. [11]
    G. ROTE, A systolic array algorithm for the algebraic path problem (shortest paths; matrix inversion), Computing 34 (1985), 191–219Google Scholar
  12. [12]
    U. SCHENDEL, Introduction to numerical methods for parallel computers, E. Horwood 1984Google Scholar
  13. [13]
    J.M. STONE, V.A. NORTON, F.D. ROGERS, E.A. MELTON, G.F. PFISTER, The VM/EPEX FORTRAN preprocessor reference, IBM Report, Yorktown Heights, NY, USA (1985)Google Scholar
  14. [14]
    U. ZIMMERMANN, Linear and combinatorial optimization in ordered algebraic structures, Ann. Discrete Math. 10, 1 (1981), 1–380Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Yves Robert
    • 1
  • Denis Trystram
    • 2
  1. 1.CNRS, Laboratoire TIM3St Martin d'Hères CedexFrance
  2. 2.Ecole Centrale ParisChatenay Malabry CedexFrance

Personalised recommendations