Advertisement

Systolic algorithms for path-finding problems

  • Yves Robert
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 316)

Abstract

This paper deals with systolic algorithms for some path-finding problems. First we present the Guibas-Kung-Thompson systolic array for computing the reflexive and transitive closure of a binary relation. Then we introduce a more general class of all-pairs shortest paths problems in complete semi-rings which can not be solved using the previous array. We introduce the well-known Gauss-Jordan algorithm to solve this general class of problems, and we show how to map it onto a systolic array whose performances overcome those of all the systolic arrays previously introduced in the literature.

Keywords

Cellular Automaton Transitive Closure Short Path Problem Systolic Array Boolean Matrix 
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]
    AHMED H.M., DELOSME J.M., MORF M., Highly concurrent computing structures for matrix arithmetic and signal processing, Computer 15 (1982), 65–82Google Scholar
  2. [2]
    ATRUBIN A.J., A one-dimensional real time iterative multiplier, IEEE Trans. Computers 14, 6 (1965), 394–399Google Scholar
  3. [3]
    CODD E.F., Cellular Automata, Academic Press, 1968Google Scholar
  4. [4]
    COLE S.N., Real-time computation by n-dimensional iterative arrays of finite-state machines, IEEE Trans. Computers 18, 4 (1969), 349–365Google Scholar
  5. [5]
    GUIBAS L.J., KUNG H.T., THOMPSON C.D., Direct VLSI implementation of combinatorial algorithms, Proc. Caltech Conference on VLSI, California Inst. of Technology, Pasadena (1979), 509–525Google Scholar
  6. [6]
    HELLER D., Partitioning big matrices for small systolic arrays, in VLSI and Modern Signal Processing, S. Y. Kung et al. eds, Prentice Hall, Englewood Cliffs, NJ (1985), 185–199Google Scholar
  7. [7]
    HENNIE, Iterative arrays of logical circuits, MIT Press, Cambridge MA, U.S.A. 1961Google Scholar
  8. [8]
    HWANG K., CHENG Y.H., Partitioned matrix algorithm for VLSI arithmetic systems, IEEE Trans. Computers 31 (1982), 1215–1224Google Scholar
  9. [9]
    KRAMER M.R., VAN LEEUWEN J., Systolic computation and VLSI, Foundations of Computer Science IV, J.W. DeBakker et aJ. Van Leeeuwen eds (1983), 75–103Google Scholar
  10. [10]
    KUNG H.T., Why systolic architectures, Computer 15, 1 (1982), 37–46Google Scholar
  11. [11]
    KUNG H.T, LAM M.S. 1984 Fault-tolerance and two-level pipelining in VLSI systolic arrays, Journal of Parallel and Distributed Computing 1, 32–63Google Scholar
  12. [12]
    KUNG H.T, LEISERSON C.E., Systolic arrays (for VLSI), Proc. of the Symposium on Sparse Matrices Computations, I.S. Duff and G.W. Stewart eds, Knoxville (1978), 256–282Google Scholar
  13. [13]
    KUNG S.Y., On supercomputing with systolic/wavefront array processors, Proceedings of the IEEE 72 (1984), 867–884Google Scholar
  14. [14]
    KUNG S.Y., VLSI array processors, IEEE ASSP Magazine 2, 3 (1985), 4–22Google Scholar
  15. [15]
    KUNG S.Y., LO S.C., A spirial systolic architecture/algorithm for transitive closure problems, IEEE Int. Conf. on Computer Design ICCD'85, New-York, USA (1985), 622–626Google Scholar
  16. [16]
    MOLLER F., A survey of systolic systems for solving the Algebraic Path Problem, Report CS-85-22 (1985), Univ. of Waterloo, CanadaGoogle Scholar
  17. [17]
    MORAGA C., Systolic Algorithms, Technical Report, Computer Science department (1984), University of Dortmund, F.R.G.Google Scholar
  18. [18]
    NASH J.G., HANSEN S., Modified Faddeev algorithm for matrix manipulation, Proc. 1984 SPIE Conf., San Diego, CA, USA, August 1984Google Scholar
  19. [19]
    ROBERT Y., Block LU decomposition of a band matrix on a systolic array, Int. J. Computer Math 17 (1985), 295–315Google Scholar
  20. [20]
    ROBERT Y., TCHUENTE M., Résolution systolique de systèmes linéaires denses, RAIRO Modélisation et Analyse Numérique 19 (1985), 315–326Google Scholar
  21. [21]
    ROBERT Y., TRYSTRAM D., Un réseau systolique orthogonal pour le problème du chemin algébrique, C.R.A.S. Paris, 302 I (1986), 241–244MathSciNetGoogle Scholar
  22. [22]
    ROTE G., A systolic array algorithm for the algebraic path problem (shortest paths; matrix inversion), Computing 34 (1985), 191–219Google Scholar
  23. [23]
    ULLMAN J.D., Computational aspects of VLSI, Chapter 5: Systolic algorithms, Computer Science Press, Rockville, Maryland, USA, 1984Google Scholar
  24. [24]
    VON NEUMANN, Theory of self-reproducing automata, University of Illinois Press, Urbana IL, U.S.A, 1966Google Scholar
  25. [25]
    WARSHALL S., A theorem on boolean matrices, J.A.C.M. 9, 1 (1972), 11–12Google Scholar
  26. [26]
    ZIMMERMANN U., Linear and combinatorial optimization in ordered algebraic structures, Ann. Discrete Math. 10 (1981), 1–380Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Yves Robert
    • 1
  1. 1.CNRS, Laboratoire TIM3Institut National Polytechnique de GrenobleSt Martin d'HèresFrance

Personalised recommendations