All-Pairs Shortest Paths Computation in the BSP Model

  • Alexandre Tiskin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2076)

Abstract

The model of bulk-synchronous parallel (BSP) computation is an emerging paradigm of general-purpose parallel computing. We propose a new p-processor BSP algorithm for the all-pairs shortest paths problem in a weighted directed dense graph. In contrast with the general algebraic path algorithm, which performs O(p1/2) to O(p2/3) global synchronisation steps, our new algorithm only requires O(log p) synchronisation steps.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    A. Aggarwal, A. K. Chandra, and M. Snir. Communication complexity of PRAMs. Theoretical Computer Science, 71(1):3–28, March 1990.MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    N. Alon, Z. Galil, and O. Margalit. On the exponent of the all pairs shortest path problem. Journal of Computer and System Sciences, 54(2):255–262, April 1997.MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    B. Carré. Graphs and Networks. Oxford Applied Mathematics and Computer Science Series. Clarendon Press, 1979.Google Scholar
  4. [4]
    D. Coppersmith and S. Winograd. Matrix multiplication via arithmetic progressions. Journal of Symbolic Computation, 9(3):251–280, March 1990.MATHMathSciNetCrossRefGoogle Scholar
  5. [5]
    T. H. Cormen, C. E. Leiserson, and R. L. Rivest. Introduction to Algorithms. The MIT Electrical Engineering and Computer Science Series. The MIT Press and McGraw-Hill, 1990.Google Scholar
  6. [6]
    E. W. Dijkstra. A note on two problems in connection with graphs. Numerische Mathematik, 1:269–271, 1959.MATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    I. Foster. Designing and Building Parallel Programs. Addison-Wesley, 1995.Google Scholar
  8. [8]
    M. Gondran and M. Minoux. Graphs and Algorithms. Wiley—Interscience Series in Discrete Mathematics. John Wiley & Sons, 1984.Google Scholar
  9. [9]
    M. Gondran and M. Minoux. Linear algebra in dioids: A survey of recent results. Annals of Discrete Mathematics, 19:147–164, 1984.MathSciNetGoogle Scholar
  10. [10]
    D. B. Johnson. Efficient algorithms for shortest paths in sparse networks. Journal of the ACM, 24(1):1–13, January 1977.MATHCrossRefGoogle Scholar
  11. [11]
    W. F. McColl. Scalable computing. In J. van Leeuwen, editor, Computer Science Today: Recent Trends and Developments, volume 1000 of Lecture Notes in Computer Science, pages 46–61. Springer-Verlag, 1995.Google Scholar
  12. [12]
    W. F. McColl. A BSP realisation of Strassen’s algorithm. In M. Kara, J. R. Davy, D. Goodeve, and J. Nash, editors, Abstract Machine Models for Parallel and Distributed Computing, pages 43–46. IOS Press, 1996.Google Scholar
  13. [13]
    W. F. McColl. Universal computing. In L. Bougé et al., editors, Proceedings of Euro-Par’ 96 (Part I), volume 1123 of Lecture Notes in Computer Science, pages 25–36. Springer-Verlag, 1996.Google Scholar
  14. [14]
    G. Rote. Path problems in graphs. Computing Supplementum, 7:155–189, 1990.MathSciNetGoogle Scholar
  15. [15]
    T. Takaoka. Subcubic cost algorithms for the all pairs shortest path problem. Algorithmica, 20:309–318, 1998.MATHCrossRefMathSciNetGoogle Scholar
  16. [16]
    A. Tiskin. The bulk-synchronous parallel random access machine. Theoretical Computer Science, 196(1-2):109–130, April 1998.MATHCrossRefMathSciNetGoogle Scholar
  17. [17]
    A. Tiskin. Bulk-synchronous parallel Gaussian elimination. In N. N. Vasil’ev and A. M. Vershik, editors, Representation Theory, Dynamical Systems, Combinatorial and Algorithmic Methods (Part 4), volume 258 of Zapiski Nauchnykh Seminarov POMI. Russian Academy of Sciences, 1999. Also to appear in Journal of Mathematical Sciences.Google Scholar
  18. [18]
    L. G. Valiant. A bridging model for parallel computation. Communications of the ACM, 33(8):103–111, August 1990.CrossRefGoogle Scholar
  19. [19]
    U. Zimmermann. Linear and Combinatorial Optimization in Ordered Algebraic Structures, volume 10 of Annals of Discrete Mathematics. North-Holland, 1981.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Alexandre Tiskin

There are no affiliations available

Personalised recommendations