BIT Numerical Mathematics

, Volume 24, Issue 3, pp 333–340 | Cite as

Graph algorithms on a tree-structured parallel computer

  • D. Y. Yeh
  • D. T. Lee
Part I Computer Science

Abstract

Parallel algorithms for some graph-theoretic problems on a tree-structured computer are presented. In particular, ifp denotes the number of processing elements, algorithms that run inO(n2/p) time for finding connected components, transitive closure and the minimum spanning tree of an undirected graph withn vertices are obtained.

Keywords

SIMD computer systolic computer parallel algorithm graph algorithm time complexity 

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References

  1. 1.
    M. J. Atallah and S. R. Kosaraju,Graph problems on a meshed-connected processor array, Proc. 14th Annual ACM Symposium on Theory of Computing, May 1982, pp. 345–353.Google Scholar
  2. 2.
    J. L. Bently and H. T. Kung,A tree machine for searching problems, Proc. 1979 International Conf. on Parallel Processing, Aug. 1979, pp. 257–266.Google Scholar
  3. 3.
    J. L. Bently,A parallel algorithm for constructing minimum spanning trees, J. Algorithm, Vol. 1, 1980, pp. 51–59.Google Scholar
  4. 4.
    F. Y. Chin, J. Lam and I. N. Chen,Efficient parallel algorithms for some graph problems, Comm. ACM, Vol. 25, No. 9, 1982, pp. 659–665.Google Scholar
  5. 5.
    E. Dekel, D. Nassimi and S. Sahni,Parallel matrix and graph algorithms, SIAM J. Computing, Vol. 10, No. 4, 1981, pp. 657–675.Google Scholar
  6. 6.
    D. S. Hirschberg, A. K. Chandra and P. V. Sarwate,Computing connected components on parallel computers, Comm. ACM, Vol. 22, No. 8, 1979, pp. 461–464.Google Scholar
  7. 7.
    H. T. Kung,The structure of parallel algorithms, Advances in Computers, Vol. 19, Academic Press.Google Scholar
  8. 8.
    D. Nassimi and S. Sahni,Finding connected components and connected ones on a meshed-connected parallel computer, SIAM J. Comput., Vol. 9, No. 4, 1980, pp. 744–751.Google Scholar
  9. 9.
    D. Nath and S. N. Maheshwari,Parallel algorithms for the connected and minimal spanning tree problems, Inform. Proc. Lett., Vol. 14, (1982), pp. 7–11.Google Scholar
  10. 10).
    E. M. Reingold, J. Nievergelt and N. Deo,Combinatorial Algorithms: Theory and Practice, Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1977.Google Scholar
  11. 11.
    C. Savage and J. Ja' Ja',Fast, efficient parallel algorithms for some graph problems, SIAM J. Comput., Vol. 10, No. 4, 1981, pp. 682–691.Google Scholar

Copyright information

© BIT Foundations 1984

Authors and Affiliations

  • D. Y. Yeh
    • 1
    • 2
  • D. T. Lee
    • 1
    • 2
  1. 1.Department of Computer and Information ScienceCleveland State UniversityClevelandUSA
  2. 2.Department of Electrical Engineering and Computer ScienceNorthwestern UniversityEvanstonUSA

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