Skip to main content
SpringerLink
Log in

A randomized linear work EREW PRAM algorithm to find a minimum spanning forest

  • Session 5A
  • Conference paper
  • First Online:
Algorithms and Computation (ISAAC 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1350))

Included in the following conference series:

Abstract

We present a randomized EREW PRAM algorithm to find a minimum spanning forest in a weighted undirected graph. On an n-vertex graph the algorithm runs in o((log n)1+ ε)) expected time for any ε > 0 and performs linear expected work. This is the first linear work, polylog time algorithm on the EREW PRAM for this problem. This also gives parallel algorithms that perform expected linear work on two more realistic models of parallel computation, the QSM and the BSP.

This research was supported in part by NSF grant CCR/GER-90-23059 and Texas Advanced Research Program Grant 003658386.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. O. Boruvka.O jistem problemu minimalnim. Praca Moravske Prirodovedecke Spolecnosti, 3:37–58, 1926. In Czech.

    Google Scholar 

  2. K. W. Chong. Finding minimum spanning trees on the EREW PRAM. In Proceedings of the 1996 International Conference on Algorithms, pages 7–14, Taiwan, 1996.

    Google Scholar 

  3. R. Cole, P.N. Klein, and R.E. Tarjan. A linear-work parallel algorithm for finding minimum spanning trees. In Proceedings of the 1994 ACM Symposium on Parallel Algorithms and Architectures, pages 11–15, 1994.

    Google Scholar 

  4. R. Cole, P.N. Klein, and R.E. Tarjan. Finding minimum spanning trees in logarithmic time and linear work using random sampling. In Proceedings of the 1996 ACM Symposium on Parallel Algorithms and Architectures, pages 213–219, 1996.

    Google Scholar 

  5. T.H. Cormen, C.E. Leiserson, and R.L. Rivest. Introduction to Algorithms. MIT Press, 1991.

    Google Scholar 

  6. F. Dehne and S. Gotz. Efficient parallel minimum spanning algorithms for coarse grained multicomputers and BSP, June 1997. Manuscript, Carleton University, Ottawa, Canada.

    Google Scholar 

  7. W. Dittrich, B. Juurlink, and I. Rieping, June 1997. Private communication by Ingo Rieping.

    Google Scholar 

  8. P.B. Gibbons, Y. Matias, and V. Ramachandran. The QRQW PRAM: Accounting for contention in parallel algorithms. In Proceedings of the Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 638–648, 1994.

    Google Scholar 

  9. P. B. Gibbons, Y. Matias, and V. Ramachandran. Can a shared-memory model serve as a bridging model for parallel computation? In Proceedings of the 1997 ACM Symposium on Parallel Algorithms and Architectures, pages 72–83, 1997.

    Google Scholar 

  10. S. Halperin and U. Zwick. Optimal randomized EREW PRAM algorithms for finding spanning forests and for other basic graph connectivity problems. In Proceedings of the Seventh ACM-SIAM Symposium on Discrete Algorithms, pages 438–447, 1996.

    Google Scholar 

  11. D. R. Karger. Random sampling in matroids, with applications to graph connectivity and minimum spanning trees. In 34th Annual Symposium on Foundations of Computer Science, pages 84–93, 1993.

    Google Scholar 

  12. D. R. Karger. Random Sampling in Graph Optimization Problems. PhD thesis, Department of Computer Science, Stanford University, 1995.

    Google Scholar 

  13. D. R. Karger, P. N. Klein, and R. E. Tarjan. A randomized linear-time algorithm to find minimum spanning trees. Journal of the ACM, 42:321–328, 1995.

    Google Scholar 

  14. V. King, C. K. Poon, V. Ramachandran, and S. Sinha. An optimal EREW PRAM algorithm for minimum spanning tree verification. Information Processing Letters, 62(3):153–159, 1997.

    Google Scholar 

  15. V. Ramachandran. Private communication to Uri Zwick, January, 1996. To be included in journal version of [HZ96].

    Google Scholar 

  16. V. Ramachandran. A general purpose shared-memory model for parallel computation. Technical Report TR97-16, Univ. of Texas at Austin, 1997.

    Google Scholar 

  17. R. E. Tarjan. Data Structures and Network Algorithms. Society for Industrial and Applied Mathematics, 1983.

    Google Scholar 

  18. L. G. Valiant. A bridging model for parallel computation. Communications of the ACM, 33(8):103–111, 1990.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong

    Chung Keung Poon

  2. Department of Computer Sciences, The University of Texas at Austin, 78712, Austin, TX, USA

    Vijaya Ramachandran

Authors
  1. Chung Keung Poon
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vijaya Ramachandran
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Hon Wai Leong Hiroshi Imai Sanjay Jain

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Poon, C.K., Ramachandran, V. (1997). A randomized linear work EREW PRAM algorithm to find a minimum spanning forest. In: Leong, H.W., Imai, H., Jain, S. (eds) Algorithms and Computation. ISAAC 1997. Lecture Notes in Computer Science, vol 1350. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63890-3_24

Download citation

  • DOI: https://doi.org/10.1007/3-540-63890-3_24

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63890-2

  • Online ISBN: 978-3-540-69662-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation