Skip to main content
SpringerLink
Log in

Parallel ear decomposition search (EDS) and st-numbering in graphs

Extended abstract

  • Conference paper
  • First Online:
VLSI Algorithms and Architectures (AWOC 1986)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 227))

Included in the following conference series:

Abstract

The linear time serial algorithm for planarity testing of [LEC-67] uses the linear time serial algorithm of [ET-76] for st-numbering. This st-numbering algorithm is based on depth-first search (DFS). A known conjecture states that DFS, which is a key technique in designing serial algorithms, is not amenable to poly-log time parallelism using "around linearly" (or even polynomially) many processors. The first contribution of this paper is a general method for searching efficiently in parallel undirected graphs, called ear-decomposition search (EDS).

The second contribution demonstrates the applicability of this search method. We present an efficient parallel algorithm for st-numbering in a biconnected graph. The algorithm is quite subtle and runs in logarithmic time using a linear number of processors on a concurrent-read concurrent-write (CRCW) PRAM. An efficient parallel algorithm for the problem did not exist before. It was not even known to be in NC.

The research of this author was supported by NSF grant NSF-DCR-8318874 and ONR grant N00014-85-K-0046.

The research of these authors was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U. S. Department of Energy under contract number DE-AC02-76ER03077.

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. Anderson, R., "A Parallel Algorithm for the Maximal Path Problem", Proc. 17th ACM Symp. on Theory of Computing (1985), pp. 33–37.

    Google Scholar 

  2. Cole, R. and Vishkin, U., "Deterministic Coin Tossing and Accelerating Cascades: Micro and Macro Techniques for Designing Parallel Algorithms", Proc. 18th ACM Symp. on Theory of Computing (1986), to appear.

    Google Scholar 

  3. Even, S., "Graph Algorithms", Computer Science Press, 1979.

    Google Scholar 

  4. Even, S., and Tarjan, R.E., "Computing an st-numbering", Th. Comp. Science 2 (1976), pp. 339–344.

    Google Scholar 

  5. Itai, A. and Rodeh, M., "The Multi-Tree Approach to Reliability in Distributed Networks", Proc. 25th Symp. on Foundations of Comp. Science (1984), pp. 137–147.

    Google Scholar 

  6. Ja'Ja' J. and Simon, J., "Parallel Algorithms in Graph Theory: Planarity Testing", SIAM J. of Computing 11 (1982), pp. 314–328.

    Google Scholar 

  7. Lempel, A., Even, S. and Cederbaum, I., "An Algorithm for Planarity Testing of Graphs", Theory of Graphs, Int. Symp., Rome, July 1966. P. Rosenstiehl, Ed., Gordon and Breach, NY (1967), pp. 215–232.

    Google Scholar 

  8. Lovasz, L., "Computing Ears and Branchings in Parallel", Proc. 26th Symp. on Foundations of Comp. Science (1985), pp. 464–467.

    Google Scholar 

  9. Maon, Y., Schieber, B. and Vishkin, U., "Parallel Ear Decomposition Search (EDS) and ST-Numbering in Graphs", TR 46/86 Dept. of Computer Science, Tel Aviv University, 1986.

    Google Scholar 

  10. Reif, J.H., "An Optimal Parallel Algorithm for Integer Sorting", Proc. 26th Symp. on Foundations of Comp. Science (1985), pp. 496–503.

    Google Scholar 

  11. Shiloach, Y. and Vishkin, U., "An O (log n) Parallel Connectivity Algorithm", J. of Algorithms 3 (1982), pp. 57–63.

    Google Scholar 

  12. Tarjan, R.E. and Vishkin, U., "An Efficient Parallel Biconnectivity Algorithm", SIAM J. of Computing 14 (1985), pp. 862–874.

    Google Scholar 

  13. Vishkin, U., "Synchronous Parallel Computation — a Survey", TR #71, Dept. of Computer Science, Courant Inst., NYU, 1983.

    Google Scholar 

  14. Vishkin, U., "On Efficient Parallel Strong Orientation", Information Proc. Letters 20 (1985), pp. 235–240.

    Google Scholar 

  15. Whitney, H., "Non-separable and Planar Graphs", Trans. Amer. Math. Soc. 34 (1932), pp. 339–362.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science School of Mathematical Sciences, Tel Aviv University, 69978, Tel Aviv, Israel

    Yael Maon, Baruch Schieber & Uzi Vishkin

  2. Department of Computer Science Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., 10012, New York, N.Y.

    Yael Maon, Baruch Schieber & Uzi Vishkin

Authors
  1. Yael Maon
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Baruch Schieber
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Uzi Vishkin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Filia Makedon Kurt Mehlhorn T. Papatheodorou P. Spirakis

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Maon, Y., Schieber, B., Vishkin, U. (1986). Parallel ear decomposition search (EDS) and st-numbering in graphs. In: Makedon, F., Mehlhorn, K., Papatheodorou, T., Spirakis, P. (eds) VLSI Algorithms and Architectures. AWOC 1986. Lecture Notes in Computer Science, vol 227. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16766-8_4

Download citation

  • DOI: https://doi.org/10.1007/3-540-16766-8_4

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16766-2

  • Online ISBN: 978-3-540-38746-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation