Skip to main content
SpringerLink
Log in
Book cover

International Symposium on Solving Irregularly Structured Problems in Parallel

IRREGULAR 1998: Solving Irregularly Structured Problems in Parallel pp 298–309Cite as

A new simple parallel tree contraction scheme and its application on distance-hereditary graphs

  • Regular Talks
  • Conference paper
  • First Online:

  • 113 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1457))

Abstract

We present a new parallel tree contraction scheme which takes O(log n) contraction phases to reduce a tree to its root, and implement this scheme in O(log n log log n) time using O(n/ log log n) processors on an arbitrary CROW PRAM. We then show a data structure to represent a connected distance-hereditary graph G in the form of a rooted tree. Applying our tree contraction scheme on the above data structure together with graph theoretical properties, we solve the problems of finding a minimum connected γ-dominating set and finding a minimum γ-dominating clique on G in O(log n log log n) time using O((n + m) /log log n) processors on an arbitrary CROW PRAM, where n and m are the number of vertices and edges in G, respectively.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H. J. Bandelt and H. M. Mulder. Distance-hereditary graphs. Journal of Combinatorial Theory Series B, 41(1):182–208, Augest 1989.

    Google Scholar 

  2. C. Berge. Graphs and hypergraphs. North-Holland, Amsterdam, 1973.

    Google Scholar 

  3. O. Berkman, B. Schieber, and U. Vishkin. Optimal doubly logarithmic parallel algorithms based on finding all nearest smaller values. Journal of Algorithms., vol. 14, pp. 344–370, 1993.

    Google Scholar 

  4. A.Brandstadt. Special graph classes-a survey. Technical Report SM-DU-199, University of Duisburg, 1993.

    Google Scholar 

  5. A. Branstadt and F. F. Dragan. A linear time algorithm for connected γ-domination and Steiner tree on distance-hereditary graphs. Technical Report, Gerhard-Mercator-Universität-Gesamthochschule Duisburg SM-DU-261, 1994.

    Google Scholar 

  6. R. Cole. Parallel merge sort. SIAM Journal on Computing, 17(4):770–785, August 1988.

    Google Scholar 

  7. E. Dahlhaus, “Optimal (parallel) algorithms for the all-to-all vertices distance problem for certain graph classes,” Lecture notes in computer science 657, pp. 60–69, 1993.

    Google Scholar 

  8. E. Dahlhaus. Efficient parallel recognition algorithms of cographs and distancehereditary graphs. Discrete Applied Mathematics, 57(1):29–44, February 1995.

    Google Scholar 

  9. A. D'atri and M. Moscarini. Distance-hereditary graphs, steiner trees, and connected domination. SIAM Journal on Computing, 17(3):521–538, June, 1988.

    Google Scholar 

  10. F. F. Dragan. Dominating cliques in distance-hereditary graphs. Technical Report SM-DU-248, University of Duisburg, 1994.

    Google Scholar 

  11. F. F. Dragan and A. Brandstadt. γ-dominating cliques in Helly graphs and chordal graphs. Technical Report SM-DU-228, University of Duisburg, 1993. Proceedings of the 11th STAGS, Caen, France, Springer, LNCS 775, pp. 735–746, 1994.

    Google Scholar 

  12. Joseph Gil and Larry Rudolph. Counting and packing in parallel. Proceedings of the 1986 International Conference on Parallel Processing, vol. 3, pp.1000–1002.

    Google Scholar 

  13. M. C. Golumbic. Algorithmic graph theory and perfect graphs, Academic press, New York, 1980.

    Google Scholar 

  14. P. L. Hammer and F. Maffray. Complete separable graphs. Discrete Applied Mathematics, 27(1):85–99, May 1990.

    Google Scholar 

  15. S. C. Hedetniemi and R. Laskar, (eds.) Topics on domination, Annals of Discrete Mathematics, 48, North-Holland, 1991.

    Google Scholar 

  16. E. Howorka. A characterization of distance-hereditary graphs. Quarterly Journal of Mathematics (Oxford), 28(2):417–420 1977.

    Google Scholar 

  17. S.-y. Hsieh, C. W. Ho, T.-s. Hsu, M. T. Ko, and G. H. Chen. Efficient parallel algorithms on distance-hereditary graphs. Parallel Processing Letters, to appear. A preliminary version of this paper is in Proceedings of the International Conference on Parallel Processing, pp. 20–23, 1997.

    Google Scholar 

  18. J. Ja'Ja'. An Introduction to Parallel Algorithms. Addison Wesley, 1992.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan, ROC

    Sun-Yuan Hsieh & Gen-Huey Chen

  2. Department of Computer Science and Information Engineering, National Central University, Chung-Li, Taiwan, ROC

    Chin-Wen Hoe

  3. Institute of Information Science, Academia Sinica, Taipei, Taiwan, ROC

    Tsan-Sheng Hsu & Ming-Tat Ko

Authors
  1. Sun-Yuan Hsieh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chin-Wen Hoe
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tsan-Sheng Hsu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ming-Tat Ko
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Gen-Huey Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Alfonso Ferreira José Rolim Horst Simon Shang-Hua Teng

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hsieh, SY., Hoe, CW., Hsu, TS., Ko, MT., Chen, GH. (1998). A new simple parallel tree contraction scheme and its application on distance-hereditary graphs. In: Ferreira, A., Rolim, J., Simon, H., Teng, SH. (eds) Solving Irregularly Structured Problems in Parallel. IRREGULAR 1998. Lecture Notes in Computer Science, vol 1457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0018548

Download citation

  • DOI: https://doi.org/10.1007/BFb0018548

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64809-3

  • Online ISBN: 978-3-540-68533-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation