Skip to main content
SpringerLink
Log in
Book cover

Annual Symposium on Theoretical Aspects of Computer Science

STACS 1996: STACS 96 pp 169–180Cite as

Parallel comparability graph recognition and modular decomposition

  • Conference paper
  • First Online:

  • 147 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1046))

Abstract

A parallelization of the algorithm of Golumbic for recognizing comparability graphs is proposed for the concurrent parallel random access machine (CRCW PRAM). Parallel algorithms for finding a transitive orientation and the modular decomposition of any undirected graph are deduced from an extension of the theory of Golumbic toward modular decomposition. The algorithms for recognizing and transitively orienting comparability graphs run in O(log n) time using δm processors and the modular decomposition algorithm runs in O(log n) time using n 3 processors (n, m and δ respectively denote the number of vertices, the number of edges and the maximal degree of the undirected input graph).

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. Richard Cole. Parallel merge sort. SIAM J. Comput., 17(4), August 1988.

    Google Scholar 

  2. A. Cournier and M. Habib. A new linear algorithm of modular decomposition. In Trees in algebra and programming—CAAP 94 (Edinburgh) Lecture Notes in Computer Science, volume 787, pages 68–84, Berlin, 1994. Springer.

    Google Scholar 

  3. Elias Dalhaus. Efficient parallel modular decomposition. In WG '95 21st International Workshop on Graph-Theoretic Concepts in Computer Science. M. Nagl, 1995. To appear in Lecture Notes in Computer Science.

    Google Scholar 

  4. Tibor Gallai. Transitiv orientierbare graphen. Acta Math. Acad. Scient. Hung. Tom., 18:25–66, 1967.

    Google Scholar 

  5. M. C. Golumbic. Algorithmic Graph Theory and Perfect Graphs. Academic Press, New York, 1980.

    Google Scholar 

  6. M.R. McConnell and J. Spinrad. Linear-time modular decomposition and efficient transitive orientation of comparability graphs. In Proceedings of the Fifth Annual ACM-SIAM Symposium on Discrete Algorithms (Arlington, VA), pages 536–545, New York, 1994. ACM.

    Google Scholar 

  7. Rolf H. Mohring. Algorithmic aspects of comparability graphs and interval graphs. In I. Rival, editor, Graphs and Orders, pages 41–101. D. Reidel Publishing Company, Dordrecht, 1985.

    Google Scholar 

  8. Rolf H. Mohring. Computationally tractable classes of ordered sets. In I. Rival, editor, Algorithms and Order, pages 105–193. Kluwer Acad. Publ., Dordrecht, 1989.

    Google Scholar 

  9. Mark B. Novick. Fast parallel algorithms for the modular decomposition. Technical Report 89-1016, Cornell University, 1989.

    Google Scholar 

  10. Mark B. Novick. Logaithmic time parallel algorithms for recognizing comparability and interval graphs. Technical Report 89-1015, Cornell University, 1989.

    Google Scholar 

  11. Y. Shiloah and U. Vishkin. An O(log n) parallel connectivity algorithm. J. Algorithms, 3:57–67, 1982.

    Article  Google Scholar 

  12. R.E. Tarjan. An efficient parallel biconnectivity algorithm. SIAM J. Computing, 14:862–874, 1985.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LITP/IBP, Université Paris 7 Denis Diderot, Case 7014, 2, place Jussieu, F-75251, Paris Cedex 05, France

    Michel Morvan & Laurent Viennot

Authors
  1. Michel Morvan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Laurent Viennot
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Claude Puech Rüdiger Reischuk

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Morvan, M., Viennot, L. (1996). Parallel comparability graph recognition and modular decomposition. In: Puech, C., Reischuk, R. (eds) STACS 96. STACS 1996. Lecture Notes in Computer Science, vol 1046. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60922-9_15

Download citation

  • DOI: https://doi.org/10.1007/3-540-60922-9_15

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60922-3

  • Online ISBN: 978-3-540-49723-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation