Skip to main content
SpringerLink
Log in

Recognition and isomorphism of two dimensional partial orders

  • Conference paper
  • First Online:
Automata, Languages and Programming (ICALP 1983)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 154))

Included in the following conference series:

Abstract

This paper presents an algorithm for recognizing two dimensional partial orders. The algorithm accepts as input an arbitrary partial order G and responds “yes” if the dimension of G is less than or equal to two and responds “no” otherwise. As part of the recognition process, the algorithm decomposes the partial order in a canonical way which can be used to determine whether two partial orders of dimension two are isomorphic. Both the recognition and the isomorphism algorithms can be implemented to run in time O(n 2) when the input is a partial order on n elements. The best previously known algorithms for these two tasks had a worst case behavior of O(n 3).

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. C.J. Colbourn, “On Testing Isomorphism of Permutation Graphs”, Networks, vol. 11, pp. 13–21 (1981).

    Google Scholar 

  2. B. Dushnik, E.W. Miller, “Partially Ordered Sets”, American Journal of Mathematics, vol. 63, pp. 600–610 (1941).

    Google Scholar 

  3. S. Even, A. Lempel, A. Pnueli, “Transitive Orientation of Graphs and Identification of Permutation Graphs”, Canadian Journal of Mathematics, vol. 23, pp. 160–175 (1971).

    Google Scholar 

  4. E. L. Lawler, “Sequencing Jobs to Minimize Total Weighted Completion Time Subject to Precedence Constraints”, Annals of Discrete Mathematics, vol. 2, pp. 75–90 (1978).

    Google Scholar 

  5. G. Luecker, K. Booth, “A Linear Time Algorithm for Deciding Interval Graph Isomorphism”, J. ACM, vol. 26, pp. 183–195 (1979).

    Google Scholar 

  6. J. Spinrad, Two Dimensional Partial Orders, Ph.D. Thesis, Department of Electrical Engineering and Computer Sciences, Princeton University, (1982).

    Google Scholar 

  7. J. Spinrad, “Transitive Orientation in O(n 2) time”, to appear in the Proceedings of the 15th Annual ACM symposium on Theory of Computing, Boston, Mass. (1983).

    Google Scholar 

  8. J. Valdes, R. E. Tarjan, E. Lawler, “The Recognition of Series-Parallel Digraphs”, Proceedings of the 11th Annual ACM Symposium on Theory of Computing, Atlanta, Georgia, pp. 1–12, (1979).

    Google Scholar 

  9. M. Yannakakis, “The Complexity of the Partial Order Dimension Problem”, to appear.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer and Information Sciences, Georgia Institute of Technology, Atlanta, Ga.

    Jeremy Spinrad

  2. Department of Electrical Engineering and Computer Science, Princeton University, Princeton, NJ

    Jacobo Valdes

Authors
  1. Jeremy Spinrad
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jacobo Valdes
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Josep Diaz

Rights and permissions

Reprints and permissions

Copyright information

© 1983 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Spinrad, J., Valdes, J. (1983). Recognition and isomorphism of two dimensional partial orders. In: Diaz, J. (eds) Automata, Languages and Programming. ICALP 1983. Lecture Notes in Computer Science, vol 154. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0036947

Download citation

  • DOI: https://doi.org/10.1007/BFb0036947

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12317-0

  • Online ISBN: 978-3-540-40038-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation