Skip to main content
Springer Nature Link
Log in

Computational complexity of geometric symmetry detection in graphs

  • Track1: Graph Algorithms
  • Conference paper
  • First Online:
Computing in the 90's (Great Lakes CS 1989)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 507))

Included in the following conference series:

Abstract

Constructing a visually informative drawing of an abstract graph is a problem of considerable practical importance, and has recently been the focus of much investigation. Displaying symmetry has emerged as one of the foremost criteria for achieving good drawings. Linear-time algorithms are already known for the detection and display of symmetry in trees, outerplanar graphs, and embedded planar graphs. The central results of this paper show that for general graphs, however, detecting the presence of even a single axial or rotational symmetry is NP-complete. A number of related results are also established, including the #P-completeness of counting the axial or rotational symmetries of a graph.

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. A. Aho, J. Hopcroft, J. Ullman. The Design and Analysis of Computer Algorithms, Addison-Wesley, 1974.

    Google Scholar 

  2. I. Fáry. “On Straight Line Representation of Planar Graphs”, Acta Scientiarum Mathematicarum Szeged 11, 4, pp 229–233, 1948.

    MATH  Google Scholar 

  3. M. Garey, D. Johnson. Computers and Intractability, W. H. Freeman, 1979.

    Google Scholar 

  4. R. Lipton, S. North, J. Sandberg. “A Method for Drawing Graphs”, Proc. of the First ACM Symposium on Computational Geometry, pp 153–160, Jun 1985.

    Google Scholar 

  5. A. Lubiw. “Some NP-Complete Problems Similar to Graph Isomorphism”, SIAM Journal on Computing 10, 1, pp 11–21, Feb 1981.

    Article  MATH  MathSciNet  Google Scholar 

  6. J. Manning. “Geometric Symmetry in Graphs”, Ph.D. Thesis, Department of Computer Sciences, Purdue University, Aug 1990 (forthcoming).

    Google Scholar 

  7. J. Manning, M. J. Atallah. “Fast Detection and Display of Symmetry in Trees”, Congressus Numerantium 64, pp 159–168, Nov 1988.

    MATH  MathSciNet  Google Scholar 

  8. J. Manning, M. J. Atallah. “Fast Detection and Display of Symmetry in Outerplanar Graphs”, Technical Report CSD-TR-606, Department of Computer Sciences, Purdue University, Jun 1986. (Submitted for publication to Discrete Applied Mathematics.)

    Google Scholar 

  9. E. Messinger. “Automatic Layout of Large Directed Graphs”, Technical Report 88-07-08, Department of Computer Science, University of Washington, Jul 1988.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Missouri - Rolla, 65401, Rolla, MO, USA

    Joseph Manning

Authors
  1. Joseph Manning
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Naveed A. Sherwani Elise de Doncker John A. Kapenga

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Manning, J. (1991). Computational complexity of geometric symmetry detection in graphs. In: Sherwani, N.A., de Doncker, E., Kapenga, J.A. (eds) Computing in the 90's. Great Lakes CS 1989. Lecture Notes in Computer Science, vol 507. Springer, New York, NY. https://doi.org/10.1007/BFb0038465

Download citation

  • DOI: https://doi.org/10.1007/BFb0038465

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-97628-0

  • Online ISBN: 978-0-387-34815-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics