Computational complexity of geometric symmetry detection in graphs
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.
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- A. Aho, J. Hopcroft, J. Ullman. The Design and Analysis of Computer Algorithms, Addison-Wesley, 1974.Google Scholar
- M. Garey, D. Johnson. Computers and Intractability, W. H. Freeman, 1979.Google Scholar
- 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
- J. Manning. “Geometric Symmetry in Graphs”, Ph.D. Thesis, Department of Computer Sciences, Purdue University, Aug 1990 (forthcoming).Google Scholar
- 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
- E. Messinger. “Automatic Layout of Large Directed Graphs”, Technical Report 88-07-08, Department of Computer Science, University of Washington, Jul 1988.Google Scholar