Crossing Minimization for Symmetries

  • Christoph Buchheim
  • Seok Hee Hong
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2518)


We consider the problem of drawing a graph with a given symmetry such that the number of edge crossings is minimal. We show that this problem is NP-hard, even if the order of orbits around the rotation center or along the reflection axis is fixed. Nevertheless, there is a linear time algorithm to test planarity and to construct a planar embedding if possible. Finally, we devise an O(m log m) algorithm for computing a crossing minimal drawing if inter-orbit edges may not cross orbits, showing in particular that intra-orbit edges do not contribute to the NP-hardness of the crossing minimization problem for symmetries. From this result, we can derive an O(mlogm) crossing minimization algorithm for symmetries with an orbit graph that is a path.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Christoph Buchheim
    • 1
  • Seok Hee Hong
    • 2
  1. 1.Institut für InformatikUniversität zu KölnGermany
  2. 2.School of Information TechnologiesUniversity of SydneyAustralia

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