• Media type: E-Article; Text
  • Title: Crossing Minimization for Symmetries (Extended Abstract)
  • Contributor: Buchheim, Christoph [Author]; Hong, Seok-Hee [Author]
  • Published: Springer, 2002
  • Language: German; English
  • Origination:
  • Footnote: Diese Datenquelle enthält auch Bestandsnachweise, die nicht zu einem Volltext führen.
  • Description: 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(m log m) crossing minimization algorithm for symmetries with an orbit graph that is a path.