## Crossing Minimization for Symmetries
Buchheim, Christoph and Hong, Seok-Hee
(2002)
Full text not available from this repository. ## AbstractWe 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.
## Available Versions of this Item-
Crossing Minimization for Symmetries. (deposited 07 Apr 2005)
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