Buchheim, Christoph and Hong, Seok-Hee (2005) Crossing Minimization for Symmetries. [Journal (Paginated)]
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Abstract
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. 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.
| Item Type: | Journal (Paginated) |
|---|---|
| Keywords: | symmetric drawings, planarity, crossing minimization |
| Classifications: | G Algorithms and Complexity > G.910 Symmetries G Algorithms and Complexity > G.420 Crossings P Styles > P.780 Symmetric |
| ID Code: | 608 |
| Deposited By: | Buchheim, Christoph |
| Deposited On: | 15 Jun 2005 |
| Last Modified: | 18 Sep 2008 13:08 |
| Alternative Locations: | http://www.springerlink.de/app/home/contribution.asp?wasp=f4007017c8c540f8bb484bc5231c1a93&referrer=parent&backto=searcharticlesresults,9,46; |
Available Versions of this Item
- Crossing Minimization for Symmetries. (deposited 07 Apr 2005)
- Crossing Minimization for Symmetries. (deposited 15 Jun 2005) [Currently Displayed]
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