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(mlog 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(mlog m) crossing minimization algorithm for symmetries with an orbit graph that is a path. © Springer-Verlag Berlin Heidelberg 2002.
CITATION STYLE
Buchheim, C., & Hong, S. H. (2002). Crossing minimization for symmetries. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2518 LNCS, pp. 563–574). https://doi.org/10.1007/3-540-36136-7_49
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