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Crossing Minimization for Symmetries

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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.

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Authors and Affiliations

  1. Institut fur Informatik, Universitat zu Koln, Pohligstasse 1, 50969 Koln, Germany

    Christoph Buchheim

  2. NICTA (National ICT Australia) and School of Information Technologies, University of Sydney, Sydney, NSW 2006, Australia

    Seok-Hee Hong

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  1. Christoph Buchheim
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  2. Seok-Hee Hong
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Correspondence to Christoph Buchheim or Seok-Hee Hong.

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Buchheim, C., Hong, SH. Crossing Minimization for Symmetries. Theory Comput Syst 38, 293–311 (2005). https://doi.org/10.1007/s00224-005-1142-5

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  • DOI: https://doi.org/10.1007/s00224-005-1142-5

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