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Crossing Minimization for Symmetries

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Algorithms and Computation (ISAAC 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2518))

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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. 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(mlogm) crossing minimization algorithm for symmetries with an orbit graph that is a path.

The second author is supported by a grant from the Australian Research Council. This paper was partially written when the first author was visiting the University of Sydney.

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Author information

Authors and Affiliations

  1. Institut für Informatik, Universität zu Köln, Germany

    Christoph Buchheim

  2. School of Information Technologies, University of Sydney, Australia

    Seok Hee Hong

Authors
  1. Christoph Buchheim
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  2. Seok Hee Hong
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Editor information

Editors and Affiliations

  1. School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, Canada, K1S 5B6

    Prosenjit Bose  & Pat Morin  & 

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© 2002 Springer-Verlag Berlin Heidelberg

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Buchheim, C., Hong, S.H. (2002). Crossing Minimization for Symmetries. In: Bose, P., Morin, P. (eds) Algorithms and Computation. ISAAC 2002. Lecture Notes in Computer Science, vol 2518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36136-7_49

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  • DOI: https://doi.org/10.1007/3-540-36136-7_49

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00142-3

  • Online ISBN: 978-3-540-36136-7

  • eBook Packages: Springer Book Archive

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