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Drawing Clustered Graphs on Disk Arrangements

  • Tamara Mchedlidze
  • Marcel RadermacherEmail author
  • Ignaz Rutter
  • Nina Zimbel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11355)

Abstract

Let \(G=(V, E)\) be a planar graph and let \(\mathcal V\) be a partition of V. We refer to the graphs induced by the vertex sets in Open image in new window as clusters. Let \(\mathcal {D}_{\mathcal C}\) be an arrangement of disks with a bijection between the disks and the clusters. Akitaya et al. [2] give an algorithm to test whether Open image in new window can be embedded onto \(\mathcal {D}_{\mathcal C}\) with the additional constraint that edges are routed through a set of pipes between the disks. Based on such an embedding, we prove that every clustered graph and every disk arrangement without pipe-disk intersections has a planar straight-line drawing where every vertex is embedded in the disk corresponding to its cluster. This result can be seen as an extension of the result by Alam et al. [3] who solely consider biconnected clusters. Moreover, we prove that it is \(\mathcal {NP} \)-hard to decide whether a clustered graph has such a straight-line drawing, if we permit pipe-disk intersections.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Tamara Mchedlidze
    • 1
  • Marcel Radermacher
    • 1
    Email author
  • Ignaz Rutter
    • 2
  • Nina Zimbel
    • 1
  1. 1.Department of Computer ScienceKarlsruhe Institute of TechnologyKarlsruheGermany
  2. 2.Department of Computer Science and MathematicsUniversity of PassauPassauGermany

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