Advances in C-Planarity Testing of Clustered Graphs

(Extended Abstract)
  • Carsten Gutwenger
  • Michael Jünger
  • Sebastian Leipert
  • Petra Mutzel
  • Merijam Percan
  • René Weiskircher
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2528)

Abstract

A clustered graph C = (G,T) consists of an undirected graph G and a rooted tree T in which the leaves of T correspond to the vertices of G = (V,E). Each vertex μ in T corresponds to a subset of the vertices of the graph called “cluster”. c-planarity is a natural extension of graph planarity for clustered graphs, and plays an important role in automaticgraph drawing. The complexity status of c-planarity testing is unknown. It has been shown in [FCE95,Dah98] that c-planarity can be tested in linear time for c-connected graphs, i.e., graphs in which the cluster induced subgraphs are connected.

In this paper, we provide a polynomial time algorithm for c-planarity testing of “almost” c-connected clustered graphs, i.e., graphs for which all nodes corresponding to the non-c-connected clusters lie on the same path in T starting at the root of T, or graphs in which for each nonconnected cluster its super-cluster and all its siblings in T are connected. The algorithm is based on the concepts for the subgraph induced planar connectivity augmentation problem presented in [GJL+02]. We regard it as a first step towards general c-planarity testing.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Carsten Gutwenger
    • 2
  • Michael Jünger
    • 1
  • Sebastian Leipert
    • 2
  • Petra Mutzel
    • 3
  • Merijam Percan
    • 1
  • René Weiskircher
    • 3
  1. 1.Universität zu Köln, Institut für InformatikKölnGermany
  2. 2.caesar research centerBonnGermany
  3. 3.Technische Universität Wien E186WienAustria

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