Radial Level Planarity Testing and Embedding in Linear Time

  • Christian Bachmaier
  • Franz J. Brandenburg
  • Michael Forster
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2912)

Abstract

Every planar graph has a concentric representation based on a breadth first search, see [21]. The vertices are placed on concentric circles and the edges are routed as curves without crossings. Here we take the opposite view. A graph with a given partitioning of its vertices onto k concentric circles is k-radial planar, if the edges can be routed monotonic between the circles without crossings. Radial planarity is a generalisation of level planarity, where the vertices are placed on k horizontal lines. We extend the technique for level planarity testing of [18,17,15,16,12,13] and show that radial planarity is decidable in linear time, and that a radial planar embedding can be computed in linear time.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Christian Bachmaier
    • 1
  • Franz J. Brandenburg
    • 1
  • Michael Forster
    • 1
  1. 1.University of PassauPassauGermany

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