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Simultaneous Visibility Representations of Plane st-graphs Using L-shapes

  • William S. Evans
  • Giuseppe Liotta
  • Fabrizio MontecchianiEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9224)

Abstract

Let \(\langle G_r,G_b \rangle \) be a pair of plane st-graphs with the same vertex set V. A simultaneous visibility representation with L-shapes of \(\langle G_r,G_b \rangle \) is a pair of bar visibility representations \(\langle \varGamma _r,\varGamma _b\rangle \) such that, for every vertex \(v \in V\), \(\varGamma _r(v)\) and \(\varGamma _b(v)\) are a horizontal and a vertical segment, which share an end-point. In other words, every vertex is drawn as an L-shape, every edge of \(G_r\) is a vertical visibility segment, and every edge of \(G_b\) is a horizontal visibility segment. Also, no two L-shapes intersect each other. An L-shape has four possible rotations, and we assume that each vertex is given a rotation for its L-shape as part of the input. Our main results are: (i) a characterization of those pairs of plane st-graphs admitting such a representation, (ii) a cubic time algorithm to recognize them, and (iii) a linear time drawing algorithm if the test is positive.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • William S. Evans
    • 1
  • Giuseppe Liotta
    • 2
  • Fabrizio Montecchiani
    • 2
    Email author
  1. 1.University of British ColumbiaVancouverCanada
  2. 2.Università degli Studi di PerugiaPerugiaItaly

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