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Low Ply Drawings of Trees

  • Patrizio Angelini
  • Michael A. Bekos
  • Till Bruckdorfer
  • Jaroslav HančlJr.
  • Michael Kaufmann
  • Stephen Kobourov
  • Antonios Symvonis
  • Pavel Valtr
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9801)

Abstract

We consider the recently introduced model of low ply graph drawing, in which the ply-disks of the vertices do not have many common overlaps, which results in a good distribution of the vertices in the plane. The ply-disk of a vertex in a straight-line drawing is the disk centered at it whose radius is half the length of its longest incident edge. The largest number of ply-disks having a common overlap is called the ply-number of the drawing.

We focus on trees. We first consider drawings of trees with constant ply-number, proving that they may require exponential area, even for stars, and that they may not even exist for bounded-degree trees. Then, we turn our attention to drawings with logarithmic ply-number and show that trees with maximum degree 6 always admit such drawings in polynomial area.

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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Patrizio Angelini
    • 1
  • Michael A. Bekos
    • 1
  • Till Bruckdorfer
    • 1
  • Jaroslav HančlJr.
    • 2
  • Michael Kaufmann
    • 1
  • Stephen Kobourov
    • 3
  • Antonios Symvonis
    • 4
  • Pavel Valtr
    • 2
  1. 1.Institut für InformatikUniversität TübingenTübingenGermany
  2. 2.Department of Applied MathematicsCharles University (KAM)PragueCzech Republic
  3. 3.Department for Computer ScienceUniversity of ArizonaTucsonUSA
  4. 4.School of Applied Mathematical and Physical SciencesNTUAAthensGreece

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