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The Approximate Rectangle of Influence Drawability Problem

  • Emilio Di Giacomo
  • Giuseppe Liotta
  • Henk Meijer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7704)

Abstract

We prove that all planar graphs have an open/closed (ε 1,ε 2)-rectangle of influence drawing for ε 1 > 0 and ε 2 > 0, while there are planar graphs which do not admit an open/closed (ε 1,0)-rectangle of influence drawing and planar graphs which do not admit a (0,ε 2)-rectangle of influence drawing. We then show that all outerplanar graphs have an open/closed (0,ε 2)-rectangle of influence drawing for any ε 2 ≥ 0. We also prove that if ε 2 > 2 an open/closed (0, ε 2)-rectangle of influence drawing of an outerplanar graph can be computed in polynomial area. For values of ε 2 such that ε 2 ≤ 2, we describe a drawing algorithm that computes (0,ε 2)-rectangle of influence drawings of binary trees in area \(O(n^{2 + f(\varepsilon _2)})\), where f(ε 2) is a logarithmic function that tends to infinity as ε 2 tends to zero, and n is the number of vertices of the input tree.

Keywords

Internal Vertex Outerplanar Graph Drawing Technique Planar Embedding Maximum Vertex Degree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Emilio Di Giacomo
    • 1
  • Giuseppe Liotta
    • 1
  • Henk Meijer
    • 2
  1. 1.Dip. di Ingegneria Elettronica e dell’InformazioneUniversità degli Studi di PerugiaItaly
  2. 2.Roosevelt AcademyThe Netherlands

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