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)


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.


Internal Vertex Outerplanar Graph Drawing Technique Planar Embedding Maximum Vertex Degree 
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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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