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Drawing Graphs with Vertices at Specified Positions and Crossings at Large Angles

  • Martin Fink
  • Jan-Henrik Haunert
  • Tamara Mchedlidze
  • Joachim Spoerhase
  • Alexander Wolff
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7034)

Introduction

In point-set-embeddability (PSE) problems one is given not just a graph that is to be drawn, but also a set of points in the plane that specify where the vertices of the graph can be placed. The problem class was introduced by Gritzmann et al. [3] twenty years ago. In their work and most other works on PSE problems, however, planarity of the output drawing was an essential requirement. Recent experiments on the readability of drawings [4] showed that polyline drawings with angles at edge crossings close to 90°. and a small number of bends per edge are just as readable as planar drawings. Motivated by these findings, Didimo et al. [2] recently introduced RAC drawings where pairs of crossing edges must form a right angle and, more generally, αAC drawings (for α ∈ (0, 90°]) where the crossing angle must be at least α. As usual, edges may not overlap and may not go through vertices. We investigate the intersection of PSE and RAC/αAC.

References

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    Di Giacomo, E., Frati, F., Fulek, R., Grilli, L., Krug, M.: Orthogeodesic point-set embedding of trees. In: Speckmann, B., van Kreveld, M. (eds.) GD2011. LNCS, vol. 7034, pp. 52–63. Springer, Heidelberg (2011)Google Scholar
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    Didimo, W., Eades, P., Liotta, G.: Drawing Graphs with Right Angle Crossings. In: Dehne, F., Gavrilova, M., Sack, J.-R., Tóth, C.D. (eds.) WADS 2009. LNCS, vol. 5664, pp. 206–217. Springer, Heidelberg (2009)CrossRefGoogle Scholar
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    Gritzmann, P., Mohar, B., Pach, J., Pollack, R.: Embedding a planar triangulation with vertices at specified positions. Amer. Math. Mon. 98, 165–166 (1991)MathSciNetCrossRefGoogle Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Martin Fink
    • 1
  • Jan-Henrik Haunert
    • 1
  • Tamara Mchedlidze
    • 2
  • Joachim Spoerhase
    • 1
  • Alexander Wolff
    • 1
  1. 1.Lehrstuhl für Informatik IUniversität WürzburgGermany
  2. 2.Department of MathematicsNational Technical University of AthensGreece

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