Combining Problems on RAC Drawings and Simultaneous Graph Drawings

  • Evmorfia N. Argyriou
  • Michael A. Bekos
  • Michael Kaufmann
  • Antonios Symvonis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7034)

Introduction and Problem Definition

We present an overview of the first combinatorial results for the so-called geometricRACsimultaneousdrawingproblem (or GRacSim drawing problem, for short), i.e., a combination of problems on geometric RAC drawings [3] and geometric simultaneous graph drawings [2]. According to this problem, we are given two planar graphs G1 = (V, E1) and G2 = (V, E2) that share a common vertex set but have disjoint edge sets, i.e., E1 ⊆ V ×V , E2 ⊆ V ×V and E1 ∩ E2 = ∅ The main task is to place the vertices on the plane so that, when the edges are drawn as straight-lines, (i) each graph is drawn planar, (ii) there are no edge overlaps, and, (iii) crossings between edges in E1 and E2 occur at right angles.

References

  1. 1.
    Argyriou, E.N., Bekos, M.A., Kaufmann, M., Symvonis, A.: Geometric simultaneous rac drawings of graphs. CoRR abs/1106.2694 (2011)Google Scholar
  2. 2.
    Brass, P., Cenek, E., Duncan, C.A., Efrat, A., Erten, C., Ismailescu, D., Kobourov, S.G., Lubiw, A., Mitchell, J.S.B.: On simultaneous planar graph embeddings. Computational Geometry: Theory and Applications 36(2), 117–130 (2007)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    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

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Evmorfia N. Argyriou
    • 1
  • Michael A. Bekos
    • 1
  • Michael Kaufmann
    • 2
  • Antonios Symvonis
    • 1
  1. 1.School of Applied Mathematical & Physical SciencesNational Technical University of AthensGreece
  2. 2.Institute for InformaticsUniversity of TübingenGermany

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