Combining Problems on RAC Drawings and Simultaneous Graph Drawings

Argyriou, Evmorfia N. and Bekos, Michael A. and Kaufmann, Michael and Symvonis, Antonios (2012) Combining Problems on RAC Drawings and Simultaneous Graph Drawings. In: Graph Drawing 19th International Symposium, GD 2011, September 21-23, 2011, Eindhoven, The Netherlands , pp. 433-434 (Official URL: http://dx.doi.org/10.1007/978-3-642-25878-7_41).

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Abstract

We present an overview of the first combinatorial results for the so-called geometric RAC simultaneous drawing problem (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 G 1 = (V, E 1) and G 2 = (V, E 2) that share a common vertex set but have disjoint edge sets, i.e., E 1 ⊆ V ×V , E 2 ⊆ V ×V and E 1 ∩ E 2 = ∅ 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 E 1 and E 2 occur at right angles.

Item Type:Conference Paper
Additional Information:10.1007/978-3-642-25878-7_41
Classifications:G Algorithms and Complexity > G.420 Crossings
G Algorithms and Complexity > G.490 Embeddings
ID Code:1276

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References

Argyriou, E.N., Bekos, M.A., Kaufmann, M., Symvonis, A.: Geometric simultaneous rac drawings of graphs. CoRR abs/1106.2694 (2011)

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)

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)