An efficient orthogonal grid drawing algorithm for cubic graphs
In this paper we present a new algorithm that constructs an orthogonal drawing of a graph G with degree at most three. Even if we do not require any limitations neither to planar nor to biconnected graphs, we reach the best known results in the literarture: each edge has at most 1 bend, the total number of bends is ≤ n/2+1, and the area is ≤(n/2−1)2.
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- 1.Aho, A., Hopcroft, J. K. Ullman, J. D.: The design and analysis of computer algorithms. Addison Wesley, Reading,MA, (1973)Google Scholar
- 2.Biedl, T., Kant, G.: A Better Euristic for Orthogonal Graph Drawings. Algorithms — ESA '94. Proceedings, Lectures Notes in Computer Science, Springer-Verlag 855 (1994) 24–35Google Scholar
- 3.Bjorken, J.D., Drell, S.D.: Quantum Electrodynamics. Mc-Graw HillGoogle Scholar
- 4.Cormen, T.H., Leiserson, C.E., Rivest, R.L.: Introduction to algorithms. the MIT Press, Cambridge,MA, (1990)Google Scholar
- 5.Di Battista, G., Liotta, G., Vargiu, F.: Spirality of Orthogonal Representations and Optimal Drawings of Series-Parallel Graphs and 3-Planar Graphs. Lectures Notes in Computer Science, Springer-Verlag 709 (1993) 151–162Google Scholar
- 6.Greenlaw, R., Petreschi, R.: Cubic graphs, Tech. Rep. University of New Hampshire, Durham,N.H.,USA 15 (1993)Google Scholar
- 7.Kant, G.: Drawing Planar Graphs Using the canonical ordering. Algorithmica — Special Issue on Graph Drawing (to appear)Google Scholar
- 8.Liu, Y. Marchioro, P., Petreschi, R.: At most single bend embedding of cubic graphs. Applied Mathematics (Chin. Journ.) 9/B/2 (1994) 127–142Google Scholar
- 9.Papakostas, A., Tollis, I.G.: Improved Algorithms and Bounds for Orthogonal Drawings. Proc.Graph Drawing '94, Lectures Notes in Computer Science, Springer-Verlag 894 (1994) 40–51Google Scholar