Graph Embedding with Minimum Depth and Maximum External Face
We present new linear time algorithms using the SPQR-tree data structure for computing planar embeddings of planar graphs optimizing certain distance measures. Experience with orthogonal drawings generated by the topology-shape-metrics approach shows that planar embeddings following these distance measures lead to improved quality of the final drawing in terms of bends, edge length, and drawing area.
Given a planar graph, the algorithms compute the planar embedding with
the minimum depth among the set of all planar embeddings of G,
the external face of maximum size among the set of all planar embeddings of G,
the external face of maximum size among the set of all embeddings of G with minimum depth.
- 1.Batini, C., Nardelli, E., Tamassia, R.: A layout algorithm for data-flow diagrams. IEEE Trans. Soft. Eng. SE-12(4), 538–546 (1986)Google Scholar
- 6.Di Battista, G., Eades, P., Tamassia, R., Tollis, I.G.: Graph Drawing. Prentice-Hall, Englewood Cliffs (1998)Google Scholar
- 11.Graph drawing toolkit: An object-oriented library for handling and drawing graphs, http://www.dia.uniroma3.it/gdt
- 13.Liotta, G., Vargiu, F., Di Battista, G.: Orthogonal drawings with the minimum number of bends. In: Proceedings of the 6th Canadian Conference on Computational Geometry, pp. 281–286. University of Saskatchewan (1994)Google Scholar
- 20.Weiskircher, R.: New Applications of SPQR-Trees in Graph Drawing. PhD thesis, Universität des Saarlandes (2002)Google Scholar