Three Approaches to 3D-Orthogonal Box-Drawings
In this paper, we study orthogonal graph drawings in three dimensions with nodes drawn as boxes. The algorithms that we present can be differentiated as resulting from three different approaches to creating 3D-drawings; we call these approaches edge-lifting, half-edge-lifting, and three-phase-method.
Let G be a graph with n vertices, m edges, and maximum degree Δ. We obtain a drawing of G in an n × n × Δ-grid where the surface area of the box of a node v is O(deg(v)); this improves significantly on previous results. We also consider drawings with at most one node per grid-plane, and exhibit constructions in an n × n × m-grid and a lower bound of Ω(m 2); hence upper and lower bounds match for graphs with θ(n 2) edges.
- T. Biedl and M. Kaufmann. Area-efficient static and incremental graph drawings. In 5th European Symposium on Algorithms, volume 1284 of Lecture Notes in Computer Science, pages 37–52. Springer-Verlag, 1997.Google Scholar
- G. Di Battista, A. Garg, G. Liotta, R. Tamassia, E. Tassinari, and F. Vargiu. An experimental comparison of four graph drawing algorithms. Computational Geometry: Theory and Applications, 7(5–6), 1997.Google Scholar
- G. DiBattista, editor. Symposium on Graph Drawing 97, volume 1353 of Lecture Notes in Computer Science. Springer-Verlag, 1998.Google Scholar
- P. Eades, A. Symvonis, and S. Whitesides. Two algorithms for three dimensional orthogonal graph drawing. In S. North, editor. Symposium on Graph Drawing 96, volume 1190 of Lecture Notes in Computer Science. Springer-Verlag, 1997, pp. 139–154.Google Scholar
- A. Papakostas and I. Tollis. High-degree orthogonal drawings with small grid-size and few bends. In 5th Workshop on Algorithms and Data Structures, volume 72 of Lecture Notes in Computer Science, pages 354–367. Springer-Verlag, 1997.Google Scholar