Three-Dimensional Orthogonal Graph Drawing with Optimal Volume

An orthogonal drawing of a graph is an embedding of the graph in the rectangular grid, with vertices represented by axis-aligned boxes, and edges represented by paths in the grid which only possibly intersect at common endpoints. In this paper, we study three-dimensional orthogonal drawings and provide lower bounds for three scenarios: (1) drawings where vertices have bounded aspect ratio, (2) drawings where the surface of vertices is proportional to their degree, and (3) drawings without any such restrictions. Then we show that these lower bounds are asymptotically optimal, by providing constructions that match the lower bounds in all scenarios within an order of magnitude. A preliminary version of this paper was presented at the 8th International Symposium on Graph Drawing (GD 2000), Colonial Williamsburg, Virginia, USA, September 20-23, 2000. Partially completed while a Ph.D. student under the supervision of Dr Graham Farr in the School of Computer Science and Software Engineering...

• Type: Conference
• Year: 2000
• Where: GD
• Authors: Therese C. Biedl, Torsten Thiele, David R. Wood
• Keywords: Computer Graphics, GD 2000, Lower Bounds, Orthogonal Drawings, Three-dimensional Orthogonal Drawings