Three Approaches to 3DOrthogonal BoxDrawings (Extended Abstract)Biedl, Therese (1998) Three Approaches to 3DOrthogonal BoxDrawings (Extended Abstract). In: Graph Drawing 6th International Symposium, GD’ 98, August 1315, 1998 , pp. 3043(Official URL: http://dx.doi.org/10.1007/3540376232_3). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/3540376232_3
AbstractIn 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 3Ddrawings; we call these approaches edgelifting, halfedgelifting, and threephasemethod. Let G be a graph with n vertices, m edges, and maximum degree \Delta. We obtain a drawing of G in an n \times n \times \Deltagrid 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 gridplane, and exhibit constructions in an n \times n \times mgrid and a lower bound of \Omega (m²); hence upper and lower bounds match for graphs with \Theta (n²) edges.
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