On embedding a graph in the grid with the minimum number of bends
SIAM Journal on Computing
Algorithms for drawing graphs: an annotated bibliography
Computational Geometry: Theory and Applications
An experimental comparison of four graph drawing algorithms
Computational Geometry: Theory and Applications
Algorithms for area-efficient orthogonal drawings
Computational Geometry: Theory and Applications - Special issue on geometric representations of graphs
A better heuristic for orthogonal graph drawings
Computational Geometry: Theory and Applications
Three-Dimensional VLSI: a case study
Journal of the ACM (JACM)
Orthogonal Drawing of High Degree Graphs with Small Area and Few Bends
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
Drawing High Degree Graphs with Low Bend Numbers
GD '95 Proceedings of the Symposium on Graph Drawing
Two Algorithms for Three Dimensional Orthogonal Graph Drawing
GD '96 Proceedings of the Symposium on Graph Drawing
The Three-Phase Method: A Unified Approach to Orthogonal Graph Drawing
GD '97 Proceedings of the 5th International Symposium on Graph Drawing
Algorithms and Area Bounds for Nonplanar Orthogonal Drawings
GD '97 Proceedings of the 5th International Symposium on Graph Drawing
Incremental Orthogonal Graph Drawing in Three Dimensions
GD '97 Proceedings of the 5th International Symposium on Graph Drawing
GD '97 Proceedings of the 5th International Symposium on Graph Drawing
Area-Efficient Static and Incremental Graph Drawings
ESA '97 Proceedings of the 5th Annual European Symposium on Algorithms
Three-Dimensional Orthogonal Graph Drawing with Optimal Volume
GD '00 Proceedings of the 8th International Symposium on Graph Drawing
Optimal three-dimensional orthogonal graph drawing in the general position model
Theoretical Computer Science
A multi-dimensional approach to force-directed layouts of large graphs
Computational Geometry: Theory and Applications - Special issue on the 10th fall workshop on computational geometry
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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 驴. We obtain a drawing of G in an n 脳 n 脳 驴-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 脳 n 脳 m-grid and a lower bound of 驴(m2); hence upper and lower bounds match for graphs with 驴(n2) edges.