On embedding a graph in the grid with the minimum number of bends
SIAM Journal on Computing
Embedding rectilinear graphs in linear time
Information Processing Letters
Combinatorial algorithms for integrated circuit layout
Combinatorial algorithms for integrated circuit layout
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Optimal Compaction of Orthogonal Grid Drawings
Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization
Computing Orthogonal Drawings with the Minimum Number of 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
On linear area embedding of planar graphs
On linear area embedding of planar graphs
An Experimental Comparison of Orthogonal Compaction Algorithms (Extended Abstract)
GD '00 Proceedings of the 8th International Symposium on Graph Drawing
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We consider three closely related optimization problems, arising from the graph drawing and the VLSI research areas, and conjectured to be NP-hard, and we prove that, in fact, they are NP-complete. Starting from an orthogonal representation of a graph, i.e., a description of the shape of the edges that does not specify segment lengths or vertex positions, the three problems consist of providing an orthogonal grid drawing of it, while minimizing the area, the total edge length, or the maximum edge length, respectively.