Computing Orthogonal Drawings with the Minimum Number of Bends
IEEE Transactions on Computers
ESA '00 Proceedings of the 8th Annual European Symposium on Algorithms
Drawings of planar graphs with few slopes and segments
Computational Geometry: Theory and Applications
Complexity results for three-dimensional orthogonal graph drawing
Journal of Discrete Algorithms
Maximum upward planar subgraphs of embedded planar digraphs
Computational Geometry: Theory and Applications
Connected Rectilinear Graphs on Point Sets
Graph Drawing
An Improved Upward Planarity Testing Algorithm and Related Applications
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
On the two-dimensional orthogonal drawing of series-parallel graphs
Discrete Applied Mathematics
Layer-free upward crossing minimization
Journal of Experimental Algorithmics (JEA)
Improving the running time of embedded upward planarity testing
Information Processing Letters
On embedding a graph in the grid with the maximum number of bends and other bad features
FUN'07 Proceedings of the 4th international conference on Fun with algorithms
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Maximum upward planar subgraphs of embedded planar digraphs
GD'07 Proceedings of the 15th international conference on Graph drawing
Layer-free upward crossing minimization
WEA'08 Proceedings of the 7th international conference on Experimental algorithms
Maximum upward planar subgraph of a single-source embedded digraph
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Upward Spirality and Upward Planarity Testing
SIAM Journal on Discrete Mathematics
GD'10 Proceedings of the 18th international conference on Graph drawing
Orthogonal graph drawing with flexibility constraints
GD'10 Proceedings of the 18th international conference on Graph drawing
Complexity of finding non-planar rectilinear drawings of graphs
GD'10 Proceedings of the 18th international conference on Graph drawing
Volume requirements of 3d upward drawings
GD'05 Proceedings of the 13th international conference on Graph Drawing
Upward spirality and upward planarity testing
GD'05 Proceedings of the 13th international conference on Graph Drawing
No-bend orthogonal drawings of series-parallel graphs
GD'05 Proceedings of the 13th international conference on Graph Drawing
Orthogonal drawings and crossing numbers of the Kronecker product of two cycles
Journal of Parallel and Distributed Computing
Orthogonal drawings of series-parallel graphs with minimum bends
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Computing upward planar drawings using switch-regularity heuristics
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
Fixed-Parameter tractable algorithms for testing upward planarity
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
Really straight graph drawings
GD'04 Proceedings of the 12th international conference on Graph Drawing
Approximating precedence-constrained single machine scheduling by coloring
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
On the perspectives opened by right angle crossing drawings
GD'09 Proceedings of the 17th international conference on Graph Drawing
On rectilinear drawing of graphs
GD'09 Proceedings of the 17th international conference on Graph Drawing
Switch-Regular upward planar embeddings of trees
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
GD'11 Proceedings of the 19th international conference on Graph Drawing
GD'11 Proceedings of the 19th international conference on Graph Drawing
Classification of planar upward embedding
GD'11 Proceedings of the 19th international conference on Graph Drawing
Upward planarity testing of embedded mixed graphs
GD'11 Proceedings of the 19th international conference on Graph Drawing
On the hardness of point-set embeddability
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
Simultaneous embedding of embedded planar graphs
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Drawing planar graphs on points inside a polygon
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
The duals of upward planar graphs on cylinders
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Open rectangle-of-influence drawings of non-triangulated planar graphs
GD'12 Proceedings of the 20th international conference on Graph Drawing
Toward a theory of planarity: hanani-tutte and planarity variants
GD'12 Proceedings of the 20th international conference on Graph Drawing
GD'12 Proceedings of the 20th international conference on Graph Drawing
Upward planarity testing via SAT
GD'12 Proceedings of the 20th international conference on Graph Drawing
Optimal orthogonal graph drawing with convex bend costs
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Dimension and height for posets with planar cover graphs
European Journal of Combinatorics
Upward planar drawings on the standing and the rolling cylinders
Computational Geometry: Theory and Applications
A linear time algorithm for testing maximal 1-planarity of graphs with a rotation system
Theoretical Computer Science
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A directed graph is upward planar if it can be drawn in the plane such that every edge is a monotonically increasing curve in the vertical direction and no two edges cross. An undirected graph is rectilinear planar if it can be drawn in the plane such that every edge is a horizontal or vertical segment and no two edges cross. Testing upward planarity and rectilinear planarity are fundamental problems in the effective visualization of various graph and network structures. For example, upward planarity is useful for the display of order diagrams and subroutine-call graphs, while rectilinear planarity is useful for the display of circuit schematics and entity-relationship diagrams. We show that upward planarity testing and rectilinear planarity testing are NP-complete problems. We also show that it is NP-hard to approximate the minimum number of bends in a planar orthogonal drawing of an n-vertex graph with an $O(n^{1-\epsilon})$ error for any $\epsilon 0$.