Fundamentals of planar ordered sets
Discrete Mathematics
Algorithms for plane representations of acyclic digraphs
Theoretical Computer Science
Representations of graphs on a cylinder
SIAM Journal on Discrete Mathematics
Light sources, obstructions and spherical orders
Discrete Mathematics
Area requirement and symmetry display of planar upward drawings
Discrete & Computational Geometry
Optimal Upward Planarity Testing of Single-Source Digraphs
SIAM Journal on Computing
Embedding planar graphs on the grid
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Discrete Mathematics
Graph Drawing: Algorithms for the Visualization of Graphs
Graph Drawing: Algorithms for the Visualization of Graphs
On the Computational Complexity of Upward and Rectilinear Planarity Testing
SIAM Journal on Computing
Recognizing Leveled-Planar Dags in Linear Time
GD '95 Proceedings of the Symposium on Graph Drawing
Implementing a General-Purpose Edge Router
GD '97 Proceedings of the 5th International Symposium on Graph Drawing
Fast and Simple Horizontal Coordinate Assignment
GD '01 Revised Papers from the 9th International Symposium on Graph Drawing
A Radial Adaptation of the Sugiyama Framework for Visualizing Hierarchical Information
IEEE Transactions on Visualization and Computer Graphics
Linear Time Planarity Testing and Embedding of Strongly Connected Cyclic Level Graphs
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Coordinate Assignment for Cyclic Level Graphs
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Upper Bounds for Monotone Planar Circuit Value and Variants
Computational Complexity
Cyclic level planarity testing and embedding
GD'07 Proceedings of the 15th international conference on Graph drawing
Plane drawings of queue and deque graphs
GD'10 Proceedings of the 18th international conference on Graph drawing
Evaluating monotone circuits on cylinders, planes and tori
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Characterizations of deque and queue graphs
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
Classification of planar upward embedding
GD'11 Proceedings of the 19th international conference on Graph Drawing
The duals of upward planar graphs on cylinders
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
On the curve complexity of upward planar drawings
CATS '12 Proceedings of the Eighteenth Computing: The Australasian Theory Symposium - Volume 128
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We consider directed graphs with an upward planar drawing on the standing and the rolling cylinders. These graphs properly extend the upward planar graphs in the plane. The drawings allow complex curves for the edges with many zig-zags and windings around the cylinder. We show that the drawings can be simplified to polyline drawings with geodesics as straight segments, at most two bends per edge, and vertices and bends on a grid of at most cubic size. On the standing cylinder the edges do not wind and they wind at most once around the rolling cylinder, where single windings can be unavoidable. The simplifications can be computed efficiently in O(@tn^3) time, where @t is the cost of computing the point of intersection of a curve and a horizontal line through a vertex. Moreover, we provide a complete classification of the classes of (regular) upward planar drawable graphs on the plane, the sphere, and the standing and rolling cylinders including their strict and weak variants. Strict is upward in two dimensions and weak allows horizontal lines. For upward planarity the standing and the rolling cylinders coincide in the strict case, rolling dominates standing in the regular case, and there is an incomparability in the weak case. The respective classes of graphs range properly between the upward planar and the quasi-upward planar graphs, and they have an NP-hard recognition problem.