Fundamentals of planar ordered sets
Discrete Mathematics
Algorithms for plane representations of acyclic digraphs
Theoretical Computer Science
Area requirement and symmetry display of planar upward drawings
Discrete & Computational Geometry
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
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
Evaluating monotone circuits on cylinders, planes and tori
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
A global k-level crossing reduction algorithm
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
Classification of planar upward embedding
GD'11 Proceedings of the 19th international conference on Graph Drawing
Upward planar drawings on the standing and the rolling cylinders
Computational Geometry: Theory and Applications
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We consider directed graphs with an upward planar drawing on the plane, the sphere, the standing and the rolling cylinders. In general, the drawings allow complex curves for the edges with many zig-zags and windings around the cylinder and the sphere. The drawings are simplified to polyline drawings with geodesics as straight segments and vertices and bends at grid points. On the standing cylinder the drawings have at most two bends per edge and no windings of edges around the cylinder. On the rolling cylinder edges may have one winding and five bends, and there are graphs where edges must wind. The drawings have a discrete description of linear size. The simplifications can be computed efficiently in O(τ n3) time, where τ is the cost of computing the point of intersection of a curve and a horizontal line through a vertex. The time complexity does not depend on the description complexity of the drawing and its curves, but only on O(n3) sample points.