Upward Embeddings and Orientations of Undirected Planar Graphs
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
A Linear Time Implementation of SPQR-Trees
GD '00 Proceedings of the 8th International Symposium on Graph Drawing
A new approach for visualizing UML class diagrams
Proceedings of the 2003 ACM symposium on Software visualization
Automatic layout of UML class diagrams in orthogonal style
Information Visualization - Special issue: Software visualization
Maximum upward planar subgraphs of embedded planar digraphs
Computational Geometry: Theory and Applications
Drawing (Complete) Binary Tanglegrams
Graph Drawing
An Improved Upward Planarity Testing Algorithm and Related Applications
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Untangling Tanglegrams: Comparing Trees by Their Drawings
ISBRA '09 Proceedings of the 5th International Symposium on Bioinformatics Research and Applications
Layer-free upward crossing minimization
Journal of Experimental Algorithmics (JEA)
Improving the running time of embedded upward planarity testing
Information Processing Letters
The SPQR-tree data structure in graph drawing
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Maximum upward planar subgraphs of embedded planar digraphs
GD'07 Proceedings of the 15th international conference on Graph drawing
The number of plane diagrams of a lattice
ICFCA'08 Proceedings of the 6th international conference on Formal concept analysis
Layer-free upward crossing minimization
WEA'08 Proceedings of the 7th international conference on Experimental algorithms
Comparing trees via crossing minimization
Journal of Computer and System Sciences
Maximum upward planar subgraph of a single-source embedded digraph
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Untangling Tanglegrams: Comparing Trees by Their Drawings
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Upward Spirality and Upward Planarity Testing
SIAM Journal on Discrete Mathematics
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
Drawing graphs using modular decomposition
GD'05 Proceedings of the 13th international conference on Graph Drawing
Fixed-Parameter tractable algorithms for testing upward planarity
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
Comparing trees via crossing minimization
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
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
Upward planar drawings on the standing and the rolling cylinders
Computational Geometry: Theory and Applications
A linear time layout algorithm for business process models
Journal of Visual Languages and Computing
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A digraph is upward planar if it has a planar drawing such that all the edges are monotone with respect to the vertical direction. Testing upward planarity and constructing upward planar drawings is important for displaying hierarchical network structures, which frequently arise in software engineering, project management, and visual languages. In this paper we investigate upward planarity testing of single-source digraphs; we provide a new combinatorial characterization of upward planarity and give an optimal algorithm for upward planarity testing. Our algorithm tests whether a single-source digraph with n vertices is upward planar in O(n) sequential time, and in O(log n) time on a CRCW PRAM with $n \log \log n/\log n$ processors, using O(n,) space. The algorithm also constructs an upward planar drawing if the test is successful. The previously known best result is an O(n2)-time algorithm by Hutton and Lubiw [Proc. 2nd ACM--SIAM Symposium on Discrete Algorithms, SIAM, Philadelphia, 1991, pp. 203--211]. No efficient parallel algorithms for upward planarity testing were previously known.