Predicting nearly as well as the best pruning of a planar decision graph
Theoretical Computer Science
GD '98 Proceedings of the 6th International Symposium on Graph Drawing
Maximum upward planar subgraphs of embedded planar digraphs
Computational Geometry: Theory and Applications
An Improved Upward Planarity Testing Algorithm and Related Applications
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Improving the running time of embedded upward planarity testing
Information Processing Letters
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
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
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
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
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An upward plane drawing of a directed acyclic graph is a plane drawing of the digraph in which each directed edge is represented as a curve monotone increasing in the vertical direction. Thomassen has given a nonalgorithmic, graph-theoretic characterization of those directed graphs with a single source that admit an upward plane drawing. This paper presents an efficient algorithm to test whether a given single-source acyclic digraph has an upward plane drawing and, if so, to find a representation of one such drawing. This result is made more significant in light of the recent proof by Garg and Tamassia that the problem is NP-complete for general digraphs. The algorithm decomposes the digraph into biconnected and triconnected components and defines conditions for merging the components into an upward plane drawing of the original digraph. To handle the triconnected components, we provide a linear algorithm to test whether a given plane drawing of a single-source digraph admits an upward plane drawing with the same faces and outer face, which also gives a simpler, algorithmic proof of Thomassen's result. The entire testing algorithm (for general single-source directed acyclic graphs) operates in $O(n^2)$ time and $O(n)$ space ($n$ being the number of vertices in the input digraph) and represents the first polynomial-time solution to the problem.