Fundamentals of planar ordered sets
Discrete Mathematics
Algorithms for plane representations of acyclic digraphs
Theoretical Computer Science
SIAM Journal on Computing
Optimal Upward Planarity Testing of Single-Source Digraphs
SIAM Journal on Computing
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
Upward Planarity Checking: ``Faces Are More than Polygons''
GD '98 Proceedings of the 6th International Symposium on Graph Drawing
A Fixed-Parameter Approach to Two-Layer Planarization
GD '01 Revised Papers from the 9th International Symposium on Graph Drawing
On the Parameterized Complexity of Layered Graph Drawing
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Building blocks of upward planar digraphs
GD'04 Proceedings of the 12th international conference on Graph Drawing
Parameterized Complexity
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
Upward spirality and upward planarity testing
GD'05 Proceedings of the 13th international conference on Graph Drawing
Upward planarity testing via SAT
GD'12 Proceedings of the 20th international conference on Graph Drawing
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We consider the problem of testing a digraph G = (V,E) for upward planarity. In particular we present two fixed-parameter tractable algorithms for testing the upward planarity of G. Let n = |V|, let t be the number of triconnected components of G, and let c be the number of cut-vertices of G. The first upward planarity testing algorithm we present runs in O(2t · t! · n2)–time. The previously known best result is an O(t! · 8t · n3 + 23·2c · t3·2c · t! · 8t · n)-time algorithm by Chan. We use the kernelisation technique to develop a second upward planarity testing algorithm which runs in O(n2 + k4(2k + 1)!) time, where k = |E| – |V|. We also define a class of non upward planar digraphs.