Fundamentals of planar ordered sets
Discrete Mathematics
Algorithms for plane representations of acyclic digraphs
Theoretical Computer Science
Bipartite graphs, upward drawings, and planarity
Information Processing Letters
Area requirement and symmetry display of planar upward drawings
Discrete & Computational Geometry
A note on optimal area algorithms for upward drawings of binary trees
Computational Geometry: Theory and Applications
A note on minimum-area upward drawing of complete and Fibonacci trees
Information Processing Letters
SIAM Journal on Computing
Optimal Upward Planarity Testing of Single-Source Digraphs
SIAM Journal on Computing
Linear area upward drawings of AVL trees
Computational Geometry: Theory and Applications - Special issue on geometric representations of graphs
Spirality and Optimal Orthogonal Drawings
SIAM Journal on Computing
Area-efficient algorithms for straight-line tree drawings
Computational Geometry: Theory and Applications
Upward Planar Drawing of Single-Source AcyclicDigraphs
SIAM Journal on Computing
On the Computational Complexity of Upward and Rectilinear Planarity Testing
SIAM Journal on Computing
Pitfalls of Using PQ-Trees in Automatic Graph Drawing
GD '97 Proceedings of the 5th International Symposium on Graph Drawing
Upward Planarity Testing of Outerplanar Dags
GD '94 Proceedings of the DIMACS International Workshop on Graph Drawing
Towards area requirements for drawing hierarchically planar graphs
Theoretical Computer Science - Algorithms,automata, complexity and games
IEEE Transactions on Software Engineering
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A digraph is upward planar if it admits a planar drawing where all edges are monotone in the upward direction. It is known that the problem of testing a digraph for upward planarity is NP-complete in general. This paper describes an $O(n^4)$-time upward planarity testing algorithm for all digraphs that have a series-parallel structure, where $n$ is the number of vertices of the input. This significantly enlarges the family of digraphs for which a polynomial-time testing algorithm is known. Furthermore, the study is extended to general digraphs, and a fixed parameter tractable algorithm for upward planarity testing is described, whose time complexity is $O(d^t \cdot t \cdot n^3 + d \cdot t^2 \cdot n + d^2 \cdot n^2)$ where $t$ is the number of triconnected components of the digraph and $d$ is an upper bound on the diameter of any split component of the digraph. Our results use the new notion of upward spirality that, informally speaking, is a measure of the “level of winding” that a triconnected component of a digraph $G$ can have in an upward planar drawing of $G$.