# Upward planar drawing of single source acyclic digraphs

@inproceedings{Hutton1991UpwardPD,
title={Upward planar drawing of single source acyclic digraphs},
author={Michael D. Hutton and Anna Lubiw},
booktitle={SODA '91},
year={1991}
}
• Published in SODA '91 1 March 1991
• Mathematics
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…
4 Citations
On Upward-Planar L-Drawings of Graphs
• Mathematics
ArXiv
• 2022
In an upward-planar L-drawing of a directed acyclic graph (DAG) each edge e is represented as a polyline composed of a vertical segment with its lowest endpoint at the tail of e and of a horizontal
Optimal Upward Planarity Testing of Single-Source Digraphs
• Computer Science
ESA
• 1993
This paper provides a new combinatorial characterization of upward planarity, and gives an optimal algorithm for upward planar testing of single-source digraphs, which was previously known.
A Parameterized Algorithm for Upward Planarity Testing of Biconnected Graphs
• H. Chan
• Computer Science, Mathematics
• 2003
This thesis investigates contracting an edge in an upward planar graph that has a specified embedding, and shows that it is possible to determine whether or not the resulting embedding is upwards planar given the orientation of the clockwise and counterclockwise neighbours of the given edge.
Comparison of Maximal Upward Planar Subgraph Computation Algorithms
• A. Rextin
• Mathematics
2012 10th International Conference on Frontiers of Information Technology
• 2012
Different algorithms to find maximal upward planar subgraph of an embedded digraph are compared to gain a deeper understanding of upward planarity and see how the different heuristics perform in practice.
Upward Planarity Testing in Practice
• Computer Science, Mathematics
ACM J. Exp. Algorithmics
• 2015
Two fundamentally different approaches based on the seemingly novel concept of ordered embeddings and on the concept of a Hanani-Tutte-type characterization of monotone drawings are proposed and it is shown that the SAT formulations outperform all known approaches for graphs with up to 400 edges.
Upward planarity testing
• Computer Science
• 1995
This survey paper sketches the proof of NP-completeness of upward planarity testing and presents several characterizations of downward planarity and describes upward plan parity testing algorithms for special classes of digraphs, such as embedded digraphS and single-source digraph's.
Upward Planarity Testing via SAT
• Computer Science
Graph Drawing
• 2012
A fundamentally different approach is proposed, based on the seemingly novel concept of ordered embeddings, to decide upward planarity for arbitrary graphs, which seems to dominate the known alternative approaches and is able to solve traditionally used graph drawing benchmarks effectively.
On the Computational Complexity of Upward and Rectilinear Planarity Testing
• Computer Science
SIAM J. Comput.
• 2001
It is shown that upward planarity testing and rectilinear planar testing are NP-complete problems and that it is NP-hard to approximate the minimum number of bends in a planar orthogonal drawing of an n-vertex graph with an $O(n^{1-\epsilon})$ error for any $\ep silon > 0$.
Area requirement and symmetry display of planar upward drawings
• Mathematics
Discret. Comput. Geom.
• 1992
A linear-time algorithm is presented that produces drawings of planar acyclic digraphs with a small number of bends, asymptotically optimal area, and such that symmetries and isomorphisms of the digraph are displayed.
Upward drawings of triconnected digraphs
• Mathematics
Algorithmica
• 2005
A polynomial-time algorithm for testing if a triconnected directed graph has an upward drkwing is presented, based on a new combinatorial characterization that maps the problem into a max-flow problem on a sparse network.

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