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
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
Upward Planarity Testing of Outerplanar Dags
GD '94 Proceedings of the DIMACS International Workshop on Graph Drawing
Small area drawings of outerplanar graphs
GD'05 Proceedings of the 13th international conference on Graph Drawing
| Hi-index | 0.02 |
It has been shown in [9] that there exist planar digraphs that require exponential area in every upward straight-line planar drawing. On the other hand, upward poly-line planar drawings of planar graphs can be realized in Θ(n2) area [9]. In this paper we consider families of DAGs that naturally arise in practice, like DAGs whose underlying graph is a tree (directed trees), is a bipartite graph (directed bipartite graphs), or is an outerplanar graph (directed outerplanar graphs). Concerning directed trees, we show that optimal Θ(n log n) area upward straight-line/polyline planar drawings can be constructed. However, we prove that if the order of the neighbors of each node is assigned, then exponential area is required for straight-line upward drawings and quadratic area is required for poly-line upward drawings, results surprisingly and sharply contrasting with the area bounds for planar upward drawings of undirected trees. After having established tight bounds on the area requirements of planar upward drawings of several families of directed trees, we show how the results obtained for trees can be exploited to determine asymptotic optimal values for the area occupation of planar upward drawings of directed bipartite graphs and directed outerplanar graphs.