On embedding a graph in the grid with the minimum number of bends
SIAM Journal on Computing
Algorithms for plane representations of acyclic digraphs
Theoretical Computer Science
Area requirement and symmetry display of planar upward drawings
Discrete & Computational Geometry
Algorithms for drawing graphs: an annotated bibliography
Computational Geometry: Theory and Applications
SIAM Journal on Computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Recognizing Leveled-Planar Dags in Linear Time
GD '95 Proceedings of the Symposium on Graph Drawing
Straight-Line Drawing Algorithms for Hierarchical Graphs and Clustered Graphs
GD '96 Proceedings of the Symposium on Graph Drawing
Pitfalls of Using PQ-Trees in Automatic Graph Drawing
GD '97 Proceedings of the 5th International Symposium on Graph Drawing
On the Compuational Complexity of Upward and Rectilinear Planarity Testing
GD '94 Proceedings of the DIMACS International Workshop on Graph Drawing
Graph Theory With Applications
Graph Theory With Applications
An approximation algorithm for the two-layered graph drawing problem
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Upward Spirality and Upward Planarity Testing
SIAM Journal on Discrete Mathematics
Hanani-Tutte and monotone drawings
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
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Hierarchical graphs are an important class of graphs for modeling many real applications in software and information visualization. In this paper, we investigate area requirements for drawing hierarchically planar graphs regarding two different drawing standards. Firstly, we show an exponential lower bound for the area needed for straight-line drawing of hierarchically planar graphs. The lower bound holds even for s-t hierarchical graphs without transitive arcs, in contrast to the results for upward planar drawing. This motivates our investigation of another drawing standard grid visibility representation, as a relaxation of straight-line drawing. An application of the existing results from upward drawing can guarantee a quadric drawing area for grid visibility representation but does not necessarily guarantee the minimum drawing area. Motivated by this, we will present a new grid visibility drawing algorithm which is efficient and guarantees the minimum drawing area with respect to a given topological embedding. This implies that the area minimization problem is polynomial time solvable restricted to the class of graphs whose planar embeddings are unique. However, we can show that the problem of area minimization of grid visibility for hierarchically planar graphs is generally NP-hard, even restricted to s-t graphs.