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
Optimizing area and aspect ratio in straight-line orthogonal tree drawings
Computational Geometry: Theory and Applications
How to Draw a Planar Clustered Graph
COCOON '95 Proceedings of the First Annual International Conference on Computing and Combinatorics
Planarity for Clustered Graphs
ESA '95 Proceedings of the Third Annual European Symposium on Algorithms
Universality considerations in VLSI circuits
IEEE Transactions on Computers
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The visualization of clustered graphs is a classical algorithmic topic that has several practical applications and is attracting increasing research interest. In this paper we deal with the visualization of clustered trees, a problem that is somehow foundational with respect to the one of visualizing a general clustered graph. We show many, in our opinion, surprising results that put in evidence how drawing clustered trees has many sharp differences with respect to drawing ''plain'' trees. We study a wide class of drawing standards, giving both negative and positive results. Namely, we show that there are clustered trees that do not have any drawing in certain standards and others that require exponential area. On the contrary, for many drawing conventions there are efficient algorithms that allow to draw clustered trees with polynomial asymptotically-optimal area.