Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Cone Trees: animated 3D visualizations of hierarchical information
CHI '91 Proceedings of the SIGCHI Conference on Human Factors in Computing Systems
A focus+context technique based on hyperbolic geometry for visualizing large hierarchies
CHI '95 Proceedings of the SIGCHI Conference on Human Factors in Computing Systems
Reconfigurable Disc Trees for Visualizing Large Hierarchical Information Space
INFOVIS '98 Proceedings of the 1998 IEEE Symposium on Information Visualization
Research report: Interacting with huge hierarchies: beyond cone trees
INFOVIS '95 Proceedings of the 1995 IEEE Symposium on Information Visualization
Circular drawings of rooted trees
Circular drawings of rooted trees
IEEE Transactions on Software Engineering
CGD --- A New Algorithm to Optimize Space Occupation in Ellimaps
INTERACT '09 Proceedings of the 12th IFIP TC 13 International Conference on Human-Computer Interaction: Part II
Smoother transitions between breadth-first-spanning-tree-based drawings
GD'06 Proceedings of the 14th international conference on Graph drawing
RELT: visualizing trees on mobile devices
VISUAL'07 Proceedings of the 9th international conference on Advances in visual information systems
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Among various styles of tree drawing, balloon drawing, where each subtree is enclosed in a circle, enjoys a desirable feature of displaying tree structures in a rather balanced fashion. We first design an efficient algorithm to optimize angular resolution and aspect ratio for the balloon drawing of rooted unordered trees. For the case of ordered trees for which the center of the enclosing circle of a subtree need not coincide with the root of the subtree, flipping the drawing of a subtree (along the axis from the parent to the root of the subtree) might change both the aspect ratio and the angular resolution of the drawing. We show that optimizing the angular resolution as well as the aspect ratio with respect to this type of rooted ordered trees is reducible to the perfect matching problem for bipartite graphs, which is solvable in polynomial time. Aside from studying balloon drawing from an algorithmic viewpoint, we also propose a local magnetic spring model for producing dynamic balloon drawings with applications to the drawings of galaxy systems, H-trees, and sparse graphs, which are of practical interest.