Tree visualization with tree-maps: 2-d space-filling approach
ACM Transactions on Graphics (TOG)
An evaluation of space-filling information visualizations for depicting hierarchical structures
International Journal of Human-Computer Studies - Empirical evaluation of information visualizations
Ordered and quantum treemaps: Making effective use of 2D space to display hierarchies
ACM Transactions on Graphics (TOG)
TennisViewer: A Browser for Competition Trees
IEEE Computer Graphics and Applications
Cushion Treemaps: Visualization of Hierarchical Information
INFOVIS '99 Proceedings of the 1999 IEEE Symposium on Information Visualization
INFOVIS '01 Proceedings of the IEEE Symposium on Information Visualization 2001 (INFOVIS'01)
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Tree-Maps: a space-filling approach to the visualization of hierarchical information structures
VIS '91 Proceedings of the 2nd conference on Visualization '91
Improving the visualization of hierarchies with treemaps: design issues and experimentation
VIS '92 Proceedings of the 3rd conference on Visualization '92
Dimension reduction for ultrametrics
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Low distortion maps between point sets
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Voronoi treemaps for the visualization of software metrics
SoftVis '05 Proceedings of the 2005 ACM symposium on Software visualization
Low-distortion embeddings of general metrics into the line
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
The complexity of low-distortion embeddings between point sets
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for low-distortion embeddings into low-dimensional spaces
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
The Effect of Animated Transitions on User Navigation in 3D Tree-Maps
IV '05 Proceedings of the Ninth International Conference on Information Visualisation
INFOVIS '05 Proceedings of the Proceedings of the 2005 IEEE Symposium on Information Visualization
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Embedding ultrametrics into low-dimensional spaces
Proceedings of the twenty-second annual symposium on Computational geometry
Embedding into l2∞ is easy embedding into l2∞ is NP-complete
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
The geometry of graphs and some of its algorithmic applications
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
On the hardness of embeddings between two finite metrics
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Treemaps with bounded aspect ratio
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Proceedings of the 6th International Symposium on Visual Information Communication and Interaction
Visualizing large trees with divide & conquer partition
Proceedings of the 6th International Symposium on Visual Information Communication and Interaction
Treemaps with bounded aspect ratio
Computational Geometry: Theory and Applications
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We introduce a hierarchical partitioning scheme of the Euclidean plane, called circular partitions. Such a partition consists of a hierarchy of convex polygons, each having small aspect ratio, and satisfying specified volume constraints. We apply these partitions to obtain a natural extension of the popular Treemap visualization method. Our proposed algorithm is not constrained in using only rectangles, and can achieve provably better guarantees on the aspect ratio of the constructed polygons. Under relaxed conditions, we can also construct circular partitions in higher-dimensional spaces. We use these relaxed partitions to obtain improved approximation algorithms for embedding ultrametrics into d-dimensional Euclidean space. In particular, we give a polylog(Delta)-approximation algorithm for embedding n-point ultrametrics into R^d with minimum distortion (Delta denotes the spread of the metric). The previously best-known approximation ratio for this problem was polynomial in n [Badoiu et al. SoCG 2006]. This is the first algorithm for embedding a non-trivial family of weighted graph metrics into a space of constant dimension that achieves polylogarithmic approximation ratio.