Computer Science – Computational Geometry
Scientific paper
2010-12-08
Computer Science
Computational Geometry
Scientific paper
Treemaps are a popular technique to visualize hierarchical data. The input is a weighted tree $\tree$ where the weight of each node is the sum of the weights of its children. A treemap for $\tree$ is a hierarchical partition of a rectangle into simply connected regions, usually rectangles. Each region represents a node of $\tree$ and its area is proportional to the weight of the corresponding node. An important quality criterion for treemaps is the aspect ratio of its regions. One cannot bound the aspect ratio if the regions are restricted to be rectangles. In contrast, \emph{polygonal partitions}, that use convex polygons, have bounded aspect ratio. We are the first to obtain convex partitions with optimal aspect ratio $O(\depth(\tree))$. However, $\depth(\tree)$ still depends on the input tree. Hence we introduce a new type of treemaps, namely \emph{orthoconvex treemaps}, where regions representing leaves are rectangles, L-, and S-shapes, and regions representing internal nodes are orthoconvex polygons. We prove that any input tree, irrespective of the weights of the nodes and the depth of the tree, admits an orthoconvex treemap of constant aspect ratio. We also obtain several specialized results for single-level treemaps, that is, treemaps where the input tree has depth~1.
Berg Mark de
der Weele Vincent van
Speckmann Bettina
No associations
LandOfFree
Treemaps with Bounded Aspect Ratio does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Treemaps with Bounded Aspect Ratio, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Treemaps with Bounded Aspect Ratio will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-558565