- Optmization problems concerning geometric graphs such as augmenting the connectivity and multi-colored spanning graphs.
- Detecting crossings in drawings with overlapping vertices and edges.
- Simultanious drawings of graphs on the same point set.
- Relative Convex Hulls
- Simplex Range Searching
- Ray Shooting and Insertion
- Convex Partitioning
Data Depth extends the concept of univariate rank into higher dimensions. Essentially, given a cloud of points in n dimensions, how deep is a point, relative to the entire cloud? Additionally, we can use depth to determine the median of a multivariate data set.
- Topological Sweep in Degenerated Cases
- Topologically Sweeping the complete graph
- LMS Regression using Guided Topological Sweep
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The goal is to determine optimal data structures with the best possible performance. Our research has been focused on creating new and efficient geometric data structures that close the gaps between known lower and upper bounds. Particular topics include: Relative Convex Hulls; Simplex Range Searching; Ray Shooting and Insertion; Convex ...