David Eppstein

TL;DR: The main result is that a polygon with n sides can be triangulated with O(n2) nonobtuse triangles, and it is shown that any triangulation (without Steiner points) of a simple polygon has a refinement with O('n4' nonobTuse triangles.

TL;DR: The results explore what is achievable with straight-line drawings and what more is achieving with Lombardi-style drawings, with respect to drawings of trees with perfect angular resolution.

TL;DR: Using dynamic data structures for half-space range reporting and for maintaining the minima of a decomposable function, the authors obtain efficient dynamic algorithms for a number of geometric problems, including closest/farthest neighbor searching, fixed dimension linear programming, bi-chromatic closest pair, diameter, and Euclidean minimum spanning tree.

TL;DR: In this article, the authors describe algorithms and data structures for maintaining a dynamic planar graph subject to edge insertions and edge deletions that preserve planarity but that can change the embedding.

TL;DR: Deterministic techniques are used to approximate several robust statistics of geometric data streams, including Tukey depth, simplicial depth, regression depth, the Thiel-Sen estimator, and the least median of squares, using only a polylogarithmic amount of memory.