Research Interests
I work in Algorithm Design and Computational Geometry. My main research focus has been on Meshing Algorithms. The goal of Meshing is to discretize a geometric domain into simple pieces such as triangles or tetrahedra. In particular, one seeks guarantees about the element-size, element-shape, output-size (number of elements) in the mesh, as well as the usual algorithmic guarantees on time and space complexity.

Currently, I spend most of my time on meshing algorithms with efficient worst-case asymptotic runtimes. Many meshing algorithms have $O(n^2)$ or worse runtime on bad inputs. We have shown that is possible and practical to reduce this to roughly $O(n\log n)$ using simple Sparse Refinement techniques to modify existing algorithms.