I am in my third year as a PhD candidate in Computer Science at CMU, advised by Gary Miller. My primary research interest is in Computational Geometry. Lately, this work has been focused on designing new algorithms for producing quality meshes to be used in scientific computing applications.

I am part of the Algorithms and Computational Complexity Group at CMU (I also update the webpage). I also help coordinate the weekly Theory Lunch.

Resume/CV: [PDF],[PS]

Research

1. Size Competitive Meshing With No Large Angles
   Joint work with Gary Miller and Todd Phillips
   ICALP 2007
   ICALP Version [PDF]

2. Compatible Triangulations and Point Partitions by Series Triangular Graphs
   Joint work with Jeff Danciger and Satyan Devadoss
   Computational Geometry: Theory and Applications 34 (2006) 195-202.
   [PDF]

3. A Homotopic Approach to Cartographic Generalizations
   Joint work with Jeff Danciger, Satyan Devadoss, John Mugno, and Rachel Ward
   preprint
   [PDF]

4. The Complexity of Domino Tiling Problems
   Senior Independent Research, Princeton University 2005
   Advised by Kevin Wayne
   [PDF]

Talks

1. Flips in Computational Geometry
   In this talk, we will be looking at a basic primitive in computational geometry, the flip. Also known as bistellar flips, edge-flips, rotations, and Pachner moves, this local change operation has been discovered and rediscovered in a variety of fields (thus the many names) and has proven useful both as an algorithmic tool as well as a proof technology. For algorithm designers working outside of computational geometry, one can consider the flip move as a higher dimensional analog of the tree rotations used in binary trees. I will survey some of the most important results about flips with an emphasis on developing a general geometric intuition that has led to many advances.
   
   Presented at Theory Lunch, Carnegie Mellon University, Nov. 15, 2006
   [PPT]

2. A Competitive Algorithm for No-Large-Angle Triangulation
   In this talk, I will present Overlay Stitch Meshing, a novel new algorithm that simultaneously solves two different problems in the field of triangulating planar straight-line graphs in the plane for scientific computing applications:
   1. It is the first Delaunay Refinement-type triangulation algorithm that terminates with a full complement of guarantees even on degenerate inputs and with no dependence on the size of the smallest input angle.
   2. It is the first algorithm that gives a log n competitive output size for the problem of no-large-angle triangulation with Steiner points.
   The workings of the algorithm are very easy to state and understand. The brunt of the talk will focus on new analytic techniques that allow us to prove strong guarantees.
   
   Presented at Theory Lunch, Carnegie Mellon University, May 2, 2007
   Short Version[PPT]
   Long Version[PPT]

Also in the works

Diagonal 2D ECC for Caches
Joint work with Michael Dinitz for CMU 15-741: Advanced Computer Architecture
We pose a formal version of the 2D error-correcting code problem. We prove lower bounds on the number of bits needed for such a scheme. We also present a new scheme that achieves matching upper bounds.
[POSTER]