I am also engaging in research problems with computer scientists in computational geometry. This work mostly involved convex optimization and path planning. The most interesting contribution was on finding geometric flows via dual programs. This introduced an idea using potentials, which has also played a significant role in my research on continuous modulus.
The goal with this research is to develop algorithms for discrete and geometric problems, and to study the efficient computability of various geometric problems. This is also an area that is excellent for undergraduate research. If you would be interested to study algorithmic problems involving games and geometry, feel free to contact me.
- Geometric k shortest paths, joint with J. Hershberger, V. Polishchuk, B. Speckmann, S. Suri, T. Talvitie, K. Verbeek, H. Yıldız. Soda 2015.
- Optimal geometric flows via dual programs, joint with V. Polishchuk, M. Sysikaski. SoCG 2014
- Optimization schemes for protective jamming, (minor contribution) joint with S. Sankararaman, K. Abu-Affash, A. Efrat, V. Polishchuk, S. Ramasubramanian, M. Segal. MobiHoc 2012.
- On Polygonal Paths with Bounded Discrete-Curvature: The Inflection-Free Case, joint with D. Kirkpatrick, V. Polishchuk. JCDCGG 2013.
- Importance Sampling for a Monte Carlo Matrix Multiplication Algorithm, with Application to Information Retrieval , coauthored with Mary Solbrig, Michael Stefanelli, Sarah Warkentin, Ralph Abbey and Ilse Ipsen, 2011.