Research

I am broadly interested in algorithms and optimization problems that arise in practical geometric settings. In particular, I study combinatorics and complexity in path routing, guarding, and other visibility problems.

Journal Articles

The Art Gallery Theorem for Simple Polygons in Terms of the Number of Reflex and Convex Vertices
(joint work with Joseph S. B. Mitchell)
Information Processing Letters, Volume  112, Issue 20, 2012, pages 778-782.

The Art Gallery Theorem for Polyominoes
(joint work with Therese Biedl, Mohammed T. Irfan, Joondong Kim, Joseph S. B. Mitchell)
Discrete and Computational Geometry, Volume 48, Number 3, 2012, pages 711-720.

Verification and Validation of a Method for the Simulation of Turbulent Mixing
(joint work with Hyunkyung Lim, Yan Yu, James Glimm and David H. Sharp)
Physica Scripta
,Volume T142, 2010, pages 014014.

Nonideal Rayleigh-Taylor Mixing
(joint work with Hyunkyung Lim, James Glimm, David H. Sharp)
Proceedings of the National Academy of Sciences of the United States of America, Volume 107, Number 29, 2010, pages 12786-12792.

• Conference Papers

Combinatorics of Edge 2-transmitter Art Gallery Problems
(joint work with Sarah Cannon, Thomas G. Fai, Undine Leopold, Christiane Schmidt)
in Proceedings of the 31st European Workshop on Computational Geometry (EuroCG 2015), Ljubljana, Slovenia, March 15-18, 2015.

NP-hardness of the Minimum Point and Edge 2-transmitter Cover Problem
(joint work with Sarah Cannon, Thomas G. Fai, Undine Leopold, Christiane Schmidt)
in Proceedings of the 24th Fall Workshop on Computational Geometry (FWCG 2014),
Storrs, CT, October 31-November 1, 2014.

Tetrahedron Contact Graphs
(joint work with Md. Jawaherul Alam, Muriel Dulieu, Joseph O’Rourke)
in Proceedings of the 23rd Fall Workshop on Computational Geometry (FWCG 2013), New York, NY, October 25-26, 2013.

Beacon-Based Algorithms for Geometric Routing
(joint work with Michael Biro, Irina Kostitsyna, Joseph S. B. Mitchell)
in Proceedings of the 13th Algorithms and Data Structures Symposium (WADS 2013), London, Ontario, Canada, August 12-14, 2013.

Combinatorics of Beacon Routing and Coverage
(joint work with Michael Biro, Jie Gao, Irina Kostitsyna, Joseph S. B. Mitchell)
in Proceedings of the 25th Canadian Conference on Computational Geometry (CCCG 2013), Waterloo, Ontario, Canada, August 8-10, 2013.

Watchman Paths in Disk Grids
(joint work with Michael Biro)
in Proceedings of the 22nd Fall Workshop on Computational Geometry (FWCG 2012), College Park, MD, November 9-10, 2012.

Guarding Polyforms
in Abstracts of the 1st Computational Geometry: Young Researchers Forum (CG:YRF 2012), Chapel Hill, NC, June 17-19, 2012.

Beacon-Based Structures in Polygonal Domains
(joint work with Michael BiroJie GaoIrina KostitsynaJoseph S. B. Mitchell)
in Abstracts of the 1st Computational Geometry: Young Researchers Forum (CG:YRF 2012), Chapel Hill, NC, June 17-19, 2012.

Beacon-Based Routing and Coverage
(joint work with Michael Biro, Jie Gao, Irina Kostitsyna, Joseph S. B. Mitchell)
in Proceedingss of the 21st Fall Workshop on Computational Geometry (FWCG 2011), New York, NY, November 4-5, 2011, pages 16-17.

Spiral Serpentine Polygonization of a Planar Point Set
(joint work with Joseph S. B. Mitchell)
in Revised Selected Papers from the Proceedings of XIV Spanish Meeting on Computational Geometry (EGC 2011), Lecture Notes in Computer Science 7579, 2012, pages 146-154.

Guarding Polyominoes
(joint work with Therese Biedl, Mohammed T. Irfan, Joondong Kim, Joseph S. B. Mitchell)
in Proceedings of the 27th Annual Symposium on Computational Geometry (SoCG 2011), Paris, France, June 13-15, 2011, pages 387-396; in Proceedings of the 19th Annual Fall Workshop on Computational Geometry (FWCG 2009), Medford, MA, November 13-14, 2009, pages 39-40.

• Presentations

Tetrahedron Contact Graphs
23rd Fall Workshop on Computational Geometry, Oct 25-26, 2013, City College of New York, NY

Guarding Polyforms
1st Computational Geometry: Young Researchers Forum, June 17-19, 2012, Chapel Hill, NC

Guarding Polyominoes
27th Annual Symposium on Computational Geometry, June 13-15, 2011, Paris, France
19th Fall Workshop on Computational Geometry, Nov 13-14, 2009, Tufts University, Medford, MA

Spiral Serpentine Polygonization of a Planar Point Set
Graduate Research Conference, April 29, 2011, Stony Brook University, Stony Brook, NY

• Theses

Combinatorics and Complexity in Geometric Visibility Problems
Ph.D. Thesis, Stony Brook University, 2012.

Design Principles for Next Generation Algebra One Video Games
Honors Thesis, University of Massachusetts Amherst, 2004.

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