My research is broadly in the areas of computational geometry and graph theory, inspired by problems in wireless networks, graphics, robotics and computational biology. My recent work includes theoretical results on geometric graphs for wireless communication, modular robot reconfiguration, polyhedra unfolding and DNA computing.
Geometric Graphs for Directional Communication
This research project studies fundamental combinatorial, geometric, and graph-theoretical problems related to the design of wireless networks with directional antennas. The types of antennas used in wireless networks can be roughly divided into omnidirectional antennas, which emit in all directions, and directional antennas, which emit only within a given wedge, whose orientation and angle can be specified. Although the properties of omnidirectional networks are by now quite well understood mathematically, configuring directional antennas appropriately to form efficient communication graphs poses additional challenges. read more
Proximity Structures for Wireless Communication
The main objective of this research project is to develop effcient algorithmic methods for building various proximity structures that lie at the heart of wireless network communication. Examples include quality spanners serving as virtual backbones for routing in wireless networks, dominating set-based structures supporting fault-tolerance and scheduling for energy savings, and clusterings aimed at conserving bandwidth and energy. read more
Modular Robot Reconfiguration
Modular robots consist of a large number of independent identical units (or atoms) that can attach together and perform local motions to arrange themselves into a structure best suited for a given environment or task. For example, a robot may reconfigure into a thin linear shape to facilitate passage through a narrow tunnel, transform into an emergency structure such as a bridge, or surround and manipulate objects. Because modular robots comprise groups of identical atoms, they are also more easily repaired by replacing damaged atoms with functional ones. Such robots are well-suited for working in unknown and remote environments. read more
I am intrigued by the following question: How can DNA molecules solve computational problems? DNA computing uses DNA and molecular biology instead of the traditional silicon-based computer technology. The fundamental chemistry of DNA is based on the double helix and the principle of complementarity. Two long DNA strands entwine like vines in the shape of a double helix, which is stabilized primarily by the bonds between complementary bases (A bonds only with T, C bonds only with G). The two strands can come apart at high temperature. read more
- NSF CCF-1218814, amount $183,505 (2012-2017). Project website.
- NSF CCF-0728909, amount $91,942 (2007-2010). Project website.
- CREU Research Award, amount $8500 (2014-2015). Project website.
- CREU Research Award, amount $17,000 (2010-2011). Project website.
- Villanova Faculty Development Grant, amount $2,000 (2009-2010).
- Villanova Summer Research Fellowship, amount $10,000, summer 2003.
Resources for Students
If you are a Villanova Computer Science major interested in working on a research project, please see me and/or send me an email. Here are some valuable CRA-E resources for students interested in research or graduate school:
- Research resources for students and faculty
- Applying to graduate school
- Report on graduate admission
Research collaborators (incomplete list)
Zachary Abel, Hugo Akitaya, Greg Aloupis, Brad Ballinger, Luis Barba, Matthew S. Bauer, Nadia M. Benbernou, Gregory R. Carmichael, Prosenjit Bose, Paz Carmi, Justin Colannino, Sébastien Collette, Valeriu Damian, Erik D. Demaine, Martin L. Demaine, Vida Dujmović, Karim Douïeb, Dania El-Khechen, Robin Flatland, Ferran Hurtado, John Iacono, Nagesh Javali, Matthew J. Katz, Jason Ku, Scott D. Kominers, Matias Korman, Abhaykumar Kumbhar, Stefan Langerman, Anna Lubiw, Anil Maheshwari, Henk Meijer, Nawar Molla, Pat Morin, Naresh Nelavalli, Joseph O'Rourke, Özgur Özkan, Saurav Pandit, Sriram V. Pemmaraju, Val Pinciu, Florian Potra, Suneeta Ramaswami, David Rappaport , André van Renssen, Vera Sacristán, Adrian Sandu, Ben Seamone, Robert T. Schweller, Michiel Smid, Diane Souvaine, Perouz Taslakian, Godfried Toussaint, Ryuhei Uehara, Sander Verdonschot, Andrew Winslow, Stefanie Wuhrer, and Ge Xia.