I am particularly interested in problems that arise in wireless networks. Today, we are entering the age of open airwaves. Every day, a plethora of new wireless applications are being developed to facilitate communication and to help people in their everyday lives. These applications rely on the open airwaves, on the unlicensed bands of spectrum, to accomplish their work. Yet the fact that the airwaves are open to all poses its own set of challenges that risk derailing the wireless revolution. First, the rapid growth of competing applications is leading to a crowding of the airwaves, creating inadvertent interference among users. Second, the open and shared spectrum verily invites malcontents and attackers that may wish to disrupt applications and corrupt data. As of today, these issues significantly complicate the development of new wireless applications, retarding growth in this exciting area. One goal of my research has been to develop tools and techniques that address these challenges.
I am also interested in more general questions of algorithmic efficiency that arise in dynamic, fault-prone distributed systems. For example, consider a set of devices that need to agree on some decision; what is the absolute minimum amount of communication needed to reach agreement? Similar questions of communication efficiency arise in multicast networks and publish-subscribe systems. In large multi-processor machines, communication typically occurs via shared memory, yet similar questions of efficiency arise. I hope to develop efficient algorithms for solving these types of problems, while exploring the fundamental limits of communication complexity.