I am primarily interested in approximation algorithms which exploit convex optimization tools (e.g. linear programming, semi-definite programming). Much of my work (though by no means all) focuses on demonstrating the potential of hierarchies of convex relaxations, which until recently remained outside the algorithmic toolkit.
My PhD Thesis, containing the most polished versions of some of the following results (specifically, from STOC’06, FOCS’07, APPROX’08), can be found here.
Publications - Theory
•Understanding Set Cover: Sub-exponential Time Approximations and Lift-and-Project Methods