We study two fundamental problems related to geometric packing and covering, and design algorithms with improved worst-case performance guarantees for them. These problems have numerous applications in resource allocation, ...

We study variants of two classical optimization problems: Bin Packing and Knapsack. Both bin packing and knapsack fall under the regime of "Packing and Covering Problems". In bin packing, we are given a set of input items, ...

In this thesis, we study algorithms for three fundamental graph problems. These are NP-hard problems which have not been understood completely as there is a signifiicant gap between the algorithmic and the hardness fronts ...