Research Rationale

My current research interest is in unifying and generalizing problems in graph network design. In general, my motivation is simple: real-world problems don't always occur in isolation. Take for instance the shortest path problem and the Maximum flow problem. These are both very natural problems which are very interesting in their own right. But, a combination of these two: where we look at length-constrained flows (e.g.) is also a very natural problem with enormous applications - in a lot of places we don't just want to deliver as many goods as possible, we also want to deliver them within a deadline. Graph network design is a space where there is significant utility in merging standard problems.

Much of my recent work has been in attempting to unify Graph Spanners with other interesting problems in network design. In the past, we unified Spanners and Steiner forests. We also unified Spanners with Buy-at-bulk network design recently. The approximation factors of all our results are comparable/identical to the state-of-the-art for the constituent subproblems of our unified problems. 

I also work on expanding the parameter ranges involved in standard network design problems. For instance, consider allowing both negative and positive edge lengths in a graph. This is a useful extension that allows us to capture several natural scenarios, e.g. resources like fuel that can both be gained and expended. My recent work allows edge lengths to be negative (among other such extensions) for Directed Spanners.

There are an enormous number of interesting and valuable problems to be solved in Network design, and I expect this space to occupy my interest for a while.