This research is focused on general area of approximation and online algorithms. Many commonly studied optimization problems are intractable, and it is natural to approximate the optimum instead. While there has been much progress on such problems in the past two decades, there is much work to be done. This research investigates some long-standing open problems of interest, it also extends the techniques beyond what is currently known, and the research also investigates richer models and problems that attempt to capture the complexity and diversity of optimization problems that arise in practice. Along the problems considered in this research is that of formulating and solving optimization problems in the presence of partial information, which is often a requirement in practice. Another class of problems concerns the algorithmic theory of finite metric spaces, and this research further investigates the embeddability of graph metrics into normed spaces.
This research broadens the scope of understanding of approximation algorithms for optimization problems by developing models and problem formulations inspired by the aspects of practicality, and by developing algorithms and algorithmic techniques which will be relevant in broader contexts. Research progress is propagated into the curriculum via specialized courses presenting the theoretical advances in the context of their applications, as well as basic courses teaching the fundamental ideas and techniques behind these research advances.
