Distributed and massively parallel graph algorithms
With the rapidly growing size of the data and the pervasiveness of distributed systems and networks, it is a certainty that distributed and parallel computations will play a vital role in the computations of the future. This project aims to advance our understanding of the foundational aspects of these areas. We tackle some of the central questions in distributed algorithms and massively parallel algorithms for graph problems, which require us to go well-beyond the current state of the art. Our research plan involves three directions:

- Developing efficient and particularly polylogarithmic-time deterministic distributed algorithms for some of the central graph problems of the area. Our hope is to do this through a general derandomization method that removes the randomness from efficient randomized algorithms. This question underlies some of the well-known open problems of the area.

- Developing improved and particularly sublogarithmic-time randomized distributed algorithms for some of the central local graph problems of the area, thus hopefully narrowing or ideally closing this decade old gap to the respective lower bounds.

- Developing improved massively parallel algorithms for some of the fundamental graph problems, with a special focus on the challenging regime of lower memory machines, which remains widely open.

Given the high risk nature of these questions, in each direction, besides our plan of attack on the bigger and more ambitious objectives, we also explain a number of smaller problems, which should be more feasible, and which would serve as stepping stones toward the bigger goal. Moreover, we are hopeful that the simultaneous study of distributed algorithms and massively parallel will lead to a strengthening of the connections between these two areas and would also bring the related scientific communities closer to each other.