Alladi Ramakrishnan Hall

Geometry and Graphs: A Tale of Two Worlds

Sujoy Bhore

IISER Bhopal

Data visualization and massive data handling are some of the primary
concerns of computer scientists. However, most big data sets are
relational, containing a set of objects and relations between these
objects. This translates to a natural mathematical model, called graph,
with the objects as the vertices and the relations as the edges. Many
important real-life problems can be modeled as combinatorial optimization
problems on graphs. In the first part of my talk, I will focus on some
classical combinatorial optimization problems, e.g., spanners, spanning
trees, Erdős-Szekeres-type problems, etc.

However, we live in a dynamic world where our everyday life involves
several decision making processes that are based on data changing
constantly over time. Algorithms are at the core of computer science. They
define the underlying computational processes of every complex system
running in today's digital world. These systems are fed enormous amounts of
data on a frequent basis. Therefore, a natural challenge for algorithms is
to not only do efficient computation at a particular point, but also to
maintain a good quality solution throughout. In the second part of my talk,
I will focus on the algorithmic journey from static to dynamic geometric
optimization problems.