  As graphs continue to grow in size, we seek ways to effectively process such
data at scale. The model of streaming graph processing, in which a compact
summary is maintained as each edge insertion/deletion is observed, is an
attractive one. However, few results are known for optimization problems over
such dynamic graph streams.
  In this paper, we introduce a new approach to handling graph streams, by
instead seeking solutions for the parameterized versions of these problems
where we are given a parameter $k$ and the objective is to decide whether there
is a solution bounded by $k$. By combining kernelization techniques with
randomized sketch structures, we obtain the first streaming algorithms for the
parameterized versions of the Vertex Cover problem. We consider the following
three models for a graph stream on $n$ nodes:
  1. The insertion-only model where the edges can only be added.
  2. The dynamic model where edges can be both inserted and deleted.
  3. The \emph{promised} dynamic model where we are guaranteed that at each
timestamp there is a solution of size at most $k$.
  In each of these three models we are able to design parameterized streaming
algorithms for the Vertex Cover problem. We are also able to show matching
lower bound for the space complexity of our algorithms.
  (Due to the arXiv limit of 1920 characters for abstract field, please see the
abstract in the paper for detailed description of our results)

Data Structures and Algorithms