# Fastest algorithm for connectivity problem

Let $$G = (V,E)$$ be any undirected graph. Let $$k$$ be some number and $$C = |u \longrightarrow v|$$ where $$u \longrightarrow v$$ means there is a path from $$u$$ to $$v$$. We want to add $$k \subseteq V \times V\ E$$ edges into $$G$$ such that $$C$$ is maximised in the new graph.

Question : What is the fastest algorithm for this problem?

I can solve the above problem in $$n^{O(k)}$$ time by brute force method.