  Real-world networks are prone to breakdowns. Typically in the underlying
graph $G$, besides the insertion or deletion of edges, the set of active
vertices changes overtime. A vertex might work actively, or it might fail, and
gets isolated temporarily. The active vertices are grouped as a set $S$. $S$ is
subjected to updates, i.e., a failed vertex restarts, or an active vertex
fails, and gets deleted from $S$. Dynamic subgraph connectivity answers the
queries on connectivity between any two active vertices in the subgraph of $G$
induced by $S$. The problem is solved by a dynamic data structure, which
supports the updates and answers the connectivity queries. In the general
undirected graph, the best results for it include $\widetilde{O}(m^{2/3})$
deterministic amortized update time, $\widetilde{O}(m^{4/5})$ and
$\widetilde{O}(\sqrt{mn})$ deterministic worst-case update time. In the paper,
we propose a randomized data structure, which has $\widetilde{O}(m^{3/4})$
worst-case update time.
