  Li and Panigrahi, in recent work, obtained the first deterministic algorithm
for the global minimum cut of a weighted undirected graph that runs in time
$o(mn)$. They introduced an elegant and powerful technique to find isolating
cuts for a terminal set in a graph via a small number of $s$-$t$ minimum cut
computations.
  In this paper we generalize their isolating cut approach to the abstract
setting of symmetric bisubmodular functions (which also capture symmetric
submodular functions). Our generalization to bisubmodularity is motivated by
applications to element connectivity and vertex connectivity. Utilizing the
general framework and other ideas we obtain significantly faster randomized
algorithms for computing global (and subset) connectivity in a number of
settings including hypergraphs, element connectivity and vertex connectivity in
graphs, and for symmetric submodular functions.
