  The problem of sparsifying a graph or a hypergraph while approximately
preserving its cut structure has been extensively studied and has many
applications. In a seminal work, Bencz\'ur and Karger (1996) showed that given
any $n$-vertex undirected weighted graph $G$ and a parameter $\varepsilon \in
(0,1)$, there is a near-linear time algorithm that outputs a weighted subgraph
$G'$ of $G$ of size $\tilde{O}(n/\varepsilon^2)$ such that the weight of every
cut in $G$ is preserved to within a $(1 \pm \varepsilon)$-factor in $G'$. The
graph $G'$ is referred to as a {\em $(1 \pm \varepsilon)$-approximate cut
sparsifier} of $G$. Subsequent recent work has obtained a similar result for
the more general problem of hypergraph cut sparsifiers. However, all known
sparsification algorithms require $\Omega(n + m)$ time where $n$ denotes the
number of vertices and $m$ denotes the number of hyperedges in the hypergraph.
Since $m$ can be exponentially large in $n$, a natural question is if it is
possible to create a hypergraph cut sparsifier in time polynomial in $n$, {\em
independent of the number of edges}. We resolve this question in the
affirmative, giving the first sublinear time algorithm for this problem, given
appropriate query access to the hypergraph.
