  Computing a dense subgraph is a fundamental problem in graph mining, with a
diverse set of applications ranging from electronic commerce to community
detection in social networks. In many of these applications, the underlying
context is better modelled as a weighted hypergraph that keeps evolving with
time.
  This motivates the problem of maintaining the densest subhypergraph of a
weighted hypergraph in a {\em dynamic setting}, where the input keeps changing
via a sequence of updates (hyperedge insertions/deletions). Previously, the
only known algorithm for this problem was due to Hu et al. [HWC17]. This
algorithm worked only on unweighted hypergraphs, and had an approximation ratio
of $(1+\epsilon)r^2$ and an update time of $O(\text{poly} (r, \log n))$, where
$r$ denotes the maximum rank of the input across all the updates.
  We obtain a new algorithm for this problem, which works even when the input
hypergraph is weighted. Our algorithm has a significantly improved
(near-optimal) approximation ratio of $(1+\epsilon)$ that is independent of
$r$, and a similar update time of $O(\text{poly} (r, \log n))$. It is the first
$(1+\epsilon)$-approximation algorithm even for the special case of weighted
simple graphs.
  To complement our theoretical analysis, we perform experiments with our
dynamic algorithm on large-scale, real-world data-sets. Our algorithm
significantly outperforms the state of the art [HWC17] both in terms of
accuracy and efficiency.
