  Given a hypergraph, influence maximization (IM) is to discover a seed set
containing $k$ vertices that have the maximal influence. Although the existing
vertex-based IM algorithms perform better than the hyperedge-based algorithms
by generating random reverse researchable (RR) sets, they are inefficient
because (i) they ignore important structural information associated with
hyperedges and thus obtain inferior results, (ii) the frequently-used sampling
methods for generating RR sets have low efficiency because of a large number of
required samplings along with high sampling variances, and (iii) the
vertex-based IM algorithms have large overheads in terms of running time and
memory costs. To overcome these shortcomings, this paper proposes a novel
approach, called \emph{HyperIM}. The key idea behind \emph{HyperIM} is to
differentiate structural information of vertices for developing stratified
sampling combined with highly-efficient strategies to generate the RR sets.
With theoretical guarantees, \emph{HyperIM} is able to accelerate the influence
spread, improve the sampling efficiency, and cut down the expected running
time. To further reduce the running time and memory costs, we optimize
\emph{HyperIM} by inferring the bound of the required number of RR sets in
conjunction with stratified sampling. Experimental results on real-world
hypergraphs show that \emph{HyperIM} is able to reduce the number of required
RR sets and running time by orders of magnitude while increasing the influence
spread by up to $2.73X$ on average, compared to the state-of-the-art IM
algorithms.
