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Given a weighted hypergraph $\mathcal{H}(V, \mathcal{E} \subseteq 2^V, w)$,the approximate $k$-cover problem seeks for a size-$k$ subset of $V$ that hasthe maximum weighted coverage by \emph{sampling only a few hyperedges} in$\mathcal{E}$. The problem has emerged from several network analysisapplications including viral marketing, centrality maximization, and landmarkselection. Despite many efforts, even the best approaches require $O(k n \logn)$ space complexities, thus, cannot scale to, nowadays, humongous networkswithout sacrificing formal guarantees. In this paper, we propose BCA, a familyof algorithms for approximate $k$-cover that can find $(1-\frac{1}{e}-\epsilon)$-approximation solutions within an \emph{$O(\epsilon^{-2}n \log n)$space}. That is a factor $k$ reduction on space comparing to thestate-of-the-art approaches with the same guarantee. We further make BCA moreefficient and robust on real-world instances by introducing a novel adaptivesampling scheme, termed DTA.

Approximate k-Cover in Hypergraphs: Efficient Algorithms, and Applications