超图的近似k-覆盖：有效算法及应用
Approximate k-Cover in Hypergraphs: Efficient Algorithms, and Applications
摘要：
给定一个加权超图$\mathcal{H}(V, \mathcal{E} \subseteq 2^V, w)$，近似$k$ -覆盖问题寻找$V$的一个大小为$k$的子集，该子集在$\mathcal{E}$中具有由\emph{sampling only a few hyperedges}加权的最大覆盖.这个问题已经出现在几个网络分析应用程序中，包括病毒式营销，中心性最大化和地标选择。尽管有许多努力，即使是最好的方法也需要$O(k n \log n)$空间复杂度，因此，不能在不牺牲形式保证的情况下扩展到当今的巨大网络。在本文中，我们提出了BCA，一个家庭的算法近似$k$覆盖，可以找到$(1-\frac{1}{e} -ε)$近似解决方案内的\emph{$O(ε^{-2}n \log n)$ space}。与具有相同保证的现有技术方法相比，这是空间上的$k$减少的一个因素。通过引入一种新的自适应采样方案（称为DTA），我们进一步使BCA在现实世界的实例中更加有效和鲁棒。
英文摘要：
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 has the maximum weighted coverage by \emph{sampling only a few hyperedges} in $\mathcal{E}$. The problem has emerged from several network analysis applications including viral marketing, centrality maximization, and landmark selection. Despite many efforts, even the best approaches require $O(k n \log n)$ space complexities, thus, cannot scale to, nowadays, humongous networks without sacrificing formal guarantees. In this paper, we propose BCA, a family of algorithms for approximate $k$-cover that can find $(1-\frac{1}{e} -ε)$-approximation solutions within an \emph{$O(ε^{-2}n \log n)$ space}. That is a factor $k$ reduction on space comparing to the state-of-the-art approaches with the same guarantee. We further make BCA more efficient and robust on real-world instances by introducing a novel adaptive sampling scheme, termed DTA.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
