In location-based social networks (LBSNs), such as Gowalla and Waze, users sense urban point-of-interest (PoI) information (e.g., restaurants' queue length and real-time traffic conditions) in the vicinity and share such information with friends in online social networks. Given each user's social connections and the severe lags in disseminating fresh PoI to all users, major LBSNs aim to enhance users' social PoI sharing by selecting a subset $k$ out of all $m$ users as hotspots and broadcasting their PoI information to the entire user community. This motivates us to study a new combinatorial optimization problem by integrating two urban sensing and online social networks. We prove that this problem is NP-hard and also renders existing approximation solutions not viable. Through analyzing the interplay effects between the sensing and social networks, we successfully transform the involved PoI-sharing process across two networks to matrix computations for deriving a closed-form objective and present a polynomial-time algorithm to ensure ($1-\frac{m-2}{m}(\frac{k-1}{k})^k$) approximation of the optimum. Furthermore, we allow each selected user to move around and sense more PoI information to share. To this end, we propose an augmentation-adaptive algorithm, which benefits from a resource-augmented technique and achieves bounded approximation, ranging from $\frac{1}{k}(1-\frac{1}{e})$ to $1-\frac{1}{e}> 0.632$ by adjusting our augmentation factors. %Particularly when all sensing nodes are associated with users, we devise, by leveraging our augmentation-adaptive algorithm as a subroutine, an algorithm that eliminates the need for augmentation while still ensuring a satisfactory approximation $1-\frac{m-2}{m}(\frac{k-1}{k})^k$. Finally, our theoretical results are corroborated by our simulation findings using both synthetic and real-world datasets.

翻译：在基于位置的社交网络（LBSN）中（如Gowalla和Waze），用户感知周边城市兴趣点（PoI）信息（例如餐厅排队长度和实时交通状况），并通过在线社交网络与朋友共享此类信息。考虑到每个用户的社交连接以及将新鲜PoI传播给所有用户时存在的严重滞后，主流LBSN旨在通过从全部$m$个用户中选择一个包含$k$个用户的子集作为热点，并将其PoI信息广播至整个用户社区，从而增强用户的社交PoI共享。这促使我们研究一个融合城市感知与在线社交网络的新型组合优化问题。我们证明该问题是NP难的，且现有近似解不可行。通过分析感知网络与社交网络之间的交互效应，我们成功将涉及两个网络的PoI共享过程转化为矩阵计算，以推导出闭式目标函数，并提出一个多项式时间算法，确保达到最优解的($1-\frac{m-2}{m}(\frac{k-1}{k})^k$)近似比。此外，我们允许每个被选中的用户移动并感知更多可共享的PoI信息。为此，我们提出一种自适应增强算法，该算法受益于资源增强技术，并通过调整增强因子实现从$\frac{1}{k}(1-\frac{1}{e})$到$1-\frac{1}{e}> 0.632$的有界近似比。%特别地，当所有感知节点均与用户关联时，我们利用该自适应增强算法作为子程序，设计了一种无需增强但仍能保证满意近似比$1-\frac{m-2}{m}(\frac{k-1}{k})^k$的算法。最后，使用合成数据集和真实世界数据集的仿真结果验证了我们的理论发现。