Approximation Algorithms to Enhance Social Sharing of Fresh Point-of-Interest Information

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.