Staying Fresh: Efficient Algorithms for Timely Social Information Distribution

In location-based social networks (LBSNs), users sense urban point-of-interest (PoI) information in the vicinity and share such information with friends in online social networks. Given users' limited social connections and severe lags in disseminating fresh PoI to all, major LBSNs aim to enhance users' social PoI sharing by selecting <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> out of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$m$</tex-math></inline-formula> users as hotspots and broadcasting their fresh PoI information to the entire user community. This motivates us to study a new combinatorial optimization problem that involves the interplay between an urban sensing network and an online social network. We prove that this problem is NP-hard and also renders existing approximation solutions not viable. Through analyzing the interplay effects between the two networks, we successfully transform the involved PoI-sharing process across two networks to matrix computations for deriving a closed-form objective to hold desirable properties (e.g., submodularity and monotonicity). This finding enables us to develop a polynomial-time algorithm that guarantees a (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1-\frac{m-2}{m}(\frac{k-1}{k})^{k}$</tex-math></inline-formula>) approximation of the optimum. Furthermore, we allow each selected user to move around and sense more PoI information to share and propose an augmentation-adaptive algorithm with decent performance guarantees. Finally, our theoretical results are corroborated by our simulation findings using both synthetic and real-world datasets.