Staying Fresh: Efficient Algorithms for Timely Social Information Distribution

TL;DR

This work addresses the problem of jointly selecting $k$ hotspot users in a location-based social network to maximize timely PoI information dissemination across an urban sensing network and an online social network. It introduces a matrix-based reformulation that yields a monotone, submodular objective, enabling a polynomial-time greedy algorithm with a proven approximation ratio of $1-\frac{m-2}{m}\left(\frac{k-1}{k}\right)^k$ for static sensing. For mobile sensing, it extends the framework via a path-based transformation and a resource-augmentation technique, producing the augmentation-aware GPS algorithm with guarantees that scale with the augmentation factor $g$, up to $1-\frac{1}{e}$ when fully augmented. Theoretical findings are validated by experiments on real and synthetic networks, demonstrating strong practical performance and the benefit of social broadcasting for PoI sharing.

Abstract

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 $k$ out of $m$ 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 ($1-\frac{m-2}{m}(\frac{k-1}{k})^k$) approximation of the optimum. Furthermore, we allow each selected user to move around and sense more PoI information to share 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.

Figures (11)

• Figure 1: An illustration example of choosing $k=1$ hotspot to show the schematic setting of an LBSN system, where $m=9$ users (at nodes 1-6, 8-10) sense the fresh PoI information around from the incident edges in the sensing graph $G_1$. Then, they share such PoIs with their friends in the online social graph $G_2$. To enhance social PoI sharing, the system selects user node 8 as a hotpot to track and broadcast her PoI collection to all users immediately.
• Figure 2: Illustrating example for Algorithm \ref{['adjusted_greedyhireg_alg']} with $k=3$ selected users and $n=2$ hops, where each $p_{xyz}$ denotes, for short, the path $(v_x,v_y,v_z)$.
• Figure 3: Grid sensing network Gowalladata.
• Figure 4: Mesh sensing network Gowalladata.
• Figure 5: Under grid sensing network: performance ratio $\underline{\rho_1}$ in (\ref{['expediment_ratio']}) of GUS (i.e., Algorithm \ref{['greedyalgforfiniteidea1']}) and its benchmarks as compared to the optimum.

Theorems & Definitions (31)

• Proposition 1
• Lemma 2
• Proposition 3
• Theorem 4
• Lemma 5
• Lemma 6
• Theorem 7
• Theorem 8
• Theorem 9
• Remark 10: A relation between our problem and the set cover problem (SCP)