Age of Information Diffusion on Social Networks

TL;DR

The recent notions of the peak and the average age of information (AoI) are adopted to measure the timeliness of promotion information received by network users and it is proved that the peak AoI problem is NP-hard by properly reducing it from the set cover problem.

Abstract

To promote viral marketing, major social platforms (e.g., Facebook Marketplace and Pinduoduo) repeatedly select and invite different users (as seeds) in online social networks to share fresh information about a product or service with their friends. Thereby, we are motivated to optimize a multi-stage seeding process of viral marketing in social networks, and adopt the recent notions of the peak and the average age of information (AoI) to measure the timeliness of promotion information received by network users. Our problem is different from the literature on information diffusion in social networks, which limits to one-time seeding and overlooks AoI dynamics or information replacement over time. As a critical step, we manage to develop closed-form expressions that characterize and trace AoI dynamics over any social network. For the peak AoI problem, we first prove the NP-hardness of our multi-stage seeding problem by a highly non-straightforward reduction from the dominating set problem, and then present a new polynomial-time algorithm that achieves good approximation guarantees (e.g., less than 2 for linear network topology). To minimize the average AoI, we also prove that our problem is NP-hard by properly reducing it from the set cover problem. Benefiting from our two-sided bound analysis on the average AoI objective, we build up a new framework for approximation analysis and link our problem to a much simplified sum-distance minimization problem. This intriguing connection inspires us to develop another polynomial-time algorithm that achieves a good approximation guarantee. Additionally, our theoretical results are well corroborated by experiments on a real social network.

Figures (12)

• Figure 1: An illustrative example of the viral marketing system where the time gap between two consecutive seeding timestamps is $\Delta=2$. Here, we consider three rounds of seeding as $(s_1,s_2,s_3)=(v_5,v_7,v_3)$ to dynamically choose users 5, 7, 3 at time $t_1=1$, $t_2=3$ and $t_3=5$ for information diffusion.
• Figure 2: Illustration example of Algorithm \ref{['ImprovedDiscontinuityPoint']}, where $k=7$, $t_1+dist(s_1,v_i)<t_6+dist(s_6,v_i)<t_2+dist(s_2,v_i)<t_3+dist(s_3,v_i)<t_7+dist(s_7,v_i)<t_4+dist(s_4,v_i)<t_5+dist(s_5,v_i)$.
• Figure 3: Peak AoI of Algorithm \ref{['peak_cycliselection_alg']} in a line-type network.
• Figure 4: Configuration of seed candidates in a line-type social network, where X-axis and Y-axis indicate candidate locations and AoI at time $1+\underline{\mu}\Delta+\overline{\varsigma}$, respectively. Note that, at time $1+\underline{\mu}\Delta$, the AoI of users covered by a rectangular of the same color is no more than the height of that rectangle.
• Figure 5: Illustration of a histogram network structure in which nodes on the diameter path are highlighted in orange.

Theorems & Definitions (48)

• Remark 2.1
• Lemma 3.1
• Definition 3.2: Discontinuity point
• Lemma 3.3
• Lemma 3.4
• Proposition 3.5
• Theorem 3.6
• Theorem 3.7
• Theorem 3.8
• proof