Influence Blocking Maximization in Social Networks under the Competitive Linear Threshold Model Technical Report (1110.4723v1)

Abstract: In many real-world situations, different and often opposite opinions, innovations, or products are competing with one another for their social influence in a networked society. In this paper, we study competitive influence propagation in social networks under the competitive linear threshold (CLT) model, an extension to the classic linear threshold model. Under the CLT model, we focus on the problem that one entity tries to block the influence propagation of its competing entity as much as possible by strategically selecting a number of seed nodes that could initiate its own influence propagation. We call this problem the influence blocking maximization (IBM) problem. We prove that the objective function of IBM in the CLT model is submodular, and thus a greedy algorithm could achieve 1-1/e approximation ratio. However, the greedy algorithm requires Monte-Carlo simulations of competitive influence propagation, which makes the algorithm not efficient. We design an efficient algorithm CLDAG, which utilizes the properties of the CLT model, to address this issue. We conduct extensive simulations of CLDAG, the greedy algorithm, and other baseline algorithms on real-world and synthetic datasets. Our results show that CLDAG is able to provide best accuracy in par with the greedy algorithm and often better than other algorithms, while it is two orders of magnitude faster than the greedy algorithm.

• The paper introduces the Competitive Linear Threshold (CLT) model to strategically inhibit negative influence in social networks.
• It proves that the influence blocking maximization problem is submodular, enabling near-optimal greedy algorithm solutions.
• The study presents the CLDAG algorithm, which efficiently computes activation probabilities and outperforms traditional heuristics in large networks.

Influence Blocking Maximization in Social Networks under the Competitive Linear Threshold Model

The paper, "Influence Blocking Maximization in Social Networks under the Competitive Linear Threshold Model," offers a detailed exploration of influence propagation dynamics, focusing on inhibiting negative influence through strategic seeding in social networks. This paper introduces and examines the competitive linear threshold (CLT) model, an extension of the classic linear threshold model, to address scenarios where opposite influences—such as rumors versus truths or competing marketing campaigns—proliferate through social networks.

Mathematical and Computational Framework

The CLT model is designed to handle the complexities of competitive diffusion by allowing vertices in a network to become either positively or negatively activated. The influence blocking maximization (IBM) problem then becomes a challenge of selecting a set of "seed" nodes to initiate counter-influence, minimizing the spread of negative influence.

The IBM objective function under the CLT model is rigorously proven to be submodular, ensuring that a greedy algorithm can reach a solution within a (1-1/e) approximation of the optimal. This is a significant theoretical foundation, as it allows for scalable algorithmic solutions.

Algorithm Development: CLDAG

Recognizing the inefficiency of simple greedy algorithms—especially for networks with thousands of nodes due to the complexity of simulating competitive influence diffusion—the authors propose the CLDAG algorithm. This novel approach exploits local graph structures, specifically local directed acyclic graphs (LDAGs), to compute influence blocking efficiently.

The CLDAG algorithm innovatively employs a dynamic programming method to compute activation probabilities within these LDAGs, significantly enhancing computation efficiency. This dynamic programming framework considers the intricate interplay of positive and negative influence propagations while maintaining computational tractability.

Empirical Validation

The authors conduct extensive simulations on both real-world and synthetic datasets to validate the efficacy of the CLDAG algorithm. Findings illustrate that CLDAG matches the influence blocking capabilities of sophisticated greedy algorithms while operating at speeds two orders of magnitude faster. The algorithm's performance is benchmarked against several heuristics, including degree-based and proximity-based approaches, where it consistently demonstrates superior performance.

Theoretical Implications and Future Directions

The exploration into influence blocking raises important considerations in the field of network theory and information spreading. The submodular nature of the IBM function under the CLT model contrasts with the findings in other models like the Independent Cascade model extensions, where submodularity is not conserved. This distinction highlights how structural modifications in diffusion models can lead to differing computational properties, thus impacting algorithm design strategies.

There is substantial potential for further research. Future studies may focus on refining the CLDAG algorithm to improve computational efficiency or adapting it to new models where influence dynamics differ. Moreover, the applicability of IBM extends into fields such as cybersecurity, epidemiology, and information warfare, where managing and counteracting negative influence is crucial.

This paper contributes not only a theoretical advancement in understanding complex influence dynamics but also provides practical algorithmic strategies for real-world applications, where time efficiency is paramount and influence propagation needs precise management.