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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.

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Uncertainty about models and data is ubiquitous in the computational social sciences, and it creates a need for robust social network algorithms, which can simultaneously provide guarantees across a spectrum of models and parameter settings. We begin an investigation into this broad domain by studying robust algorithms for the Influence Maximization problem, in which the goal is to identify a set of k nodes in a social network whose joint influence on the network is maximized. We define a Robust Influence Maximization framework wherein an algorithm is presented with a set of influence functions, typically derived from different influence models or different parameter settings for the same model. The different parameter settings could be derived from observed cascades on different topics, under different conditions, or at different times. The algorithm's goal is to identify a set of k nodes who are simultaneously influential for all influence functions, compared to the (function-specific) optimum solutions. We show strong approximation hardness results for this problem unless the algorithm gets to select at least a logarithmic factor more seeds than the optimum solution. However, when enough extra seeds may be selected, we show that techniques of Krause et al. can be used to approximate the optimum robust influence to within a factor of 1 − 1/e. We evaluate this bicriteria approximation algorithm against natural heuristics on several real-world data sets. Our experiments indicate that the worst-case hardness does not necessarily translate into bad performance on real-world data sets; all algorithms perform fairly well.

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