Social networks allow rapid spread of ideas and innovations while the negative information can also propagate widely. When the cascades with different opinions reaching the same user, the cascade arriving first is the most likely to be taken by the user. Therefore, once misinformation or rumor is detected, a natural containment method is to introduce a positive cascade competing against the rumor. Given a budget @math , the rumor blocking problem asks for @math seed users to trigger the spread of the positive cascade such that the number of the users who are not influenced by rumor can be maximized. The prior works have shown that the rumor blocking problem can be approximated within a factor of @math by a classic greedy algorithm combined with Monte Carlo simulation with the running time of @math , where @math and @math are the number of users and edges, respectively. Unfortunately, the Monte-Carlo-simulation-based methods are extremely time consuming and the existing algorithms either trade performance guarantees for practical efficiency or vice versa. In this paper, we present a randomized algorithm which runs in @math expected time and provides a @math -approximation with a high probability. The experimentally results on both the real-world and synthetic social networks have shown that the proposed randomized rumor blocking algorithm is much more efficient than the state-of-the-art method and it is able to find the seed nodes which are effective in limiting the spread of rumor.
Online Social Networks (OSNs) have recently emerged as an effective medium for information sharing. Unfortunately, it has been frequently observed that malicious rumors being spread over an OSN are not controllable, and this is not desirable. This paper proposes a new problem, namely the γ - k rumor restriction problem, whose goal is, given a social network, to find a set S of nodes with k protectors (γ * k protectors from the contaminated set, and (1 - γ) * k protectors from the decontaminated set) to protect the network such that the number of decontaminated nodes is maximum. We show that the objective function of the γ - k rumor restriction problem is submodular, and use this result to design a greedy approximation algorithm with performance ratio of 1 - 1 e for the problem under the linear threshold model and independent cascade model, respectively. To verify our algorithms, we conduct experiments on real word social networks including NetHEPT, WikiVote and Slashdot0811. The results show that our algorithm works efficiently and effectively.  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. In this paper, we study the Misinformation Containment (MC) problem. In particular, taking into account the faster development of misinformation detection techniques, we mainly focus on the limiting the misinformation with known sources case. We prove that under the Competitive Activation Model, the MC problem is NP-hard and show that it cannot be approximated in polynomial time within a ratio of ( e (e-1) ) unless (NP DTIME (n^ O( n) ) ). Due to its hardness, we propose an effective algorithm, exploiting the critical nodes and using the greedy approach as well as applying the CELF heuristic to achieve the goal. Comprehensive experiments on real social networks are conducted, and results show that our algorithm can effectively expand the awareness of correct information as well as limit the spread of misinformation.  In many real-world scenarios, social network serves as a platform for information diffusion, alongside with positive information (truth) dissemination, negative information (rumor) also spread among the public. To make the social network as a reliable medium, it is necessary to have strategies to control rumor diffusion. In this article, we address the Least Cost Rumor Blocking (LCRB) problem where rumors originate from a community Cr in the network and a notion of protectors are used to limit the bad influence of rumors. The problem can be summarized as identifying a minimal subset of individuals as initial protectors to minimize the number of people infected in neighbor communities of Cr at the end of both diffusion processes. Observing the community structure property, we pay attention to a kind of vertex set, called bridge end set, in which each node has at least one direct in-neighbor in Cr and is reachable from rumors. Under the OOAO model, we study LCRB-P problem, in which α (0 <; α <; 1) fraction of bridge ends are required to be protected. We prove that the objective function of this problem is submodular and a greedy algorithm is adopted to derive a (1-1 e)-approximation. Furthermore, we study LCRB-D problem over the DOAA model, in which all the bridge ends are required to be protected, we prove that there is no polynomial time o(ln n)-approximation for the LCRB-D problem unless P = NP, and propose a Set Cover Based Greedy (SCBG) algorithm which achieves a O(ln n)-approximation ratio. Finally, to evaluate the efficiency and effectiveness of our algorithm, we conduct extensive comparison simulations in three real-world datasets, and the results show that our algorithm outperforms other heuristics.