Influence maximization problem is to find a set of seeds in social networks such that the cascade influence is maximized. Traditional models assume that all nodes are willing to spread the influence once they are influenced, and they ignore the disparity between influence and profit of a product. In this paper, by considering the role that price plays in viral marketing, we propose price related (PR) frame that contains PR-I and PR-L models for classic independent cascade and linear threshold models, respectively, which is a pioneer work. Two pricing strategies are designed, one is binary pricing (BYC), in which the seeds are offered free samples. The other is panoramic pricing (PAP), in which the seeds are offered different discounts. Furthermore, we find that influence and profit are like two sides of the coin, high price hinders the influence propagation and to enlarge the influence some sacrifice on profit is inevitable. Based on this observation under PR frame, by adopting a parameter to denote the decision maker's preference toward influence and profit, we propose balanced influence and profit (BIP) maximization problem. We prove the NP-hardness of BIP maximization under PR-I and PR-L model. Unlike influence maximization, the BIP objective function is not monotone. Despite the nonmonotony, we show BIP objective function is submodular under certain conditions. Two unbudgeted greedy algorithms separately, named algorithm of BYC and algorithm of PAP are devised. We conduct extensive simulations on real world data sets, test the effectiveness of our proposed parameters, compare the algorithms' performances, and evaluate the superiority of our algorithms over existing ones.

A boy wants to make friends with a pretty girl. He feels that he may get rejected if he invites her directly. In this situation, what he could do is to influence the girl's friends. Similar situations may occur in social activities. Based on this background, we formulate a new optimization problem, the Target Influence Maximization (TIM) problem and show that this problem can be solved in polynomial-time in networks with no directed cycles. Motivated by this, we study a special strategy to construct solutions for TIM, i.e., The Target Influence Maximization through Sub graph without Directed Cycle (TIMSDC). Two polynomial-time approximation algorithms are designed for TIMSDC. Through extensive experiments on real-world data sets, we demonstrate that our algorithms work efficiently and outperform existing methods.

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 < 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.

Social influence has been widely studied in areas of viral marketing, information diffusion and health care. Currently, most influence models only deal with a single influence without the interference of other influences. Also, the influence spreading in previous models must be triggered by individuals who have been activated by the influence. In this paper, we argue that it is the attraction from a specific influence makes an individual choose to spread it among multiple influences. Inspired by charged system theory in physics, a new influence model is proposed, considering individual features and social structure features. It also gives a natural description about how individuals make decisions among multiple influences. Then a novel algorithm based on this model is provided to predict human behavior. Extensive experiments on three real-world datasets demonstrate that our model and algorithm statistically outperform the state-of-the-art methods in terms of prediction accuracy.

Influence maximization problem is to find a set of seeds in social networks such that the cascade influence is maximized. Traditional models assume all nodes are willing to spread the influence once they are influenced, and they ignore the disparity between influence and profit of a product. In this paper by considering the role that price plays in viral marketing, we propose price related (PR) frame that contains PR-I and PR-L models for classic IC and LT models respectively, which is a pioneer work. We find that influence and profit are like two sides of the coin, high price hinders the influence propagation and to enlarge the influence some sacrifice on profit is inevitable. We propose Balanced Influence and Profit (BIP) maximization problem. We prove the NP-hardness of BIP maximization under PR-I and PR-L model. Unlike influence maximization, the BIP objective function is not monotone. Despite the non-monotony, we show BIP objective function is sub modular under certain conditions. Two unbudgeted greedy algorithms separately are devised. We conduct simulations on real-world datasets and evaluate the superiority of our algorithms over existing ones.