Maximizing the Influence and Profit in Social Networks

Abstract

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.