We consider the fractional influence maximization problem, i.e., identifying users on a social network to be incentivized with potentially partial discounts to maximize the influence on the network. The larger the discount given to a user, the higher the likelihood of its activation (adopting a new product or innovation), who then attempts to activate its neighboring users, causing a cascade effect of influence through the network. Our goal is to devise efficient algorithms that assign initial discounts to the network's users to maximize the total number of activated users at the end of the cascade, subject to a constraint on the total sum of discounts given. In general, the activation likelihood could be any non-decreasing function of the discount, whereas, our focus lies on the case when the activation likelihood is an affine function of the discount, potentially varying across different users. As this problem is shown to be NP-hard, we propose and analyze an efficient (1-1/e)-approximation algorithm. Furthermore, we run experiments on real-world social networks to show the performance and scalability of our method.

翻译：本文研究分数影响力最大化问题，即在社交网络中识别应给予潜在部分折扣激励的用户，以最大化网络影响力。给予用户的折扣越大，其激活（采用新产品或创新）的可能性越高，随后该用户会尝试激活其相邻用户，从而引发网络中的级联影响效应。我们的目标是设计高效算法，为网络用户分配初始折扣，在给定折扣总额约束条件下，最大化级联过程结束时被激活用户的总数。一般而言，激活概率可以是折扣的任意非递减函数，而本文重点研究激活概率为折扣仿射函数的情形，且该函数可能随用户不同而变化。由于该问题被证明是NP难问题，我们提出并分析了一种高效的(1-1/e)近似算法。此外，我们在真实社交网络上进行实验，以验证所提方法的性能与可扩展性。