In the past decade, influence maximization becomes one of the fundamental problems in online social networks. It has popular applications such as viral marketing and rumor blocking. This problem asks for some influential users to maximize the expected followers. Unlike traditional influence maximization, we discuss the problem of influence towards a special target user in this paper. We define the targeted activation probability maximization problem, which aims at finding k intermediate users so that a given target user is more likely to be influenced by the start user. Motivated by the need for modeling the diffusion process from one user to another, we propose the Targeted Linear Threshold (TLT) model and Targeted Independent Cascade (TIC) model. We prove that the problem is NP-hard, computation of the objective function is #P-hard, and the objective functions are non-submodular. Moreover, the objective function in the TLT model is an upper bound of that in the TIC model. Based on the sandwich approximation strategy, we obtain their data-dependent approximate solutions. Finally, we use three real datasets to evaluate the effectiveness of our algorithms. The experimental results indicate that our methods can effectively increase the activation probability of the target user.

中文翻译：

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在线社交网络中的目标激活概率最大化问题


在过去的十年中，影响力最大化成为在线社交网络的基本问题之一。它具有病毒式营销和谣言拦截等流行应用。这个问题要求一些有影响力的用户最大化预期的追随者。与传统的影响力最大化不同，我们在本文中讨论了对特定目标用户的影响力问题。我们定义了目标激活概率最大化问题，其目的是找到k个中间用户，使得给定的目标用户更有可能受到起始用户的影响。出于对从一个用户到另一个用户的扩散过程进行建模的需要，我们提出了目标线性阈值（TLT）模型和目标独立级联（TIC）模型。我们证明该问题是 NP 困难的，目标函数的计算是 #P 困难的，并且目标函数是非子模的。此外，TLT模型中的目标函数是TIC模型中目标函数的上限。基于三明治近似策略，我们获得了它们的数据相关的近似解。最后，我们使用三个真实数据集来评估我们算法的有效性。实验结果表明，我们的方法可以有效提高目标用户的激活概率。