Influence Maximization (IM) over the online social networks have been widely explored in recent years, which selects a seed set from nodes in the network using a limited budget such that the expected number of nodes influenced by the seed set is maximized. However, how to activate a considered set of targeting users $\mathcal{T}$, e.g., selling a product to a specific target group, is a more practical problem. To address this problem, we respectively propose the Target Users' Activation Probability Maximization with Constraint (TUAPM-WC) problem and the Target Users' Activation Probability Maximization without Constraint (TUAPM-WOC) problem, i.e., to select a seed set S with/without size constraints such that the activation probabilities of the target users in $\mathcal{T}$ are maximized. Considering that the influence will decay during information propagation, we propose a novel and practical Influence Decay Model (IDM) as the information diffusion model.

Based on the IDM, we show that the TUAPM-WC and the TUAPM-WOC problems are NP-hard. We also prove that the objective functions of TUAPM-WC and TUAPM-WOC problems are monotone non-decreasing and submodular. On one hand, we employ a Double Greedy Algorithm (DGA) to guarantee a (1/3)-approximation ratio for TUAPM-WOC problem when $|S|$ is unconstrained. On the other hand, we propose a series of algorithms to solve the TUAPM-WC when $|S|\le b$, where b is a positive integer. More specifically, we provide a ($1-1/e$)-approximation Basic Greedy Algorithm (BGA). Furthermore, a speed-up Scalable Algorithm (SA) is proposed for online large social networks. Finally, we run our algorithms by simulations on synthetic and real-life social networks to evaluate the effectiveness and efficiency of the proposed algorithms. Experimental results validate our algorithms' superior to the comparison algorithms.

近年来，对在线社交网络上的影响力最大化（IM）进行了广泛的探索，它使用有限的预算从网络中的节点中选择了一个种子集，从而使受种子集影响的节点的预期数量最大化。但是，如何激活一组经过考虑的定位用户$\mathcal{Ť}$例如将产品销售给特定的目标群体是一个更实际的问题。为了解决这个问题，我们分别提出目标用户的有约束的激活概率最大化（TUAPM-WC）问题和目标用户的无约束的激活概率最大化（TUAPM-WOC）问题，即选择具有/的种子集S没有大小限制，因此目标用户的激活概率$\mathcal{Ť}$被最大化。考虑到影响会在信息传播过程中衰减，我们提出了一种新颖实用的影响力衰减模型（IDM）作为信息扩散模型。

基于IDM，我们表明TUAPM-WC和TUAPM-WOC问题是NP难题。我们还证明了TUAPM-WC和TUAPM-WOC问题的目标函数是单调非递减的和亚模的。一方面，我们采用双重贪婪算法（DGA）来保证TUAPM-WOC问题的近似（1/3）比率$|\mathrm{小号}|$是不受约束的。另一方面，我们提出了一系列算法来解决TUAPM-WC$|\mathrm{小号}|\le b$，其中b是一个正整数。更具体地说，我们提供了一个$\mathrm{1个}-\mathrm{1个}/Ë$）-近似基本贪婪算法（BGA）。此外，针对在线大型社交网络提出了一种加速可扩展算法（SA）。最后，我们通过在合成和现实社会网络上进行仿真来运行算法，以评估所提出算法的有效性和效率。实验结果证明了我们的算法优于比较算法。