Given a social network where the users are associated with non-uniform selection cost, the problem of Budgeted Influence Maximization (BIM in short) asks for selecting a subset of the nodes within an allocated budget for initial activation, such that due to the cascading effect, influence in the network is maximized. In this paper, we study this problem with a variation, where a subset of the users are marked as target users, each of them is assigned with a benefit and this can be earned by influencing them. The goal here is to maximize the earned benefit by initially activating a set of nodes within the budget. This problem is referred to as the Earned Benefit Maximization Problem. First, we show that this problem is NP-Hard and the benefit function follows the monotonicity, sub-modularity property under the Independent Cascade Model of diffusion. We propose an incremental greedy strategy for this problem and show, with minor modification it gives $(1-\frac{1}{\sqrt{e}})$-factor approximation guarantee on the earned benefit. Next, by exploiting the sub-modularity property of the benefit function, we improve the efficiency of the proposed greedy algorithm. Then, we propose a hop-based heuristic method, which works based on the computation of the ‘expected earned benefit’. Finally, we perform a series of extensive experiments with four publicly available, real-life social network datasets. From the experiments, we observe that the seed sets selected by the proposed algorithms can achieve more benefit compared to many existing methods. Particularly, the hop-based approach is found to be more efficient than the other ones for solving this problem.

给定一个用户与非均匀选择成本相关联的社交网络，预算影响最大化（简称BIM）问题要求在分配的预算中选择节点的子集以进行初始激活，例如由于级联效应，网络中的影响力将最大化。在本文中，我们以变体形式研究了此问题，其中一部分用户被标记为目标用户，每个用户都被分配了一项利益，而这可以通过影响他们来获得。这里的目标是通过最初激活预算内的一组节点来最大化所获得的收益。此问题称为“获利最大化”问题。首先，我们证明这个问题是NP-Hard，且收益函数遵循独立级联扩散模型下的单调性，亚模性质。我们针对此问题提出了一种渐进式贪婪策略，并展示了它的细微修改，它给出了$（\mathrm{1个}-\frac{\mathrm{1个}}{\sqrt{Ë}}）$所得利益的因子近似保证。接下来，通过利用利益函数的子模属性，我们提高了所提出的贪婪算法的效率。然后，我们提出了一种基于跃点的启发式方法，该方法基于“期望的收益”的计算。最后，我们对四个公开可用的现实生活中的社交网络数据集进行了一系列广泛的实验。从实验中，我们观察到，与许多现有方法相比，所提出的算法选择的种子集可以实现更大的收益。特别地，发现基于跳的方法比其他方法更有效地解决了该问题。