In social advertising, the social platform host may run marketing campaigns for multiple competing clients simultaneously. In this case, each client comes up with a budget and an influence spread requirement. The host runs campaigns by allocating a set of seed nodes for each client. If the influence spread triggered by a seed set meets the requirement, the host can earn the budget from the corresponding client. In this paper, we study the problem of Profit Maximization, considering that different seeds incur different costs. Given all the clients' requirements met, we aim to find the optimal seed allocation with minimum cost. Under the competitive K-LT propagation model, we show the Profit Maximization problem is NP-hard and NP-hard to approximate with any factor. To find a feasible solution, we propose an effective algorithm that iteratively selects a candidate set and obtains an approximate allocation. The experimental results over a real-world dataset validate the effectiveness of the proposed methods.

在社交广告中，社交平台主机可以同时为多个竞争客户运行营销活动。在这种情况下，每个客户都会提出预算和影响力扩展要求。主机通过为每个客户端分配一组种子节点来运行活动。如果由种子集触发的影响散布满足要求，则主持人可以从相应的客户那里获得预算。在本文中，我们考虑到不同的种子产生不同的成本，研究了利润最大化的问题。鉴于所有客户的要求均得到满足，我们旨在以最低的成本找到最佳的种子分配。在竞争性K-LT传播模型下，我们表明获利最大化问题是NP-难和NP-难以任何因子近似的问题。为了找到可行的解决方案，我们提出了一种有效的算法，该算法迭代地选择一个候选集并获得一个近似分配。真实数据集上的实验结果验证了所提出方法的有效性。