We introduce the discount allocation problem to a new online social networks (OSNs) scenario where the nodes and the relationships between nodes are determined but the states of edges between nodes are unknown. We can know the states of all the edges centered on a node only when it becomes active. Different from most previous work on influence maximization discount allocation problem in OSNs, our goal is to minimize the discount cost that the marketer spends while ensuring at least Q customers who adopt the target product in the end in OSNs. We propose an online discount allocation policy to select seed users to spread the product information. The marketer initially selects one seed user to offer him a discount and observes whether he accepts the discount. If he accepts the discount, the marketer needs to observe how well this seed user contributes to the diffusion of product adoptions and how much discount he accepts. The remaining seeds are chosen based on the feedback of diffusion results obtained by all previous selected seeds. We propose two online discount allocation greedy algorithms under two different situations: uniform and non-uniform discounts allocation. We offer selected users discounts changing from the lowest to highest in the discount rate set until the users receive the discount and become seed users in non-uniform discount allocation situation, which saves the cost of firms comparing with the previous method that providing product to users for free. We present a theoretical analysis with bounded approximation ratios for the algorithms. Extensive experiments are conducted to evaluate the performance of the proposed online discount allocation algorithms on real-world online social networks datasets and the results demonstrate the effectiveness and efficiency of our methods.

我们将折扣分配问题引入到一种新的在线社交网络（OSN）场景中，在该场景中，确定了节点和节点之间的关系，但节点之间的边缘状态未知。只有当节点变为活动状态时，我们才能知道以该节点为中心的所有边的状态。与以往大多数OSN中影响最大化折扣分配问题的工作不同，我们的目标是在确保至少Q最终在OSN中采用目标产品的客户。我们提出一种在线折扣分配政策，以选择种子用户来传播产品信息。营销商最初选择一个种子用户为他提供折扣，然后观察他是否接受折扣。如果他接受折扣，则营销人员需要观察该种子用户对产品采用的传播有多大贡献，以及他接受多少折扣。基于所有先前选择的种子获得的扩散结果的反馈来选择剩余的种子。在两种不同情况下，我们提出了两种在线折扣分配贪婪算法：统一折扣折扣和非统一折扣折扣。我们为选定的用户提供折扣率从折扣率设置的最低到最高的折扣，直到用户获得折扣并在不一致的折扣分配情况下成为种子用户为止，与以前向用户提供产品的方法相比，这节省了公司的成本免费。我们提出了算法的有限近似比率的理论分析。进行了大量实验，以评估所提出的在线折扣分配算法在现实世界中的在线社交网络数据集上的性能，结果证明了我们方法的有效性和效率。我们提出了算法的有限近似比率的理论分析。进行了大量实验，以评估所提出的在线折扣分配算法在现实世界中的在线社交网络数据集上的性能，结果证明了我们方法的有效性和效率。我们提出了算法的有限近似比率的理论分析。进行了大量实验，以评估所提出的在线折扣分配算法在现实世界中的在线社交网络数据集上的性能，结果证明了我们方法的有效性和效率。