Given a social network G and an integer k, the influence maximization (IM) problem asks for a seed set S of k nodes from G to maximize the expected number of nodes influenced via a propagation model. The majority of the existing algorithms for the IM problem are developed only under the non-adaptive setting, i.e., where all k seed nodes are selected in one batch without observing how they influence other users in real world. In this paper, we study the adaptive IM problem where the k seed nodes are selected in batches of equal size b, such that the i-th batch is identified after the actual influence results of the former \(i-1\) batches are observed. In this paper, we propose the first practical algorithm for the adaptive IM problem that could provide the worst-case approximation guarantee of \(1-{\mathrm {e}}^{\rho _b(\varepsilon -1)}\), where \(\rho _b=1-(1-1/b)^b\) and \(\varepsilon \in (0, 1)\) is a user-specified parameter. In particular, we propose a general framework AdaptGreedy that could be instantiated by any existing non-adaptive IM algorithms with expected approximation guarantee. Our approach is based on a novel randomized policy that is applicable to the general adaptive stochastic maximization problem, which may be of independent interest. In addition, we propose a novel non-adaptive IM algorithm called EPIC which not only provides strong expected approximation guarantee, but also presents superior performance compared with the existing IM algorithms. Meanwhile, we clarify some existing misunderstandings in recent work and shed light on further study of the adaptive IM problem. We conduct experiments on real social networks to evaluate our proposed algorithms comprehensively, and the experimental results strongly corroborate the superiorities and effectiveness of our approach.

给定一个社交网络G和一个整数k，影响最大化（IM）问题要求G的k个节点的种子集S最大化通过传播模型影响的预期节点数。大多数针对IM问题的现有算法仅在非自适应设置下开发，即，在不观察它们如何影响现实世界中的其他用户的情况下，成批选择了所有k个种子节点。在本文中，我们研究了自适应IM问题，其中k个种子节点以相等大小b的批次被选择，使得i观察前\（i-1 \）个批次的实际影响结果后，才能确定第四个批次。在本文中，我们针对自适应IM问题提出了第一个实用算法，该算法可以提供\（1-{\ mathrm {e}} ^ {\ rho _b（\ varepsilon -1）} \）的最坏情况下的近似保证。，其中\（\ rho _b = 1-（1-1 / b）^ b \）和\（\ varepsilon \ in（0，1）\）是用户指定的参数。特别是，我们提出了一个通用框架AdaptGreedy可以由任何现有的具有预期近似保证的非自适应IM算法实例化。我们的方法基于一种新颖的随机策略，该策略适用于可能具有独立利益的一般自适应随机最大化问题。此外，我们提出了一种新的非自适应IM算法，称为EPIC与现有的IM算法相比，它不仅提供了强大的预期近似保证，而且还提供了卓越的性能。同时，我们澄清了近期工作中存在的一些误解，为进一步研究自适应IM问题提供了参考。我们在真实的社交网络上进行实验，以全面评估我们提出的算法，实验结果强烈证实了该方法的优越性和有效性。