We initiate a systematic study on $\mathit{dynamic}$ $\mathit{influence}$ $\mathit{maximization}$ (DIM). In the DIM problem, one maintains a seed set $S$ of at most $k$ nodes in a dynamically involving social network, with the goal of maximizing the expected influence spread while minimizing the amortized updating cost. We consider two involution models. In the $\mathit{incremental}$ model, the social network gets enlarged over time and one only introduces new users and establishes new social links, we design an algorithm that achieves $(1-1/e-\epsilon)$-approximation to the optimal solution and has $k \cdot\mathsf{poly}(\log n, \epsilon^{-1})$ amortized running time, which matches the state-of-art offline algorithm with only poly-logarithmic overhead. In the $\mathit{fully}$ $\mathit{dynamic}$ model, users join in and leave, influence propagation gets strengthened or weakened in real time, we prove that under the Strong Exponential Time Hypothesis (SETH), no algorithm can achieve $2^{-(\log n)^{1-o(1)}}$-approximation unless the amortized running time is $n^{1-o(1)}$. On the technical side, we exploit novel adaptive sampling approaches that reduce DIM to the dynamic MAX-k coverage problem, and design an efficient $(1-1/e-\epsilon)$-approximation algorithm for it. Our lower bound leverages the recent developed distributed PCP framework.
翻译:我们开始系统研究$[mathit{hild{hild}$\mathit{maximization}$$\mathit{mathimization}(DIM ) 美元。 在DIM 问题中,在动态参与的社会网络中,我们维持一个种子设定$S$最多为$k$的节点,目标是最大限度地扩大预期的影响扩散,同时尽量减少摊销更新成本。 我们考虑两种进化模式。 在 $\mathit{incretoinfilt} 模式中,社会网络随着时间的流化而扩大,只有引入新的用户和建立新的社会链接,我们设计一个实现1/e-e-e-e-e-esilon) 美元覆盖的运行算法。 运行算法中, 不断变现的用户在不断变现的模型中, 将不断变现的变现的模型中, 正在变现的模型中, 将变现的用户在变现的模型中, 将变现的变现的变现的模型中, 将变现的变变变的 。