Influence Maximization (IM) seeks to identify a small set of seed nodes in a social network to maximize expected information spread under a diffusion model. While community-based approaches improve scalability by exploiting modular structure, they typically assume independence between communities, overlooking inter-community influence$\unicode{x2014}$a limitation that reduces effectiveness in real-world networks. We introduce Community-IM++, a scalable framework that explicitly models cross-community diffusion through a principled heuristic based on community-based diffusion degree (CDD) and a progressive budgeting strategy. The algorithm partitions the network, computes CDD to prioritize bridging nodes, and allocates seeds adaptively across communities using lazy evaluation to minimize redundant computations. Experiments on large real-world social networks under different edge weight models show that Community-IM++ achieves near-greedy influence spread at up to 100 times lower runtime, while outperforming Community-IM and degree heuristics across budgets and structural conditions. These results demonstrate the practicality of Community-IM++ for large-scale applications such as viral marketing, misinformation control, and public health campaigns, where efficiency and cross-community reach are critical.

翻译：影响力最大化（Influence Maximization, IM）旨在社交网络中选取一小部分种子节点，以在特定传播模型下最大化预期信息传播范围。基于社区的方法通过利用模块化结构提升了可扩展性，但通常假设社区间相互独立，忽略了社区间影响力——这一局限降低了其在真实网络中的有效性。我们提出了Community-IM++，一个可扩展的框架，该框架通过基于社区扩散度（community-based diffusion degree, CDD）的原则性启发式方法以及渐进式预算分配策略，显式地对跨社区传播进行建模。该算法首先对网络进行划分，计算CDD以优先选择桥接节点，并利用惰性评估自适应地在社区间分配种子节点，从而最小化冗余计算。在不同边权重模型下的大型真实社交网络上的实验表明，Community-IM++以高达100倍的更低运行时间实现了接近贪婪算法的影响力传播范围，并且在各种预算和结构条件下均优于Community-IM及度启发式方法。这些结果证明了Community-IM++在大规模应用（如病毒式营销、虚假信息控制和公共卫生宣传）中的实用性，其中效率和跨社区覆盖范围至关重要。