The COVID-19 pandemic has been a recent example for the spread of a harmful contagion in large populations. Moreover, the spread of harmful contagions is not only restricted to an infectious disease, but is also relevant to computer viruses and malware in computer networks. Furthermore, the spread of fake news and propaganda in online social networks is also of major concern. In this study, we introduce the measure-based spread minimization problem (MBSMP), which can help policy makers in minimizing the spread of harmful contagions in large networks. We develop exact solution methods based on branch-and-Benders-cut algorithms that make use of the application of Benders decomposition method to two different mixed-integer programming formulations of the MBSMP: an arc-based formulation and a path-based formulation. We show that for both formulations the Benders optimality cuts can be generated using a combinatorial procedure rather than solving the dual subproblems using linear programming. Additional improvements such as using scenario-dependent extended seed sets, initial cuts, and a starting heuristic are also incorporated into our branch-and-Benders-cut algorithms. We investigate the contribution of various components of the solution algorithms to the performance on the basis of computational results obtained on a set of instances derived from existing ones in the literature.

翻译：摘要：COVID-19疫情是近年来大规模人群中有害传染物传播的典型案例。此外，有害传染物的传播不仅局限于传染病，还涉及计算机网络中的计算机病毒与恶意软件。同时，在线社交网络中虚假新闻与宣传的传播同样令人高度关注。本研究提出了一种基于度量的传播最小化问题（MBSMP），该问题可帮助决策者减少大规模网络中传染物的传播。我们开发了基于分支-Benders割的精确求解方法，该方法将Benders分解应用于MBSMP的两种混合整数规划模型：弧段模型与路径模型。研究表明，两种模型的Benders最优性割均可通过组合程序生成，而无需通过线性规划求解对偶子问题。我们还融入了情景依赖的扩展种子集、初始割及起始启发式等改进策略。基于文献中现有实例集的计算结果，我们分析了求解算法各组成部分对性能的贡献。