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：新冠肺炎疫情是近期有害传播物在大规模人群中扩散的典型案例。此外，有害传播物的扩散不仅限于传染病，还涉及计算机网络中的计算机病毒和恶意软件。同时，在线社交网络中虚假新闻和宣传的传播也备受关注。本研究提出了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有害传播物的扩散。我们开发了基于分支-切割- Benders算法的精确求解方法，该方法将Benders分解应用于MBSMP的两种混合整数规划形式：基于弧的模型和基于路径的模型。我们证明，对于这两种模型，可以通过组合程序而非线性规划求解对偶子问题来生成Benders最优性割。此外，我们的分支-切割-Benders算法还引入了基于情景的扩展种子集、初始割切以及初始启发式算法等改进措施。基于文献中现有实例的数值实验结果，我们分析了求解算法各组成部分对性能的贡献。