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染病在人群中传播的一个例子。此外，有害传染病的传播不仅限于传染病本身，还与计算机网络中的计算机病毒和恶意软件相关。进一步地，在线社交网络中虚假新闻和宣传的传播也令人高度关注。在本研究中，我们引入了基于度量的传播最小化问题（MBSMP），该问题可帮助政策制定者最小化大型网络中有害传染病的传播。我们开发了基于分支Benders切割算法的精确求解方法，该方法将Benders分解技术应用于MBSMP的两种混合整数规划公式：弧基公式和路径基公式。我们证明了对于这两种公式，Benders最优性切割可以通过组合程序生成，而无需通过线性规划求解对偶子问题。此外，我们的分支Benders切割算法还融入了其他改进措施，如使用场景依赖的扩展种子集、初始切割和起始启发式算法。基于文献中现有实例衍生的测试集所获得的计算结果，我们研究了求解算法各组成部分对性能的贡献。