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The COVID-19 pandemic has been a recent example for the spread of a harmfulcontagion in large populations. Moreover, the spread of harmful contagions isnot only restricted to an infectious disease, but is also relevant to computerviruses and malware in computer networks. Furthermore, the spread of fake newsand propaganda in online social networks is also of major concern. In thisstudy, we introduce the measure-based spread minimization problem (MBSMP),which can help policy makers in minimizing the spread of harmful contagions inlarge networks. We develop exact solution methods based onbranch-and-Benders-cut algorithms that make use of the application of Bendersdecomposition method to two different mixed-integer programming formulations ofthe MBSMP: an arc-based formulation and a path-based formulation. We show thatfor both formulations the Benders optimality cuts can be generated using acombinatorial procedure rather than solving the dual subproblems using linearprogramming. Additional improvements such as using scenario-dependent extendedseed sets, initial cuts, and a starting heuristic are also incorporated intoour branch-and-Benders-cut algorithms. We investigate the contribution ofvarious components of the solution algorithms to the performance on the basisof computational results obtained on a set of instances derived from existingones in the literature.

Benders decomposition algorithms for minimizing the spread of harmful contagions in networks