The spread of a computer virus among the Internet of Things (IoT) devices can be modeled as an Epidemic Containment (EC) game, where each owner decides the strategy, e.g., installing anti-virus software, to maximize his utility against the susceptible-infected-susceptible (SIS) model of the epidemics on graphs. The EC game’s canonical solution concepts are the Minimum/Maximum Nash Equilibria (MinNE/MaxNE). However, computing the exact MinNE/MaxNE is NP-hard, and only several heuristic algorithms are proposed to approximate the MinNE/MaxNE. To calculate the exact MinNE/MaxNE, we provide a thorough analysis of some special graphs and propose scalable and exact algorithms for general graphs. Especially, our contributions are four-fold. First, we analytically give the MinNE/MaxNE for EC on special graphs based on spectral radius. Second, we provide an integer linear programming formulation (ILP) to determine MinNE/MaxNE for the general graphs with the small epidemic threshold. Third, we propose a branch-and-bound (BnB) framework to compute the exact MinNE/MaxNE in the general graphs with several heuristic methods to branch the variables. Fourth, we adopt NetShiled (NetS) method to approximate the MinNE to improve the scalability. Extensive experiments demonstrate that our BnB algorithm can outperform the naive enumeration method in scalability, and the NetS can improve the scalability significantly and outperform the previous heuristic method in solution quality.

中文翻译：

---

保护IoT网络成为流行病遏制游戏

可以将计算机病毒在物联网（IoT）设备之间的传播建模为一种流行病遏制（EC）游戏，在此游戏中，每个所有者都可以决定策略，例如安装防病毒软件，以最大程度地利用其对易受攻击的计算机的攻击力-图上流行病的易感感染（SIS）模型。EC游戏的规范解决方案概念是最小/最大纳什均衡（MinNE / MaxNE）。然而，计算精确的MinNE / MaxNE是NP困难的，并且仅提出了几种启发式算法来近似MinNE / MaxNE。为了计算精确的MinNE / MaxNE，我们提供了对一些特殊图形的透彻分析，并为一般图形提供了可扩展的精确算法。特别是，我们的贡献是四倍。首先，我们根据频谱半径在特殊图表上分析给出EC的MinNE / MaxNE。第二，我们提供一个整数线性规划公式（ILP）来确定具有流行病阈值的一般图的MinNE / MaxNE。第三，我们提出了一种分支定界（BnB）框架，使用几种启发式方法来对变量进行分支，以计算通用图中的精确MinNE / MaxNE。第四，我们采用NetShiled（NetS）方法对MinNE进行近似以提高可伸缩性。大量实验表明，我们的BnB算法在可伸缩性方面优于单纯的枚举方法，而NetS可以显着提高可伸缩性并在解决方案质量方面优于以前的启发式方法。我们提出了一种分支定界（BnB）框架，使用几种启发式方法来对变量进行分支，以计算通用图中的精确MinNE / MaxNE。第四，我们采用NetShiled（NetS）方法对MinNE进行近似以提高可伸缩性。大量实验表明，我们的BnB算法在可伸缩性方面优于单纯的枚举方法，而NetS可以显着提高可伸缩性并在解决方案质量方面优于以前的启发式方法。我们提出了一种分支定界（BnB）框架，使用几种启发式方法来对变量进行分支，以计算通用图中的精确MinNE / MaxNE。第四，我们采用NetShiled（NetS）方法对MinNE进行近似以提高可伸缩性。大量实验表明，我们的BnB算法在可伸缩性方面优于单纯的枚举方法，而NetS可以显着提高可伸缩性并在解决方案质量方面优于以前的启发式方法。