Optimal network topologies for mitigating security and epidemic risks
Optimal network topologies for mitigating security and epidemic risks
复制标题
用于降低安全和流行病风险的最佳网络拓扑
DOI：
10.1109/allerton.2016.7852362
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
S. Sundaram
中科院分区：
文献类型：
--
作者：
A. Hota;S. Sundaram
我们考虑在安全和流行病风险下的网络环境，其中每个顶点成功攻击或感染的概率取决于其邻居的行为或状态。在这种情况下，我们考虑的问题是设计一个具有给定数量的顶点和边的最优网络拓扑，以最小化受攻击或感染顶点的预期比例。我们证明了这类问题可以转换为最小化顶点度的凹函数的和，并推广了网络设计的现有结果，以获得关于最优网络拓扑的见解。我们首先考虑一类相互依赖的安全博弈，其中每个顶点代表一个投资安全以保护自己的用户。在任意给定顶点成功攻击的概率是该顶点附近安全投资的函数。我们引入了行为风险态度的概念，其中每个用户以一种扭曲的方式感知安全风险（正如行为经济学文献中建立的模型所规定的那样）。在这种情况下，我们描述了在纳什均衡安全投资下成功攻击的期望顶点数量的上界，并确定了使该上界最小化的网络拓扑结构。然后，我们考虑SIS流行病动力学的n缠绕近似，并表征使稳定状态下感染顶点的比例最小（界限）的图。
We consider networked environments under security and epidemic risks, where the probability of successful attack or infection at each vertex depends on the actions or states of its neighbors. In such settings, we consider the problem of designing an optimal network topology with a given number of vertices and edges in order to minimize the expected fraction of attacked or infected vertices. We show that such problems can be cast as minimizing the sum of a concave function of the vertex degrees, and generalize existing results on network design to obtain insights about the optimal network topologies. We first consider a class of interdependent security games where each vertex represents a user that invests in security to protect herself. The probability of successful attack at any given vertex is a function of the security investments in the neighborhood of that vertex. We introduce the notion of behavioral risk-attitudes, where each user perceives the security risks in a skewed manner (as prescribed by established models from the behavioral economics literature). We characterize an upper bound on the expected number of vertices that are successfully attacked under the Nash equilibrium security investments in such settings, and identify the network topologies that minimize this bound. We then consider the N-intertwined approximation of SIS epidemic dynamics, and characterize graphs that minimize (bounds on) the fraction of infected vertices in steady state.