自适应网络中代价最优的开关保护策略
Cost-Optimal Switching Protection Strategy in Adaptive Networks
摘要：
本文研究了切换接触网络中控制传播过程的网络适应机制模型，即自适应易感-感染-易感模型。网络模型中的边会随机删除或添加，具体取决于通过它们传播的风险。通过分析“网络中”的传播动态和“网络的结构动态”的联合演化，我们推导出控制所得到的切换网络中的传播动态的自适应律的条件。与文献中的结果相比，我们允许网络的初始拓扑是任意的图。此外，假设存在与网络中的切换边缘相关联的成本，我们提出了一个优化框架来找到成本最优的网络自适应律，即，成本最优边缘切换概率。在一定条件下的切换成本，我们表明，最佳的适应法律可以找到使用凸优化。我们用数值模拟来说明我们的结果。
英文摘要：
In this paper, we study a model of network adaptation mechanism to control spreading processes over switching contact networks, called adaptive susceptible-infected-susceptible model. The edges in the network model are randomly removed or added depending on the risk of spread through them. By analyzing the joint evolution of the spreading dynamics "in the network" and the structural dynamics "of the network", we derive conditions on the adaptation law to control the dynamics of the spread in the resulting switching network. In contrast with the results in the literature, we allow the initial topology of the network to be an arbitrary graph. Furthermore, assuming there is a cost associated to switching edges in the network, we propose an optimization framework to find the cost-optimal network adaptation law, i.e., the cost-optimal edge switching probabilities. Under certain conditions on the switching costs, we show that the optimal adaptation law can be found using convex optimization. We illustrate our results with numerical simulations.
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