论文标题
加权稀疏随机图的洪水是主动节点和被动节点的
Flooding in weighted sparse random graphs of active and passive nodes
论文作者
论文摘要
本文讨论了具有两种类型的节点的大加权稀疏随机图上的第一次通道渗透和洪水：主动和被动节点。在数学物理学中，可以将被动节点解释为流体流或水无法通过的封闭门，并且可以将活性节点解释为开放的大门，水可能会进一步流动。本文的模型在现实生活中有许多应用程序，例如，信息传播，被动节点被解释为被动接收器，他们可能会读取消息但不会响应消息。在流行病上，被动节点可以解释为在患有疾病后自我分离以停止进一步传播疾病的个体。当活动节点之间以及主动节点和被动节点之间的边缘上的所有权重是独立的，并且分布指数分布（但不是必需的分布式）时，本文为加权典型的洪水时间提供了一个近似公式。
This paper discusses first passage percolation and flooding on large weighted sparse random graphs with two types of nodes: active and passive nodes. In mathematical physics passive nodes can be interpreted as closed gates where fluid flow or water cannot pass through and active nodes can be interpreted as open gates where water may keep flowing further. The model of this paper has many applications in real life, for example, information spreading, where passive nodes are interpreted as passive receivers who may read messages but do not respond to them. In the epidemic context passive nodes may be interpreted as individuals who self-isolate themselves after having a disease to stop spreading the disease any further. When all weights on edges between active nodes and between active and passive nodes are independent and exponentially distributed (but not necessary identically distributed), this article provides an approximation formula for the weighted typical flooding time.
