The spread of an infection, a contagion, meme, emotion, message and various other spreadable objects have been discussed in several works. Burning and firefighting have been discussed in particular on static graphs. Burning simulates the notion of the spread of "fire" throughout a graph (plus, one unburned node burned at each time-step), graph firefighting simulates the defending of nodes by placing firefighters on the nodes which have not been already burned while the fire is being spread (started by a single fire source). This article studies a combination of firefighting and burning on a graph class which is a variation (generalization) of temporal graphs. Nodes can be infected from "outside" a network. We present a notion of both upgrading (of unburned nodes, similar to firefighting) and repairing (of infected nodes). The nodes which are burned, firefighted, or repaired are chosen probabilistically. So a variable amount of nodes are infected, upgraded and repaired in each time step. In the model presented in this article, both burning and firefighting proceed concurrently, we introduce such a system to enable the community to study the notion of spread of an infection and the notion of upgrade/repair against each other. The graph class that we study these processes is a variation of temporal graph class in which at each time-step, probabilistically, a communication takes place (iff an edge exists in that time step). In addition, a node can be "worn out" and thus can be removed from the network, a new healthy node can be added to the network. This class of graphs enables systems with high complexity to be able to be simulated and studied.
翻译:感染、 传染、 传染、 meme、 情感、 信息 和其他各种可传播对象的传播在数个作品中讨论过。 火和消防的结合在静态图形中特别讨论过。 燃烧模拟“ 火” 概念在图表中( 加上, 每步都燃烧一个未燃烧的节点 ), 图形消防模拟节点的防守, 将消防员放在火蔓延时尚未燃烧的节点上( 由单一的消防源启动 ) 。 文章研究的是健康消防和燃烧的结合, 图表类是时间图的变异( 概括化) 。 节点可以从“ 外部” 网络被“ 外” 感染。 我们展示的是升级( 未燃烧的节点, 类似消防的节点) 和修复( 被感染的节点) 的概念被选择为具有危险性。 因此, 每步调节点的数量会变异的节点会被感染、 升级和修复。 在本文中展示的模型中, 燃烧和灭火和灭火运动会同时进行。 我们引入了这样的系统可以让社区 滚变换 。 因此, 每个方向的网络可以让这些变变换到 。