发表机构
University of Glasgow; University of Lethbridge; University of Birmingham; Mount Allison University（格拉斯哥大学; 莱斯布里奇大学; 伯明翰大学; 蒙莫斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究消防员问题变体，其中防御可扩散，提供算法、难度及无限网格图的遏制结果。
AI 中文摘要
消防员问题模拟了图上的扩散过程（最初是火灾，也可以是感染或谣言等）。防御者每回合拯救一个顶点；每次防御后，火势会蔓延到所有燃烧顶点的未燃烧且未防御的邻居。在一般图中，决定防御者是否存在一种策略来保护一定数量的目标顶点在计算上是困难的，但在某些受限情况下是可处理的。受可扩散狂犬病疫苗研究启发，我们研究了消防员问题的一个变体，其中防御也会扩散。该问题已有一些近似结果；我们提供了算法和难度结果，以及无限$n$维笛卡尔网格图和强网格图的遏制结果。
英文摘要
The Firefighter Problem models a spreading process (originally a fire, alternatively an infection or rumour, for example) on a graph. A defender saves a single vertex per turn; after each defence, the fire spreads to the unburned and undefended neighbours of all burning vertices. Deciding whether a strategy exists for the defender to protect some targeted number of vertices is computationally hard in graphs in general, but tractable in some restricted cases. Inspired by research into spreadable rabies vaccines for bats, we study a variant of the Firefighter problem in which defence also spreads. Some approximation results are already known for this problem; we provide algorithmic and hardness results, as well as containment results for the infinite $n$-dimensional Cartesian and strong grid graphs.
Comments17 pages
