标题： 燃烧游戏：一种缓慢的智能火焰 显示英文标题

标题： The Pyro game: a slow intelligent fire

摘要： 在消防员问题中，火灾在一个图的顶点处爆发，并且在每个后续时间步骤中，消防员选择一个顶点进行保护，然后火灾从每个燃烧的顶点传播到每一个未受保护的邻居。这个问题可以被视为网络中谣言或疾病传播的简化模型。我们引入了一个新的双人变种，称为Pyro游戏，在每一步中，火灾从一个燃烧的顶点传播到该顶点的所有未受保护的邻居。火灾不再自动进行，并旨在最大化燃烧的顶点数量。我们证明，与消防员问题不同，在Pyro游戏中，一个消防员可以在笛卡尔网格上控制火灾。我们还在无限强网格上研究了Pyro游戏和消防员问题以及Pyro游戏的复杂性。 显示英文摘要

摘要： In the Firefighter problem, a fire breaks out at a vertex of a graph and at each subsequent time step, the firefighter chooses a vertex to protect and then the fire spreads from each burned vertex to every unprotected neighbour. The problem can be thought of as a simplified model for the spread of gossip or disease in a network. We introduce a new two-player variation called the Pyro game, in which at each step, the fire spreads from one burned vertex to all unprotected neighbours of that vertex. The fire is no longer automated and aims to maximize the number of burned vertices. We show, that unlike the Firefighter problem, one firefighter can contain a fire on the Cartesian grid in the Pyro game. We also study both the Pyro Game and the Firefighter Problem on the infinite strong grid and the complexity of the Pyro game.