AI 中文总结
该研究针对图上含单个追击者与不可见逃避者的追逃游戏，提出追击者可自定义边旅行时间与查询序列的策略，证明其能在多项式时间内于任意图取胜，即便逃避者可更早开始也能在指数时间内获胜。
AI 中文摘要
我们研究图上的追逃游戏，游戏包含一个追击者和一个不可见的逃避者。追击者可给图的边分配整数旅行时间，并指定一个有限顶点序列，每一时间步查询一个顶点。逃避者则在相同时间范围内选择一条路径，目标是避开所有查询。当旅行时间为单位时间时，逃避者必须每时间步移动的设定被称为猎人与兔子游戏；而逃避者可在顶点等待的变体可表述为消防游戏：燃烧图的顶点必须被扑灭，任何未被扑灭的顶点会重新点燃其邻居。对于这两种设定，我们证明，选择旅行时间的能力使单个追击者能在多项式时间内于任意图上成功，这与无权图形成对比——在无权图中，所需猎人或消防员的数量可随顶点数量线性增长。若逃避者除等待外，还可在追击者未知的更早时间开始，我们证明追击者仍可在指数时间内于任意图上获胜。
英文摘要
We study pursuit-evasion games on graphs with a single pursuer and an invisible evader. The pursuer may assign integer travel times to the edges of the graph and specify a finite sequence of vertices to query, one per time step. The evader then chooses a walk over the same time horizon, aiming to elude all queries. With unit travel times, the setting in which the evader must move at every time step is known as the hunter and rabbit game, while the variant in which the evader can wait at a vertex can be phrased as a firefighting game: the vertices of a burning graph must be extinguished, and any vertex left burning reignites its neighbors. For both settings, we show that the power to choose travel times allows a single pursuer to succeed in polynomial time on any graph. This contrasts with unweighted graphs, where the number of hunters or firefighters needed can grow linearly in the number of vertices. If the evader, in addition to waiting, may start at an earlier time unknown to the pursuer, we show that the pursuer still wins on any graph given exponential time.
