In the fast evacuation problem, we study the path planning problem for two robots who want to minimize the worst-case evacuation time on the unit disk, that is, the time till both of them evacuate. The robots are initially placed at the center of the disk. In order to evacuate, they need to reach an unknown point, the exit, on the boundary of the disk. Once one of the robots finds the exit, it will instantaneously, i.e., using wireless communication, notify the other agent who will then follow a straight line to it.

The problem has been studied for robots with the same speed [13]. We study a more general case where one robot has speed 1 and the other has speed $s\ge 1$. We provide optimal evacuation strategies in the case that $s\ge 2.75$ by showing matching upper and lower bounds on the worst-case evacuation time. For $1\le s<2.75$, we show (non-matching) upper and lower bounds on the evacuation time with a ratio less than 1.22. Moreover, we demonstrate that a different-speeds generalization of the two-robot search strategy from [13] is outperformed by our proposed strategies for any $s\ge 1.71$.

在快速疏散问题中，我们研究了两个机器人的路径规划问题，这些机器人希望最大程度地减少单位磁盘上最坏情况下的疏散时间，即两个人都疏散的时间。机械手最初位于磁盘的中心。为了撤离，它们需要到达磁盘边界上的一个未知点，即出口。一旦其中一个机器人找到出口，它将立即（即，使用无线通信）通知另一位代理，然后该代理将沿着一条直线到达该出口。

对于具有相同速度的机器人，已经研究了该问题[13]。我们研究了一个更普遍的情况，其中一个机器人的速度为1，而另一个机器人的速度为$s\ge \mathrm{1个}$。在以下情况下，我们提供最佳疏散策略$s\ge 2.75$通过显示最坏情况下疏散时间的匹配上限和下限。对于$\mathrm{1个}\le s<2.75$，我们显示撤离时间的上限（下限）小于1.22。此外，我们证明，对于任何情况，我们提出的策略都优于[13]提出的两机器人搜索策略的不同速度推广。$s\ge 1.71$。