Abstract
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. 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 (using wireless communication) notify the other agent, who will make a beeline to it.
The problem has been studied for robots with the same speedĀ [8]. 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 \(s \ge c_{2.75} \approx 2.75\) by showing matching upper and lower bounds on the worst-case evacuation time. For \(1\le s < c_{2.75}\), 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 fromĀ [8] is outperformed by our proposed strategies for any \(s \ge c_{1.71} \approx 1.71\).
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Lamprou, I., Martin, R., Schewe, S. (2016). Fast Two-Robot Disk Evacuation with Wireless Communication. In: Gavoille, C., Ilcinkas, D. (eds) Distributed Computing. DISC 2016. Lecture Notes in Computer Science(), vol 9888. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53426-7_1
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