Queen Daniela of Sardinia is asleep at the center of a round room at the top of the tower in her castle. She is accompanied by her faithful servant, Eva. Suddenly, they are awakened by cries of "Fire". The room is pitch black and they are disoriented. There is exactly one exit from the room somewhere along its boundary. They must find it as quickly as possible in order to save the life of the queen. It is known that with two people searching while moving at maximum speed 1 anywhere in the room, the room can be evacuated (i.e., with both people exiting) in 1 + (2 pi)/3 + sqrt{3} ~~ 4.8264 time units and this is optimal [Czyzowicz et al., DISC'14], assuming that the first person to find the exit can directly guide the other person to the exit using her voice. Somewhat surprisingly, in this paper we show that if the goal is to save the queen (possibly leaving Eva behind to die in the fire) there is a slightly better strategy. We prove that this "priority" version of evacuation can be solved in time at most 4.81854. Furthermore, we show that any strategy for saving themore »
Priority Evacuation from a Disk Using Mobile Robots
We introduce and study a new searchtype problem with ( 𝑛+1 )robots on a disk. The searchers (robots) all start from the center of the disk, have unit speed, and can communicate wirelessly. The goal is for a distinguished robot (the queen) to reach and evacuate from an exit that is hidden on the perimeter of the disk in as little time as possible. The remaining n robots (servants) are there to facilitate the queen’s objective and are not required to reach the hidden exit. We provide upper and lower bounds for the time required to evacuate the queen. Namely, we propose an algorithm specifying the trajectories of the robots which guarantees evacuation of the queen in time always better than 2+4(\sqrt{2}1)\pi/n for 𝑛≥4 servants. We also demonstrate that for 𝑛≥4 servants the queen cannot be evacuated in time less than 2 + \pi/n + 2/n^2.
 Award ID(s):
 1813940
 Publication Date:
 NSFPAR ID:
 10092714
 Journal Name:
 Lecture notes in computer science
 Volume:
 11085
 Page Range or eLocationID:
 392  407
 ISSN:
 03029743
 Sponsoring Org:
 National Science Foundation
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