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Priority evacuation from a disk: The case of n ≥ 4
Theoretical Computer Science ( IF 0.9 ) Pub Date : 2020-09-15 , DOI: 10.1016/j.tcs.2020.09.023
J. Czyzowicz , K. Georgiou , R. Killick , E. Kranakis , D. Krizanc , L. Narayanan , J. Opatrny , S. Shende

We introduce and study a new search-type 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 from a unit disk. Namely, we propose an algorithm specifying the trajectories of the robots which guarantees evacuation of the queen in time always better than 2+4(21)πn for n4 servants. We also demonstrate that for n4 servants the queen cannot be evacuated in time less than 2+πn+2n2.



中文翻译:

从磁盘优先疏散:的情况下Ñ  ≥4

我们引入并研究了一个带有(ñ+1个)-磁盘上的机器人。搜索者(机器人)都从磁盘的中心开始,具有单位速度,并且可以进行无线通信。目标是让杰出的机器人(女王)在尽可能短的时间内到达隐藏在磁盘外围的出口并从中撤离。剩下的n个机器人(仆人)在那里帮助女王的目标,并且不需要到达隐藏的出口。我们提供了从单位磁盘撤离女王/王后所需时间的上限和下限。即,我们提出了一种指定机器人轨迹的算法,该算法可以确保女王/王后及时疏散始终比2+42-1个πñ 对于 ñ4仆人。我们还证明了ñ4 女王/王后的疏散时间不得少于 2+πñ+2ñ2

更新日期:2020-10-30
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