eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-06-04
16:1
16:20
10.4230/LIPIcs.FUN.2018.16
article
God Save the Queen
Czyzowicz, Jurek
1
Georgiou, Konstantinos
2
Killick, Ryan
3
Kranakis, Evangelos
3
Krizanc, Danny
4
Narayanan, Lata
5
Opatrny, Jaroslav
5
Shende, Sunil
6
Université du Québec en Outaouais, Gatineau, Québec, Canada
Department of Mathematics, Ryerson University, Toronto, Ontario, Canada
School of Computer Science, Carleton University, Ottawa, Ontario, Canada
Department of Mathematics & Comp. Sci., Wesleyan University, Middletown, CT, USA
Department of Comp. Sci. and Software Eng., Concordia University, Montreal, Québec, Canada
Department of Computer Science, Rutgers University, Camden, NJ, USA
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 the queen requires time at least 3 + pi/6 + sqrt{3}/2 ~~ 4.3896 in the worst case. If one or both of the queen's other servants (Biddy and/or Lili) are with her, we show that the time bounds can be improved to 3.8327 for two servants, and 3.3738 for three servants. Finally we show lower bounds for these cases of 3.6307 (two servants) and 3.2017 (three servants). The case of n >= 4 is the subject of an independent study by Queen Daniela's Royal Scientific Team.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol100-fun2018/LIPIcs.FUN.2018.16/LIPIcs.FUN.2018.16.pdf
Algorithm
Evacuation
Exit
Disk
Wireless Communication
Queen
Priority
Robots
Search
Servants
Trajectory