# God save the queen

Jurek Czyzowicz, Konstantinos Georgiou, Ryan Killick, Evangelos Kranakis, Danny Krizanc, Lata Narayanan, Jaroslav Opatrny, Sunil Shende

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations

## Abstract

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 + 2π/3 + √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 + π/6 + v3/2 ~ 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.

Original language English (US) 9th International Conference on Fun with Algorithms, FUN 2018 Giuseppe Prencipe, Hiro Ito, Stefano Leonardi, Linda Pagli Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing 161-1620 1460 9783959770675 https://doi.org/10.4230/LIPIcs.FUN.2018.16 Published - Jun 1 2018 9th International Conference on Fun with Algorithms, FUN 2018 - La Maddalena Island, ItalyDuration: Jun 13 2018 → Jun 15 2018

### Publication series

Name Leibniz International Proceedings in Informatics, LIPIcs 100 1868-8969

### Other

Other 9th International Conference on Fun with Algorithms, FUN 2018 Italy La Maddalena Island 6/13/18 → 6/15/18

• Software

## Keywords

• Algorithm
• Disk
• Evacuation
• Exit
• Priority
• Queen
• Robots
• Search
• Servants
• Trajectory
• Wireless communication

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