License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FUN.2018.16
URN: urn:nbn:de:0030-drops-88074
URL: https://drops.dagstuhl.de/opus/volltexte/2018/8807/
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### God Save the Queen

 pdf-format:

### 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 + (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.

### BibTeX - Entry

```@InProceedings{czyzowicz_et_al:LIPIcs:2018:8807,
author =	{Jurek Czyzowicz and Konstantinos Georgiou and Ryan Killick and Evangelos Kranakis and Danny Krizanc and Lata Narayanan and Jaroslav Opatrny and Sunil Shende},
title =	{{God Save the Queen}},
booktitle =	{9th International Conference on Fun with Algorithms (FUN 2018)},
pages =	{16:1--16:20},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-95977-067-5},
ISSN =	{1868-8969},
year =	{2018},
volume =	{100},
editor =	{Hiro Ito and Stefano Leonardi and Linda Pagli and Giuseppe Prencipe},
publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address =	{Dagstuhl, Germany},
URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8807},
URN =		{urn:nbn:de:0030-drops-88074},
doi =		{10.4230/LIPIcs.FUN.2018.16},
annote =	{Keywords: Algorithm, Evacuation, Exit, Disk, Wireless Communication, Queen, Priority, Robots, Search, Servants, Trajectory}
}
```

 Keywords: Algorithm, Evacuation, Exit, Disk, Wireless Communication, Queen, Priority, Robots, Search, Servants, Trajectory Collection: 9th International Conference on Fun with Algorithms (FUN 2018) Issue Date: 2018 Date of publication: 04.06.2018

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