God Save the Queen

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



PDF
Thumbnail PDF

File

LIPIcs.FUN.2018.16.pdf
  • Filesize: 0.96 MB
  • 20 pages

Document Identifiers

Author Details

Jurek Czyzowicz
  • Université du Québec en Outaouais, Gatineau, Québec, Canada
Konstantinos Georgiou
  • Department of Mathematics, Ryerson University, Toronto, Ontario, Canada
Ryan Killick
  • School of Computer Science, Carleton University, Ottawa, Ontario, Canada
Evangelos Kranakis
  • School of Computer Science, Carleton University, Ottawa, Ontario, Canada
Danny Krizanc
  • Department of Mathematics & Comp. Sci., Wesleyan University, Middletown, CT, USA
Lata Narayanan
  • Department of Comp. Sci. and Software Eng., Concordia University, Montreal, Québec, Canada
Jaroslav Opatrny
  • Department of Comp. Sci. and Software Eng., Concordia University, Montreal, Québec, Canada
Sunil Shende
  • Department of Computer Science, Rutgers University, Camden, NJ, USA

Cite As Get BibTex

Jurek Czyzowicz, Konstantinos Georgiou, Ryan Killick, Evangelos Kranakis, Danny Krizanc, Lata Narayanan, Jaroslav Opatrny, and Sunil Shende. God Save the Queen. In 9th International Conference on Fun with Algorithms (FUN 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 100, pp. 16:1-16:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.FUN.2018.16

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.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Distributed artificial intelligence
  • Computing methodologies → Mobile agents
Keywords
  • Algorithm
  • Evacuation
  • Exit
  • Disk
  • Wireless Communication
  • Queen
  • Priority
  • Robots
  • Search
  • Servants
  • Trajectory

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads

References

  1. R. Ahlswede and I. Wegener. Search problems. Wiley-Interscience, 1987. Google Scholar
  2. S. Alpern and S. Gal. The theory of search games and rendezvous, volume 55. Kluwer Academic Publishers, 2002. Google Scholar
  3. Steve Alpern, Robbert Fokkink, Leszek Gąsieniec, Roy Lindelauf, and V.S. Subrahmanian, editors. Ten Open Problems in Rendezvous Search, pages 223-230. Springer NY, New York, NY, 2013. Google Scholar
  4. R. Baeza Yates, J. Culberson, and G. Rawlins. Searching in the plane. Information and Computation, 106(2):234-252, 1993. Google Scholar
  5. R. Baeza-Yates and R. Schott. Parallel searching in the plane. Computational Geometry, 5(3):143-154, 1995. Google Scholar
  6. A. Beck. On the linear search problem. Israel J. of Mathematics, 2(4):221-228, 1964. Google Scholar
  7. R. Bellman. An optimal search. SIAM Review, 5(3):274-274, 1963. Google Scholar
  8. S. Brandt, F. Laufenberg, Y. Lv, D. Stolz, and R. Wattenhofer. Collaboration without communication: Evacuating two robots from a disk. In Proceedings of Algorithms and Complexity - 10th International Conference, CIAC 2017, Athens, Greece, May 24-26, 2017, pages 104-115, 2017. Google Scholar
  9. J. Czyzowicz, S. Dobrev, K. Georgiou, E. Kranakis, and F. MacQuarrie. Evacuating two robots from multiple unknown exits in a circle. Theor. Comput. Sci., 709:20-30, 2018. Google Scholar
  10. J. Czyzowicz, L. Gasieniec, T. Gorry, E. Kranakis, R. Martin, and D. Pajak. Evacuating robots from an unknown exit located on the perimeter of a disc. In Proceedings DISC, Austin, Texas, pages 122-136. Springer, 2014. Google Scholar
  11. J. Czyzowicz, K. Georgiou, M. Godon, E. Kranakis, D. Krizanc, W. Rytter, and M. Wlodarczyk. Evacuation from a disc in the presence of a faulty robot. In Proceedings SIROCCO 2017, 19-22 June 2017, Porquerolles, France, pages 158-173, 2018. Google Scholar
  12. J. Czyzowicz, K. Georgiou, R. Killick, E. Kranakis, D. Krizanc, L. Narayanan, J. Opatrny, and S. Shence. God Save the Queen. CoRR, abs/1804.06011, 2018. Google Scholar
  13. J. Czyzowicz, K. Georgiou, R. Killick, E. Kranakis, D. Krizanc, L. Narayanan, J. Opatrny, and S. Shende. Priority evacuation from a disk using mobile robots, 2018, Submitted. Google Scholar
  14. J. Czyzowicz, K. Georgiou, E. Kranakis, L. Narayanan, J. Opatrny, and B. Vogtenhuber. Evacuating robots from a disk using face-to-face communication (extended abstract). In Proceedings of Algorithms and Complexity, CIAC 2015, Paris, France, May 20-22, 2015, pages 140-152, 2015. Google Scholar
  15. J. Czyzowicz, E. Kranakis, D. Krizanc, L. Narayanan, J. Opatrny, and S. Shende. Wireless autonomous robot evacuation from equilateral triangles and squares. In Proceedings of Ad-hoc, Mobile, and Wireless Networks, ADHOC-NOW, Athens, Greece, June 29 - July 1, 2015, pages 181-194, 2015. Google Scholar
  16. Konstantinos Georgiou, George Karakostas, and Evangelos Kranakis. Search-and-fetch with one robot on a disk - (track: Wireless and geometry). In Algorithms for Sensor Systems - 12th International Symposium on Algorithms and Experiments for Wireless Sensor Networks, ALGOSENSORS 2016, Aarhus, Denmark, August 25-26, 2016, Revised Selected Papers, pages 80-94, 2016. Google Scholar
  17. Konstantinos Georgiou, George Karakostas, and Evangelos Kranakis. Search-and-fetch with 2 robots on a disk - wireless and face-to-face communication models. In Federico Liberatore, Greg H. Parlier, and Marc Demange, editors, Proceedings of the 6th International Conference on Operations Research and Enterprise Systems, ICORES 2017, Porto, Portugal, February 23-25, 2017, pages 15-26. SciTePress, 2017. Google Scholar
  18. I. Lamprou, R. Martin, and S. Schewe. Fast two-robot disk evacuation with wireless communication. In Proceedings DISC, Paris, France, pages 1-15, 2016. Google Scholar
  19. D. Pattanayak, H. Ramesh, P.S. Mandal, and S. Schmid. Evacuating two robots from two unknown exits on the perimeter of a disk with wireless communication. In Proceedings of the 19th International Conference on Distributed Computing and Networking, ICDCN 2018, Varanasi, India, January 4-7, 2018, pages 20:1-20:4, 2018. Google Scholar
  20. L. Stone. Theory of optimal search. Academic Press New York, 1975. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail