Evacuating robots via unknown exit in a disk

Jurek Czyzowicz, Leszek Gąsieniec, Thomas Gorry, Evangelos Kranakis, Russell Martin, Dominik Pajak

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

31 Scopus citations

Abstract

Consider k mobile robots inside a circular disk of unit radius. The robots are required to evacuate the disk through an unknown exit point situated on its boundary. We assume all robots having the same (unit) maximal speed and starting at the centre of the disk. The robots may communicate in order to inform themselves about the presence (and its position) or the absence of an exit. The goal is for all the robots to evacuate through the exit in minimum time.

We consider two models of communication between the robots: in non-wireless (or local) communication model robots exchange information only when simultaneously located at the same point, and wireless communication in which robots can communicate one another at any time.

We study the following question for different values of k: what is the optimal evacuation time for k robots? We provide algorithms and show lower bounds in both communication models for k = 2 and k = 3 thus indicating a difference in evacuation time between the two models. We also obtain almost-tight bounds on the asymptotic relation between evacuation time and team size, for large k. We show that in the local communication model, a team of k robots can always evacuate in time, 3 + whereas at least 3 + +O(k−2) time is sometimes required. In the wireless communication model, time 3+ (k−4/3) always suffices to complete evacuation, and at least 3+ is sometimes required. This shows a clear separation between the local and the wireless communication models.

Original languageEnglish (US)
Title of host publicationDistributed Computing - 28th International Symposium, DISC 2014, Proceedings
EditorsFabian Kuhn
PublisherSpringer Verlag
Pages122-136
Number of pages15
ISBN (Electronic)9783662451731
DOIs
StatePublished - Jan 1 2014
Externally publishedYes
Event28th International Symposium on Distributed Computing, DISC 2014 - Austin, United States
Duration: Oct 12 2014Oct 15 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8784
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference28th International Symposium on Distributed Computing, DISC 2014
CountryUnited States
CityAustin
Period10/12/1410/15/14

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Czyzowicz, J., Gąsieniec, L., Gorry, T., Kranakis, E., Martin, R., & Pajak, D. (2014). Evacuating robots via unknown exit in a disk. In F. Kuhn (Ed.), Distributed Computing - 28th International Symposium, DISC 2014, Proceedings (pp. 122-136). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8784). Springer Verlag. https://doi.org/10.1007/978-3-662-45174-8_9