Observe and Remain Silent (Communication-Less Agent Location Discovery)

  • Tom Friedetzky
  • Leszek Gąsieniec
  • Thomas Gorry
  • Russell Martin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7464)

Abstract

We study a randomised distributed communication-less coordination mechanism for n uniform anonymous agents located on a circle with unit circumference. We assume the agents are located at arbitrary but distinct positions, unknown to other agents. The agents perform actions in synchronised rounds. At the start of each round an agent chooses the direction of its movement (clockwise or anticlockwise), and moves at unit speed during this round. Agents are not allowed to overpass, i.e., when an agent collides with another it instantly starts moving with the same speed in the opposite direction. Agents cannot leave marks on the ring, have zero vision and cannot exchange messages. However, on the conclusion of each round each agent has access to (some, not necessarily all) information regarding its trajectory during this round. This information can be processed and stored by the agent for further analysis.

The location discovery task to be performed by each agent is to determine the initial position of every other agent and eventually to stop at its initial position, or proceed to another task, in a fully synchronised manner. Our primary motivation is to study distributed systems where agents collect the minimum amount of information that is necessary to accomplish this location discovery task.

Our main result is a fully distributed randomised (Las Vegas type) algorithm, solving the location discovery problemw.h.p. in O(nlog2n) rounds (assuming the agents collect sufficient information). Note that our result also holds if initially the agents do not know the value of n and they have no coherent sense of direction.

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References

  1. 1.
    Ando, H., Suzuki, I., Yamashita, M.: Formation and agreement problems for synchronous mobile robots with limited visibility. In: Proc. IEEE Symposium on Intelligent Control, pp. 453–460 (1995)Google Scholar
  2. 2.
    Attiya, H., Welch, J.: Distributed Computing. McGraw-Hill (1998)Google Scholar
  3. 3.
    Bender, M.A., Slonim, D.: The power of team exploration: Two robots can learn unlabeled directed graphs. In: Proc. 35th Annual Symposium on Foundations of Computer Science, FOCS 1994, pp. 75–85 (1994)Google Scholar
  4. 4.
    Chalopin, J., Flocchini, P., Mans, B., Santoro, N.: Network Exploration by Silent and Oblivious Robots. In: Thilikos, D.M. (ed.) WG 2010. LNCS, vol. 6410, pp. 208–219. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  5. 5.
    Cieliebak, M., Flocchini, P., Prencipe, G., Santoro, N.: Solving the Robots Gathering Problem. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 1181–1196. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  6. 6.
    Cohen, R., Peleg, D.: Local spreading algorithms for autonomous robot systems. Theoretical Computer Science 399(1-2), 71–82 (2008)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Cooper, C., Frieze, A., Radzik, T.: Multiple Random Walks and Interacting Particle Systems. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009. LNCS, vol. 5556, pp. 399–410. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  8. 8.
    Czyzowicz, J., Gąsieniec, L., Kosowski, A., Kranakis, E.: Boundary Patrolling by Mobile Agents with Distinct Maximal Speeds. In: Demetrescu, C., Halldórsson, M.M. (eds.) ESA 2011. LNCS, vol. 6942, pp. 701–712. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  9. 9.
    Czyzowicz, J., Labourel, A., Pelc, A.: Optimality and competitiveness of exploring polygons by mobile robots. Information and Computation 209(1), 74–88 (2011)MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Deng, X., Kameda, T., Papadimitriou, C.: How to learn an unknown environment I: the rectilinear case. Journal of ACM 45(2), 215–245 (1998)MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    Dolev, S.: Self-Stabilization. MIT Press (2000)Google Scholar
  12. 12.
    Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Hard Tasks for Weak Robots: The Role of Common Knowledge in Pattern Formation by Autonomous Mobile Robots. In: Aggarwal, A.K., Pandu Rangan, C. (eds.) ISAAC 1999. LNCS, vol. 1741, pp. 93–102. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  13. 13.
    Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Pattern formation by autonomous robots without chirality. In: SIROCCO 2001, pp. 147–162 (2001)Google Scholar
  14. 14.
    Fraigniaud, P., Gąsieniec, L., Kowalski, D.R., Pelc, A.: Collective tree exploration. Networks 48(3), 166–177 (2006)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Hoffmann, F., Icking, C., Klein, R., Kriegel, K.: The polygon exploration problem. SIAM J. Computing 31(2), 577–600 (2001)MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    Klasing, R., Markou, E., Pelc, A.: Gathering asynchronous oblivious mobile robots in a ring. Theoretical Computer Science 390, 27–39 (2008)MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Kong, C.S., Peng, N.A., Rekleitis, I.: Distributed coverage with multi-robot systems. In: Proc. Robotics and Automation, pp. 2423–2429 (2006)Google Scholar
  18. 18.
    Kranakis, E., Krizanc, D., Markou, E.: The Mobile Agent Rendezvous Problem in the Ring. Morgan and Claypool Publishers (2010)Google Scholar
  19. 19.
    Lynch, N.A.: Distributed Algorithms. Morgan Kaufmann Publishers (1996)Google Scholar
  20. 20.
    Massias, J.-P., Robin, G.: Bornes effectives pour certaines fonctions concernant les nombres premiers. Journal de Théorie des Nombres de Bordeaux 8, 215–242 (1996)MathSciNetMATHCrossRefGoogle Scholar
  21. 21.
    Motwani, R., Raghavan, P.: Randomized Algorithms. Cambridge University Press (1995)Google Scholar
  22. 22.
    Santoro, N.: Design and Analysis of Distributed Algorithms. Wiley (2006)Google Scholar
  23. 23.
    Sugihara, K., Suzuki, I.: Distributed algorithms for formation of geometric patterns with many mobile robots. J. Robotic Systems 13(3), 127–139 (1996)MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Tom Friedetzky
    • 1
  • Leszek Gąsieniec
    • 2
  • Thomas Gorry
    • 2
  • Russell Martin
    • 2
  1. 1.School of Engineering and Computing SciencesDurham UniversityUK
  2. 2.Department of Computer ScienceUniversity of LiverpoolUK

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