Gathering of Six Robots on Anonymous Symmetric Rings

  • Gianlorenzo D’Angelo
  • Gabriele Di Stefano
  • Alfredo Navarra
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6796)


The paper deals with a recent model of robot-based computing which makes use of identical, memoryless mobile robots placed on nodes of anonymous graphs. The robots operate in Look-Compute-Move cycles; in one cycle, a robot takes a snapshot of the current configuration (Look), takes a decision whether to stay idle or to move to one of its adjacent nodes (Compute), and in the latter case makes an instantaneous move to this neighbor (Move). Cycles are performed asynchronously for each robot.

In particular, we consider the case of only six robots placed on the nodes of an anonymous ring in such a way they constitute a symmetric placement with respect to one single axis of symmetry, and we ask whether there exists a strategy that allows the robots to gather at one single node. This is in fact the first case left open after a series of papers [1,2,3,4] dealing with the gathering of oblivious robots on anonymous rings. As long as the gathering is feasible, we provide a new distributed approach that guarantees a positive answer to the posed question. Despite the very special case considered, the provided strategy turns out to be very interesting as it neither completely falls into symmetry-breaking nor into symmetry-preserving techniques.


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  1. 1.
    Haba, K., Izumi, T., Katayama, Y., Inuzuka, N., Wada, K.: On gathering problem in a ring for 2n autonomous mobile robots. In: Kulkarni, S., Schiper, A. (eds.) SSS 2008. LNCS, vol. 5340. Springer, Heidelberg (2008)Google Scholar
  2. 2.
    Klasing, R., Kosowski, A., Navarra, A.: Taking advantage of symmetries: Gathering of many asynchronous oblivious robots on a ring. Theor. Comput. Sci. 411, 3235–3246 (2010)CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Klasing, R., Markou, E., Pelc, A.: Gathering asynchronous oblivious mobile robots in a ring. Theor. Comput. Sci. 390, 27–39 (2008)CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Koren, M.: Gathering small number of mobile asynchronous robots on ring. Zeszyty Naukowe Wydzialu ETI Politechniki Gdanskiej. Technologie Informacyjne 18, 325–331 (2010)Google Scholar
  5. 5.
    Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Gathering of asynchronous robots with limited visibility. Theor. Comput. Sci. 337, 147–168 (2005)CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Izumi, T., Izumi, T., Kamei, S., Ooshita, F.: Randomized gathering of mobile robots with local-multiplicity detection. In: Guerraoui, R., Petit, F. (eds.) SSS 2009. LNCS, vol. 5873, pp. 384–398. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  7. 7.
    Izumi, T., Izumi, T., Kamei, S., Ooshita, F.: Mobile robots gathering algorithm with local weak multiplicity in rings. In: Patt-Shamir, B., Ekim, T. (eds.) SIROCCO 2010. LNCS, vol. 6058, pp. 101–113. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  8. 8.
    Prencipe, G.: Impossibility of gathering by a set of autonomous mobile robots. Theor. Comput. Sci. 384, 222–231 (2007)CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    D’Angelo, G., Di Stefano, G., Navarra, A.: Gathering of six robots on anonymous symmetric rings. Technical Report R.11-112, Dipartimento di Ingegneria Elettrica e dell’Informazione, Università dell’Aquila (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Gianlorenzo D’Angelo
    • 1
  • Gabriele Di Stefano
    • 1
  • Alfredo Navarra
    • 2
  1. 1.Dipartimento di Ingegneria Elettrica e dell’InformazioneUniversità degli Studi dell’AquilaItaly
  2. 2.Dipartimento di Matematica e InformaticaUniversità degli Studi di PerugiaItaly

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