Gathering and Exclusive Searching on Rings under Minimal Assumptions

  • Gianlorenzo D’Angelo
  • Alfredo Navarra
  • Nicolas Nisse
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8314)

Abstract

Consider a set of mobile robots with minimal capabilities placed over distinct nodes of a discrete anonymous ring. Asynchronously, each robot takes a snapshot of the ring, determining which nodes are either occupied by robots or empty. Based on the observed configuration, it decides whether to move to one of its adjacent nodes or not. In the first case, it performs the computed move, eventually. The computation also depends on the required task. In this paper, we solve both the well-known Gathering and Exclusive Searching tasks. In the former problem, all robots must simultaneously occupy the same node, eventually. In the latter problem, the aim is to clear all edges of the graph. An edge is cleared if it is traversed by a robot or if both its endpoints are occupied. We consider the exclusive searching where it must be ensured that two robots never occupy the same node. Moreover, since the robots are oblivious, the clearing is perpetual, i.e., the ring is cleared infinitely often. In the literature, most contributions are restricted to a subset of initial configurations. Here, we design two different algorithms and provide a characterization of the initial configurations that permit the resolution of the problems under minimal assumptions.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bampas, E., Czyzowicz, J., Gąsieniec, L., Ilcinkas, D., Labourel, A.: Almost optimal asynchronous rendezvous in infinite multidimensional grids. In: Lynch, N.A., Shvartsman, A.A. (eds.) DISC 2010. LNCS, vol. 6343, pp. 297–311. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  2. 2.
    Blin, L., Burman, J., Nisse, N.: Brief announcement: Distributed exclusive and perpetual tree searching. In: Aguilera, M.K. (ed.) DISC 2012. LNCS, vol. 7611, pp. 403–404. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  3. 3.
    Blin, L., Milani, A., Potop-Butucaru, M., Tixeuil, S.: Exclusive perpetual ring exploration without chirality. In: Lynch, N.A., Shvartsman, A.A. (eds.) DISC 2010. LNCS, vol. 6343, pp. 312–327. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  4. 4.
    Bonnet, F., Milani, A., Potop-Butucaru, M., Tixeuil, S.: Asynchronous exclusive perpetual grid exploration without sense of direction. In: Fernàndez Anta, A., Lipari, G., Roy, M. (eds.) OPODIS 2011. LNCS, vol. 7109, pp. 251–265. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  5. 5.
    Chalopin, J., Das, S.: Rendezvous of mobile agents without agreement on local orientation. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6199, pp. 515–526. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  6. 6.
    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
  7. 7.
    D’Angelo, G., Di Stefano, G., Klasing, R., Navarra, A.: Gathering of robots on anonymous grids without multiplicity detection. In: Even, G., Halldórsson, M.M. (eds.) SIROCCO 2012. LNCS, vol. 7355, pp. 327–338. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  8. 8.
    D’Angelo, G., Di Stefano, G., Navarra, A.: Gathering of six robots on anonymous symmetric rings. In: Kosowski, A., Yamashita, M. (eds.) SIROCCO 2011. LNCS, vol. 6796, pp. 174–185. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  9. 9.
    D’Angelo, G., Di Stefano, G., Navarra, A.: How to gather asynchronous oblivious robots on anonymous rings. In: Aguilera, M.K. (ed.) DISC 2012. LNCS, vol. 7611, pp. 326–340. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  10. 10.
    D’Angelo, G., Di Stefano, G., Navarra, A.: Gathering asynchronous and oblivious robots on basic graph topologies under the look-compute-move model. In: Alpern, S., Fokkink, R., Gąsieniec, L., Lindelauf, R., Subrahmanian, V. (eds.) Search Theory: A Game Theoretic Perspective, pp. 197–222. Springer (2013)Google Scholar
  11. 11.
    D’Angelo, G., Di Stefano, G., Navarra, A., Nisse, N., Suchan, K.: A unified approach for different tasks on rings in robot-based computing systems. In: Proc. of 15th IEEE IPDPS APDCM (to appear. 2013)Google Scholar
  12. 12.
    D’Angelo, G., Navarra, A., Nisse, N.: Robot Searching and Gathering on Rings under Minimal Assumptions, Tech. Rep. RR-8250, Inria (2013)Google Scholar
  13. 13.
    Dieudonne, Y., Pelc, A., Peleg, D.: Gathering despite mischief. In: Proc. of 23rd SODA, pp. 527–540 (2012)Google Scholar
  14. 14.
    Flocchini, P., Ilcinkas, D., Pelc, A., Santoro, N.: Computing without communicating: Ring exploration by asynchronous oblivious robots. In: Tovar, E., Tsigas, P., Fouchal, H. (eds.) OPODIS 2007. LNCS, vol. 4878, pp. 105–118. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  15. 15.
    Flocchini, P., Ilcinkas, D., Pelc, A., Santoro, N.: Remembering without memory: Tree exploration by asynchronous oblivious robots. Theor. Comput. Sci. 411(14-15), 1583–1598 (2010)CrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    Flocchini, P., Ilcinkas, D., Pelc, A., Santoro, N.: How many oblivious robots can explore a line. Inf. Process. Lett. 111(20), 1027–1031 (2011)CrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    Flocchini, P., Prencipe, G., Santoro, N.: Distributed Computing by oblivious mobile robots. Morgan and Claypool (2012)Google Scholar
  18. 18.
    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)Google Scholar
  19. 19.
    Fomin, F.V., Thilikos, D.M.: An annotated bibliography on guaranteed graph searching. Theor. Comput. Sci. 399(3), 236–245 (2008)CrossRefMATHMathSciNetGoogle Scholar
  20. 20.
    Ilcinkas, D., Nisse, N., Soguet, D.: The cost of monotonicity in distributed graph searching. Distributed Computing 22(2), 117–127 (2009)CrossRefMATHGoogle Scholar
  21. 21.
    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
  22. 22.
    Kamei, S., Lamani, A., Ooshita, F., Tixeuil, S.: Asynchronous mobile robot gathering from symmetric configurations without global multiplicity detection. In: Kosowski, A., Yamashita, M. (eds.) SIROCCO 2011. LNCS, vol. 6796, pp. 150–161. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  23. 23.
    Kamei, S., Lamani, A., Ooshita, F., Tixeuil, S.: Gathering an even number of robots in an odd ring without global multiplicity detection. In: Rovan, B., Sassone, V., Widmayer, P. (eds.) MFCS 2012. LNCS, vol. 7464, pp. 542–553. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  24. 24.
    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
  25. 25.
    Klasing, R., Markou, E., Pelc, A.: Gathering asynchronous oblivious mobile robots in a ring. Theor. Comput. Sci. 390, 27–39 (2008)CrossRefMATHMathSciNetGoogle Scholar
  26. 26.
    Kranakis, E., Krizanc, D., Markou, E.: The Mobile Agent Rendezvous Problem in the Ring. Morgan & Claypool (2010)Google Scholar
  27. 27.
    Prencipe, G.: Instantaneous actions vs. full asynchronicity: Controlling and coordinating a set of autonomous mobile robots. In: Restivo, A., Ronchi Della Rocca, S., Roversi, L. (eds.) ICTCS 2001. LNCS, vol. 2202, pp. 154–171. Springer, Heidelberg (2001)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Gianlorenzo D’Angelo
    • 1
  • Alfredo Navarra
    • 1
  • Nicolas Nisse
    • 2
  1. 1.Dipartimento di Matematica e InformaticaUniversità degli Studi di PerugiaItaly
  2. 2.CNRS, I3S, UMR 7271Inria and Univ. Nice Sophia AntipolisFrance

Personalised recommendations