On Gathering of Semi-synchronous Robots in Graphs

  • Serafino Cicerone
  • Gabriele Di Stefano
  • Alfredo NavarraEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11914)


We consider the Gathering problem where a swarm of weak robots disposed on the vertices of an anonymous graph are required to meet at one vertex from where they do not move anymore. In our recent work [Cicerone et al., SIROCCO’19], we have shown how synchronicity heavily affects the design of resolution algorithms within the standard Look-Compute-Move (LCM) model. In particular, we have investigated two dense and highly symmetric topologies: complete graphs and complete bipartite graphs. We characterized all solvable configurations for synchronous robots, whereas it is known that in complete graphs asynchronous robots cannot solve the problem, ever. Instead of approaching directly the asynchronous case in complete bipartite graphs, we asked what happens in the so-called semi-synchronous model, that is robots are synchronized but they are not necessarily all active within all LCM cycles. It turns out that still the gathering can never be accomplished on complete graphs, whereas challenging cases arise in complete bipartite graphs. We provide a distributed algorithm solving the problem for a wide set of possible configurations. For most of the remaining ones instead we provide impossibility results and a few of ad hoc resolution algorithms studied for very specific cases. Over all, still a full characterization is missing but our study points out how difficult might be to derive a general argument that catches all peculiarities. Moreover, some of our approaches reveal new insights that might be very useful for the resolution of other tasks.


  1. 1.
    Bose, K., Kundu, M.K., Adhikary, R., Sau, B.: Optimal gathering by asynchronous oblivious robots in hypercubes. In: Gilbert, S., Hughes, D., Krishnamachari, B. (eds.) ALGOSENSORS 2018. LNCS, vol. 11410, pp. 102–117. Springer, Cham (2019). Scholar
  2. 2.
    Cicerone, S., Di Stefano, G., Navarra, A.: MinMax-distance gathering on given meeting points. In: Paschos, V.T., Widmayer, P. (eds.) CIAC 2015. LNCS, vol. 9079, pp. 127–139. Springer, Cham (2015). Scholar
  3. 3.
    Cicerone, S., Di Stefano, G., Navarra, A.: Gathering of robots on meeting-points: feasibility and optimal resolution algorithms. Distrib. Comput. 31(1), 1–50 (2018)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Cicerone, S., Di Stefano, G., Navarra, A.: Asynchronous arbitrary pattern formation: the effects of a rigorous approach. Distrib. Comput. 32(2), 91–132 (2019)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Cicerone, S., Di Stefano, G., Navarra, A.: Asynchronous robots on graphs: gathering. In: Flocchini, P., Prencipe, G., Santoro, N. (eds.) Distributed Computing by Mobile Entities. Lecture Notes in Computer Science, vol. 11340, pp. 184–217. Springer, Cham (2019). Scholar
  6. 6.
    Cicerone, S., Di Stefano, G., Navarra, A.: Gathering synchronous robots in graphs: from general properties to dense and symmetric topologies. In: Censor-Hillel, K., Flammini, M. (eds.) SIROCCO 2019. LNCS, vol. 11639, pp. 170–184. Springer, Cham (2019). Scholar
  7. 7.
    Cieliebak, M., Flocchini, P., Prencipe, G., Santoro, N.: Distributed computing by mobile robots: gathering. SIAM J. Comput. 41(4), 829–879 (2012)MathSciNetCrossRefGoogle Scholar
  8. 8.
    D’Angelo, G., Di Stefano, G., Klasing, R., Navarra, A.: Gathering of robots on anonymous grids and trees without multiplicity detection. Theor. Comput. Sci. 610, 158–168 (2016)MathSciNetCrossRefGoogle Scholar
  9. 9.
    D’Angelo, G., Di Stefano, G., Navarra, A.: Gathering on rings under the look-compute-move model. Distrib. Comput. 27(4), 255–285 (2014)MathSciNetCrossRefGoogle Scholar
  10. 10.
    D’Angelo, G., Di Stefano, G., Navarra, A.: Gathering six oblivious robots on anonymous symmetric rings. J. Discret. Algorithms 26, 16–27 (2014)MathSciNetCrossRefGoogle Scholar
  11. 11.
    D’Angelo, G., Di Stefano, G., Navarra, A., Nisse, N., Suchan, K.: Computing on rings by oblivious robots: a unified approach for different tasks. Algorithmica 72(4), 1055–1096 (2015)MathSciNetCrossRefGoogle Scholar
  12. 12.
    D’Angelo, G., Navarra, A., Nisse, N.: A unified approach for gathering and exclusive searching on rings under weak assumptions. Distrib. Comput. 30(1), 17–48 (2017)MathSciNetCrossRefGoogle Scholar
  13. 13.
    D’Emidio, M., Di Stefano, G., Frigioni, D., Navarra, A.: Characterizing the computational power of mobile robots on graphs and implications for the Euclidean plane. Inf. Comput. 263, 57–74 (2018)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Di Stefano, G., Navarra, A.: Gathering of oblivious robots on infinite grids with minimum traveled distance. Inf. Comput. 254, 377–391 (2017)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Di Stefano, G., Navarra, A.: Optimal gathering of oblivious robots in anonymous graphs and its application on trees and rings. Distrib. Comput. 30(2), 75–86 (2017)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Guilbault, S., Pelc, A.: Gathering asynchronous oblivious agents with local vision in regular bipartite graphs. Theor. Comput. Sci. 509, 86–96 (2013)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Izumi, T., Izumi, T., Kamei, S., Ooshita, F.: Time-optimal gathering algorithm of mobile robots with local weak multiplicity detection in rings. IEICE Trans. 96–A(6), 1072–1080 (2013)CrossRefGoogle Scholar
  18. 18.
    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)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Serafino Cicerone
    • 1
  • Gabriele Di Stefano
    • 1
  • Alfredo Navarra
    • 2
    Email author
  1. 1.Dipartimento di Ingegneria e Scienze dell’Informazione e MatematicaUniversità degli Studi dell’AquilaL’AquilaItaly
  2. 2.Dipartimento di Matematica e InformaticaUniversità degli Studi di PerugiaPerugiaItaly

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