Advertisement

Asynchronous Robots on Graphs: Gathering

  • Serafino Cicerone
  • Gabriele Di Stefano
  • Alfredo NavarraEmail author
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11340)

Abstract

Gathering a swarm of robots is one of the basic tasks in distributed computing. Varying of the robots’ capabilities as well as on the environments where robots move lead to very different approaches. In general, the problem requires the design of a distributed algorithm that brings all robots to meet at some common location, not known in advance. We consider asynchronous robots subject to the well-established Look-Compute-Move model. Each time a robot wakes up, it perceives the current configuration in terms of robots’ positions (Look), it decides whether and where to move (Compute), and makes the computed move (Move), if any. Starting from the case of robots moving in the Euclidean plane, we highlight pros and cons for robots moving along the edges of a graph. We survey on the most recent results about robots moving in general graphs and in specific topologies like trees, rings, grids, and cliques. Further, we show how the design of an algorithm for general graphs naturally leads to optimization issues. In particular, we survey on optimal gathering algorithms in terms of total number of edges traversed by robots in order to accomplish the gathering task. Also in this case, results concern general graphs and specific topologies. In doing so, we highlight how the problem and the resolution algorithms change when optimal constraints are included.

Keywords

Asynchrony Mobile robots Gathering Discrete environment 

References

  1. 1.
    Aho, A., Hopcroft, J., Ullman, J.: Data Structures and Algorithms. Addison Wesley, Boston (1983)zbMATHGoogle Scholar
  2. 2.
    Ausiello, G., Crescenzi, P., Gambosi, G., Kann, V., Marchetti-Spaccamela, A., Protasi, M.: Complexity and Approximation. Combinatorial Optimization Problems and Their Approximability Properties. Springer, Heidelberg (1999).  https://doi.org/10.1007/978-3-642-58412-1CrossRefzbMATHGoogle Scholar
  3. 3.
    Bonnet, F., Potop-Butucaru, M., Tixeuil, S.: Asynchronous gathering in rings with 4 robots. In: Mitton, N., Loscri, V., Mouradian, A. (eds.) ADHOC-NOW 2016. LNCS, vol. 9724, pp. 311–324. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-40509-4_22CrossRefGoogle Scholar
  4. 4.
    Buss, S.R.: Alogtime algorithms for tree isomorphism, comparison, and canonization. In: Gottlob, G., Leitsch, A., Mundici, D. (eds.) KGC 1997. LNCS, vol. 1289, pp. 18–33. Springer, Heidelberg (1997).  https://doi.org/10.1007/3-540-63385-5_30CrossRefGoogle Scholar
  5. 5.
    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
  6. 6.
    Cicerone, S., Di Stefano, G., Navarra, A.: “Semi-asynchronous”: a new scheduler for robot based computing systems. In: Proceedings of the 38th IEEE International Conference on Distributed Computing Systems, (ICDCS), pp. 176–187. IEEE (2018)Google 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.
    Cockayne, E.J., Melzak, Z.A.: Euclidean constructibility in graph-minimization problems. Math. Mag. 42(4), 206–208 (1969)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Cohen, R., Peleg, D.: Convergence properties of the gravitational algorithm in asynchronous robot systems. SIAM J. Comput. 34(6), 1516–1528 (2005)MathSciNetCrossRefGoogle Scholar
  10. 10.
    D’Angelo, G., Di Stefano, G., Klasing, R., Navarra, A.: Gathering of robots on anonymous grids and trees without multiplicity detection. Theoret. Comput. Sci. 610, 158–168 (2016)MathSciNetCrossRefGoogle Scholar
  11. 11.
    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, New York (2013).  https://doi.org/10.1007/978-1-4614-6825-7_13CrossRefGoogle Scholar
  12. 12.
    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
  13. 13.
    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
  14. 14.
    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
  15. 15.
    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
  16. 16.
    D’Emidio, M., Frigioni, D., Navarra, A.: Characterizing the computational power of anonymous mobile robots. In: Proceedings of the 36th IEEE International Conference on Distributed Computing Systems, (ICDCS), pp. 293–302. IEEE (2016)Google Scholar
  17. 17.
    Di Stefano, G., Montanari, P., Navarra, A.: About ungatherability of oblivious and asynchronous robots on anonymous rings. In: Lipták, Z., Smyth, W.F. (eds.) IWOCA 2015. LNCS, vol. 9538, pp. 136–147. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-29516-9_12CrossRefGoogle Scholar
  18. 18.
    Di Stefano, G., Navarra, A.: Gathering of oblivious robots on infinite grids with minimum traveled distance. Inf. Comput. 254, 377–391 (2017)MathSciNetCrossRefGoogle Scholar
  19. 19.
    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
  20. 20.
    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).  https://doi.org/10.1007/978-3-642-13284-1_9CrossRefGoogle Scholar
  21. 21.
    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).  https://doi.org/10.1007/978-3-642-22212-2_14CrossRefGoogle Scholar
  22. 22.
    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).  https://doi.org/10.1007/978-3-642-32589-2_48CrossRefzbMATHGoogle Scholar
  23. 23.
    Klasing, R., Kosowski, A., Navarra, A.: Taking advantage of symmetries: Gathering of many asynchronous oblivious robots on a ring. Theoret. Comput. Sci. 411, 3235–3246 (2010)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Klasing, R., Markou, E., Pelc, A.: Gathering asynchronous oblivious mobile robots in a ring. Theoret. Comput. Sci. 390, 27–39 (2008)MathSciNetCrossRefGoogle Scholar
  25. 25.
    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
  26. 26.
    Santoro, N.: Design and Analysis of Distributed Algorithms. Wiley, Hoboken (2007)zbMATHGoogle 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

Personalised recommendations