Advertisement

Algorithmica

, Volume 72, Issue 4, pp 1055–1096 | Cite as

Computing on Rings by Oblivious Robots: A Unified Approach for Different Tasks

  • Gianlorenzo D’Angelo
  • Gabriele Di Stefano
  • Alfredo Navarra
  • Nicolas Nisse
  • Karol Suchan
Article

Abstract

A set of autonomous robots have to collaborate in order to accomplish a common task in a ring-topology where neither nodes nor edges are labeled (that is, the ring is anonymous). We present a unified approach to solve three important problems: the exclusive perpetual exploration, the exclusive perpetual clearing, and the gathering problems. In the first problem, each robot aims at visiting each node infinitely often while avoiding that two robots occupy a same node (exclusivity property); in exclusive perpetual clearing (also known as graph searching), the team of robots aims at clearing the whole ring infinitely often (an edge is cleared if it is traversed by a robot or if both its endpoints are occupied); and in the gathering problem, all robots must eventually occupy the same node. We investigate these tasks in the Look–Compute–Move model where the robots cannot communicate but can perceive the positions of other robots. Each robot is equipped with visibility sensors and motion actuators, and it operates in asynchronous cycles. In each cycle, a robot takes a snapshot of the current global configuration (Look), then, based on the perceived configuration, takes a decision to stay idle or to move to one of its adjacent nodes (Compute), and in the latter case it eventually moves to this neighbor (Move). Moreover, robots are endowed with very weak capabilities. Namely, they are anonymous, asynchronous, oblivious, uniform (execute the same algorithm) and have no common sense of orientation. In this setting, we devise algorithms that, starting from an exclusive and rigid (i.e. aperiodic and asymmetric) configuration, solve the three above problems in anonymous ring-topologies.

Keywords

Distributed computing Exploration Searching Gathering Oblivious anonymous robots Asynchronous anonymous networks Look–Compute–Move 

Notes

Acknowledgments

This work has been partially supported by the Research Grant 2010N5K7EB ‘PRIN 2010’ ARS TechnoMedia (Algoritmica per le Reti Sociali Tecno-mediate) from the Italian Ministry of University and Research, Project ECOS-SUD Chile (Action ECOS C12E03), Inria Associated Team AlDyNet and Basal-CMM of Conicyt Chile.

References

  1. 1.
    Ambühl, C., Gąsieniec, L., Pelc, A., Radzik, T., Zhang, X.: Tree exploration with logarithmic memory. ACM Trans. Algorithms 7(2), 17:1–17:21 (2011)CrossRefGoogle Scholar
  2. 2.
    Baldoni, R., Bonnet, F., Milani, A., Raynal, M.: Anonymous graph exploration without collision by mobile robots. Inf. Process. Lett. 109(2), 98–103 (2008)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Baldoni, R., Bonnet, F., Milani, A., Raynal, M.: On the solvability of anonymous partial grids exploration by mobile robots. In: Proceedings of the 12th International Conference On Principles Of Distributed Systems (OPODIS). volume 5401 of Lecture Notes in Computer Science, pp. 428–445. Springer (2008)Google Scholar
  4. 4.
    Bampas, E., Czyzowicz, J., Gąsieniec, L., Ilcinkas, D., Labourel, A.: Almost optimal asynchronous rendezvous in infinite multidimensional grids. In: Proceedings of the 24th International Symposium on Distributed Computing (DISC). volume 6343 of Lecture Notes in Computer Science, pp. 297–311 (2010)Google Scholar
  5. 5.
    Bienstock, D., Seymour, P.D.: Monotonicity in graph searching. J. Algorithms 12(2), 239–245 (1991)zbMATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Blin, L., Milani, A., Potop-Butucaru, M., Tixeuil, S.: Exclusive perpetual ring exploration without chirality. In: Proceedings of the 24th International Symposium on Distributed Computing (DISC). volume 6343 of Lecture Notes in Computer Science, pp. 312–327 (2010)Google Scholar
  7. 7.
    Blin, L., Burman, J., Nisse, N.: Exclusive graph searching. In: Proceedings of the 21st European Symposium on Algorithms (ESA). volume 8125 of Lecture Notes in Computer Science, pp. 181–192. Springer (2013)Google Scholar
  8. 8.
    Bonnet, F., Milani, A., Potop-Butucaru, M., Tixeuil, S.: Asynchronous exclusive perpetual grid exploration without sense of direction. In: Proceedings of the 15th International Conference On Principles Of Distributed Systems (OPODIS). volume 7109 of Lecture Notes in Computer Science, pp. 251–265. Springer (2011)Google Scholar
  9. 9.
    Brandes, P., Degener, B., Kempkes, B., Meyer auf der Heide, F.: Energy-efficient strategies for building short chains of mobile robots locally. Theor. Comput. Sci. 509, 97–112 (2013)zbMATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    Clément, J., Défago, X., Potop-Butucaru, M.G., Izumi, T., Messika, S.: The cost of probabilistic agreement in oblivious robot networks. Inf. Process. Lett. 110(11), 431–438 (2010)zbMATHCrossRefGoogle Scholar
  11. 11.
    Cohen, R., Fraigniaud, P., Ilcinkas, D., Korman, A., Peleg, D.: Label-guided graph exploration by a finite automaton. ACM Trans. Algorithms 4(4), 42:1–42:18 (2008)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Czyzowicz, J., Gąsieniec, L., Pelc, A.: Gathering few fat mobile robots in the plane. Theor. Comput. Sci. 410(6–7), 481–499 (2009)zbMATHCrossRefGoogle Scholar
  13. 13.
    D’Angelo, G., Di Stefano, G., Navarra, A.: Gathering of six robots on anonymous symmetric rings. In: Proceedings of the 18th International Colloquium on Structural Information and Commnication Complexity (SIROCCO). volume 6796 of Lecture Notes in Computer Science, pp. 174–185 (2011)Google Scholar
  14. 14.
    D’Angelo, G., Di Stefano, G., Klasing, R., Navarra, A.: Gathering of robots on anonymous grids without multiplicity detection. In: Proceedings of the 19th International Colloquium on Structural Information and Communication Complexity (SIROCCO). volume 7355 of Lecture Notes in Computer Science, pp. 327–338 (2012)Google Scholar
  15. 15.
    D’Angelo, G., Di Stefano, G., Navarra, A.: How to gather asynchronous oblivious robots on anonymous rings. In: Proceedings of the 26th International Symposium on Distributed Computing (DISC). volume 7611 of Lecture Notes in Computer Science, pp. 330–344 (2012)Google Scholar
  16. 16.
    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, Berlin (2013)CrossRefGoogle Scholar
  17. 17.
    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: Proceedings of the 15th IEEE IPDPS Workshop on Advances in Parallel and Distributed Computing Models (APDCM), pp. 667–676 (2013)Google Scholar
  18. 18.
    Devismes, S., Petit, F., Tixeuil, S.: Optimal probabilistic ring exploration by semi-synchronous oblivious robots. In: Proceedings of the 16th International Colloquium on Structural Information and Communication Complexity (SIROCCO). volume 5869 of Lecture Notes in Computer Science, pp. 195–208 (2009)Google Scholar
  19. 19.
    Dieudonne, Y., Petit, F.: Scatter of robots. Parallel Process. Lett. 19(1), 175–184 (2009)MathSciNetCrossRefGoogle Scholar
  20. 20.
    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)zbMATHMathSciNetCrossRefGoogle Scholar
  21. 21.
    Flocchini, P., Prencipe, G., Santoro, N.: Distributed Computing by Oblivious Mobile Robots. Morgan and Claypool, San Rafael (2012)Google Scholar
  22. 22.
    Flocchini, P., Ilcinkas, D., Pelc, A., Santoro, N.: Computing without communicating: ring exploration by asynchronous oblivious robots. Algorithmica 65, 562–583 (2013)zbMATHMathSciNetCrossRefGoogle Scholar
  23. 23.
    Fomin, F.V., Thilikos, D.M.: An annotated bibliography on guaranteed graph searching. Theoret. Comput. Sci. 399(3), 236–245 (2008)zbMATHMathSciNetCrossRefGoogle Scholar
  24. 24.
    Ilcinkas, D., Nisse, N., Soguet, D.: The cost of monotonicity in distributed graph searching. Distrib. Comput. 22(2), 117–127 (2009)zbMATHCrossRefGoogle Scholar
  25. 25.
    Izumi, T., Izumi, T., Kamei, S., Ooshita, F.: Mobile robots gathering algorithm with local weak multiplicity in rings. In: Proceedings of the 17th International Colloquium on Structural Information and Communication Complexity (SIROCCO). volume 6058 of Lecture Notes in Computer Science, pp. 101–113 (2010)Google Scholar
  26. 26.
    Izumi, T., Izumi, T., Kamei, S., Ooshita, F.: Feasibility of polynomial-time randomized gathering for oblivious mobile robots. IEEE Trans. Parallel Distrib. Syst. 24(4), 716–723 (2013)CrossRefGoogle Scholar
  27. 27.
    Kamei, S., Lamani, A., Ooshita, F., Tixeuil, S.: Asynchronous mobile robot gathering from symmetric configurations. In: Proceedings of the 18th International Colloquium on Structural Information and Communication Complexity (SIROCCO). volume 6796 of Lecture Notes in Computer Science, pp. 150–161 (2011)Google Scholar
  28. 28.
    Kamei, S., Lamani, A., Ooshita, F., Tixeuil, S.: Gathering an even number of robots in an odd ring without global multiplicity detection. In: Proceedings of the 37th International Symposium on Mathematical Foundations of Computer Science (MFCS). volume 7464 of Lecture Notes in Computer Science, pp. 542–553 (2012)Google Scholar
  29. 29.
    Kempkes, B., Kling, P., Meyer auf der Heide, F.: Optimal and competitive runtime bounds for continuous, local gathering of mobile robots. In: Proceedings of the 24th Annual ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pp. 18–26. ACM (2012)Google Scholar
  30. 30.
    Klasing, R., Markou, E., Pelc, A.: Gathering asynchronous oblivious mobile robots in a ring. Theor. Comput. Sci. 390, 27–39 (2008)zbMATHMathSciNetCrossRefGoogle Scholar
  31. 31.
    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)zbMATHMathSciNetCrossRefGoogle Scholar
  32. 32.
    Pelc, A.: Deterministic rendezvous in networks: a comprehensive survey. Networks 59(3), 331–347 (2012)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Prencipe, G.: Impossibility of gathering by a set of autonomous mobile robots. Theor. Comput. Sci. 384, 222–231 (2007)zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Gianlorenzo D’Angelo
    • 1
  • Gabriele Di Stefano
    • 2
  • Alfredo Navarra
    • 3
  • Nicolas Nisse
    • 4
    • 5
  • Karol Suchan
    • 6
    • 7
  1. 1.Gran Sasso Science Institute (GSSI)L’AquilaItaly
  2. 2.Dipartimento di Ingegneria e Scienze dell’Informazione e MatematicaUniversità degli Studi dell’AquilaCoppito L’AquilaItaly
  3. 3.Dipartimento di Matematica e InformaticaUniversità degli Studi di PerugiaPerugiaItaly
  4. 4.COATI Project, INRIASophia AntipolisFrance
  5. 5.University Nice Sophia Antipolis, CNRS, I3S, UMR 7271Sophia AntipolisFrance
  6. 6.Facultad de Ingeniería y CienciasUniversidad Adolfo IbáñezRegión MetropolitanaChile
  7. 7.WMS - Faculty of Science and EngineeringAGH - University of Science and TechnologyKrakówPoland

Personalised recommendations