Abstract
In this paper, we investigate the exclusive perpetual exploration of grid shaped networks using anonymous, oblivious and fully asynchronous robots. Our results hold for robots without sense of direction (i.e. they do not agree on a common North, nor do they agree on a common left and right ; furthermore, the “North” and “left” of each robot is decided by an adversary that schedules robots for execution, and may change between invocations of particular robots). We focus on the minimal number of robots that are necessary and sufficient to solve the problem in general grids.
In more details, we prove that three deterministic robots are necessary and sufficient, provided that the size of the grid is n ×m with 3 ≤ n ≤ m or n = 2 and m ≥ 4. Perhaps surprisingly, and unlike results for the exploration with stop problem (where grids are “easier” to explore and stop than rings with respect to the number of robots), exclusive perpetual exploration requires as many robots in the ring as in the grid.
Furthermore, we propose a classification of configurations such that the space of configurations to be checked is drastically reduced. This pre-processing lays the bases for the automated verification of our algorithm for general grids as it permits to avoid combinatorial explosion.
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References
Baldoni, R., Bonnet, F., Milani, A., Raynal, M.: On the Solvability of Anonymous Partial Grids Exploration by Mobile Robots. In: Baker, T.P., Bui, A., Tixeuil, S. (eds.) OPODIS 2008. LNCS, vol. 5401, pp. 428–445. Springer, Heidelberg (2008)
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)
Bonnet, F., Milani, A., Potop-Butucaru, M., Tixeuil, S.: Asynchronous exclusive perpetual grid exploration without sense of direction. Tech. rep. (2011), http://hal.archives-ouvertes.fr/hal-00626155/fr/
Devismes, S.: Optimal exploration of small rings. In: Proceedings of the Third International Workshop on Reliability, Availability, and Security, WRAS 2010, pp. 9:1–9:6. ACM, New York (2010), http://doi.acm.org/10.1145/1953563.1953571
Devismes, S., Lamani, A., Petit, F., Raymond, P., Tixeuil, S.: Optimal grid exploration by asynchronous oblivious robots. Tech. rep., CoRR (2011), http://arxiv.org/abs/1105.2461
Devismes, S., Petit, F., Tixeuil, S.: Optimal Probabilistic Ring Exploration by Semi-Synchronous Oblivious Robots. In: Kutten, S., Žerovnik, J. (eds.) SIROCCO 2009. LNCS, vol. 5869, pp. 195–208. Springer, Heidelberg (2010), http://hal.inria.fr/inria-00360305/fr/
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)
Flocchini, P., Ilcinkas, D., Pelc, A., Santoro, N.: Remembering Without Memory: Tree Exploration by Asynchronous Oblivious Robots. In: Shvartsman, A.A., Felber, P. (eds.) SIROCCO 2008. LNCS, vol. 5058, pp. 33–47. Springer, Heidelberg (2008)
Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Arbitrary pattern formation by asynchronous, anonymous, oblivious robots. Theor. Comput. Sci. 407(1-3), 412–447 (2008)
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), http://arxiv.org/abs/1104.5660
Klasing, R., Kosowski, A., Navarra, A.: Taking Advantage of Symmetries: Gathering of Asynchronous Oblivious Robots on a Ring. In: Baker, T.P., Bui, A., Tixeuil, S. (eds.) OPODIS 2008. LNCS, vol. 5401, pp. 446–462. Springer, Heidelberg (2008)
Klasing, R., Markou, E., Pelc, A.: Gathering asynchronous oblivious mobile robots in a ring. Theor. Comput. Sci. 390(1), 27–39 (2008)
Lamani, A., Potop-Butucaru, M.G., Tixeuil, S.: Optimal Deterministic Ring Exploration with Oblivious Asynchronous Robots. In: Patt-Shamir, B., Ekim, T. (eds.) SIROCCO 2010. LNCS, vol. 6058, pp. 183–196. Springer, Heidelberg (2010)
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)
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Bonnet, F., Milani, A., Potop-Butucaru, M., Tixeuil, S. (2011). Asynchronous Exclusive Perpetual Grid Exploration without Sense of Direction. In: Fernàndez Anta, A., Lipari, G., Roy, M. (eds) Principles of Distributed Systems. OPODIS 2011. Lecture Notes in Computer Science, vol 7109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25873-2_18
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DOI: https://doi.org/10.1007/978-3-642-25873-2_18
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