Abstract
We propose a new probabilistic pattern formation algorithm for oblivious mobile robots that operates in the ASYNC model. Unlike previous work, our algorithm makes no assumptions about the local coordinate systems of robots (the robots do not share a common “North” nor a common “Right”), yet it preserves the ability from any initial configuration that contains at least 5 robots to form any general pattern (and not just patterns that satisfy symmetricity predicates). Our proposal also gets rid of the previous assumption (in the same model) that robots do not pause while moving (so, our robots really are fully asynchronous), and the amount of randomness is kept low – a single random bit per robot per Look-Compute-Move cycle is used. Our protocol consists in the combination of two phases, a probabilistic leader election phase, and a deterministic pattern formation one. As the deterministic phase does not use chirality, it may be of independent interest in the deterministic context. A noteworthy feature of our algorithm is the ability to form patterns with multiplicity points (except the gathering case due to impossibility results), a new feature in the context of pattern formation that we believe is an important asset of our approach.
This work was performed within the Labex SMART supported by French state funds managed by the ANR within the Investissements d’Avenir programme under reference ANR-11-IDEX-0004-02. A preliminary version of this work appears as a brief announcement in PODC’16.
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References
Bouzid, Z., Lamani, A.: Robot networks with homonyms: the case of patterns formation. In: Défago, X., Petit, F., Villain, V. (eds.) SSS 2011. LNCS, vol. 6976, pp. 92–107. Springer, Heidelberg (2011). doi:10.1007/978-3-642-24550-3_9
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)
Fujinaga, N., Yamauchi, Y., Kijima, S., Yamashita, M.: Asynchronous pattern formation by anonymous oblivious mobile robots. In: Aguilera, M.K. (ed.) DISC 2012. LNCS, vol. 7611, pp. 312–325. Springer, Heidelberg (2012). doi:10.1007/978-3-642-33651-5_22
Prencipe, G.: Impossibility of gathering by a set of autonomous mobile robots. Theor. Comput. Sci. 384(2), 222–231 (2007)
Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots: formation of geometric patterns. SIAM J. Comput. 28(4), 1347–1363 (1999)
Yamauchi, Y., Yamashita, M.: Randomized pattern formation algorithm for asynchronous oblivious mobile robots. In: Kuhn, F. (ed.) DISC 2014. LNCS, vol. 8784, pp. 137–151. Springer, Heidelberg (2014). doi:10.1007/978-3-662-45174-8_10
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Bramas, Q., Tixeuil, S. (2016). Probabilistic Asynchronous Arbitrary Pattern Formation (Short Paper). In: Bonakdarpour, B., Petit, F. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2016. Lecture Notes in Computer Science(), vol 10083. Springer, Cham. https://doi.org/10.1007/978-3-319-49259-9_7
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DOI: https://doi.org/10.1007/978-3-319-49259-9_7
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