Optimal Deterministic Ring Exploration with Oblivious Asynchronous Robots
We consider the problem of exploring an anonymous unoriented ring of size n by k identical, oblivious, asynchronous mobile robots, that are unable to communicate, yet have the ability to sense their environment and take decisions based on their local view. Previous works in this weak scenario prove that k must not divide n for a deterministic solution to exist. Also, it is known that the minimum number of robots (either deterministic or probabilistic) to explore a ring of size n is 4. An upper bound of 17 robots holds in the deterministic case while 4 probabilistic robots are sufficient. In this paper, we close the complexity gap in the deterministic setting, by proving that no deterministic exploration is feasible with less than five robots, and that five robots are sufficient for any n that is coprime with five. Our protocol completes exploration in O(n) robot moves, which is also optimal.
KeywordsRobots Anonymity Obliviousness Exploration Asynch-ronous system Ring
Unable to display preview. Download preview PDF.
- 3.Devismes, S., Petit, F., Tixeuil, S.: Optimal probabilistic ring exploration by asynchronous oblivious robots. In: Proceedings of SIROCCO 2009 (2009)Google Scholar
- 4.Dieudonné, Y., Labbani-Igbida, O., Petit, F.: Circle formation of weak mobile robots. TAAS 3(16) (2008)Google Scholar
- 7.Flocchini, P., Kranakis, E., Krizanc, D., Santoro, N., Sawchuk, C.: Multiple mobile agent rendezvous in a ring. In: Farach-Colton, M. (ed.) LATIN 2004. LNCS, vol. 2976, pp. 599–608. Springer, Heidelberg (2004)Google Scholar
- 9.Klasing, R., Kosowski, A., Navarra, A.: Taking advantage of symmetries: Gathering of asynchronous oblivious robots on a ring. In: OPODIS, pp. 446–462 (2008)Google Scholar
- 11.Kowalski, D., Pelc, A.: Polynomial deterministic rendezvous in arbitrary graphs. In: Fleischer, R., Trippen, G. (eds.) ISAAC 2004. LNCS, vol. 3341, pp. 644–656. Springer, Heidelberg (2004)Google Scholar
- 12.Lamani, A., Potop-Butucaru, M., Tixeuil, S.: Optimal deterministic ring exploration with oblivious asynchronous robots. CoRR abs/0910.0832 (2009)Google Scholar
- 13.Prencipe, G.: CORDA: Distributed coordination of a set of autonomous mobile robots. In: Proc. 4th European Research Seminar on Advances in Distributed Systems (ERSADS 2001), Bertinoro, Italy, May 2001, pp. 185–190 (2001)Google Scholar