Abstract
Leader election and arbitrary pattern formation are fundamental tasks for a set of autonomous mobile robots. The former consists in distinguishing a unique robot, called the leader. The latter aims in arranging the robots in the plane to form any given pattern. The solvability of both these tasks turns out to be necessary in order to achieve more complex tasks.
In this paper, we study the relationship between these two tasks in a model, called CORDA, wherein the robots are weak in several aspects. In particular, they are fully asynchronous and they have no direct means of communication. They cannot remember any previous observation nor computation performed in any previous step. Such robots are said to be oblivious. The robots are also uniform and anonymous, i.e, they all have the same program using no global parameter (such as an identity) allowing to differentiate any of them. Moreover, none of them share any kind of common coordinate mechanism or common sense of direction, except that they agree on a common handedness (chirality).
In such a system, Flochini et al. proved in [9] that it is possible to elect a leader for n ≥ 3 robots if it is possible to form any pattern for n ≥ 3. In this paper, we show that the converse is true for n ≥ 4 and thus, we deduce that both problems are equivalent for n ≥ 4 in CORDA provided the robots share the same chirality.
This work has been supported by the ANR projet R-Discover (08-ANR-CONTINT).
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References
Canepa, D., Gradinariu Potop-Butucaru, M.: Stabilizing flocking via leader election in robot networks. In: Masuzawa, T., Tixeuil, S. (eds.) SSS 2007. LNCS, vol. 4838, pp. 52–66. Springer, Heidelberg (2007)
Cieliebak, M., Prencipe, G.: Gathering autonomous mobile robots. In: 9th International Colloquium on Structural Information and Communication Complexity (SIROCCO 9), pp. 57–72 (2002)
Cohen, R., Peleg, D.: Local spreading algorithms for autonomous robot systems. Theor. Comput. Sci. 399(1-2), 71–82 (2008)
Defago, X., Konagaya, A.: Circle formation for oblivious anonymous mobile robots with no common sense of orientation. In: 2nd ACM International Annual Workshop on Principles of Mobile Computing (POMC 2002), pp. 97–104 (2002)
Dieudonné, Y., Labbani-Igbida, O., Petit, F.: Circle formation of weak mobile robots. TAAS 3(4) (2008)
Dieudonné, Y., Petit, F.: Deterministic leader election in anonymous sensor networks without common coordinated system. In: Tovar, E., Tsigas, P., Fouchal, H. (eds.) OPODIS 2007. LNCS, vol. 4878, pp. 132–142. Springer, Heidelberg (2007)
Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Hard tasks for weak robots: The role of common knowledge in pattern formation by autonomous mobile robots. In: Aggarwal, A.K., Pandu Rangan, C. (eds.) ISAAC 1999. LNCS, vol. 1741, pp. 93–102. Springer, Heidelberg (1999)
Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Distributed coordination of a set of autonomous mobile robots. In: IEEE Intelligent Veichle Symposium (IV 2000), pp. 480–485 (2000)
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)
Katreniak, B.: Biangular circle formation by asynchronous mobile robots. In: Pelc, A., Raynal, M. (eds.) SIROCCO 2005. LNCS, vol. 3499, pp. 185–199. Springer, Heidelberg (2005)
Megiddo, N.: Linear-time algorithms for linear programming in r3 and related problems. SIAM J. Comput. 12(4), 759–776 (1983)
Prencipe, G.: Distributed coordination of a set of autonomous mobile robots. Technical Report TD-4/02, Dipartimento di Informatica, University of Pisa (2002)
Suzuki, I., Yamashita, M.: Agreement on a common x-y coordinate system by a group of mobile robots. Intelligent Robots: Sensing, Modeling and Planning, 305–321 (1996)
Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots - formation of geometric patterns. SIAM Journal of Computing 28(4), 1347–1363 (1999)
Welzl, E.: Smallest enclosing disks (balls and ellipsoids). In: Maurer, H.A. (ed.) New Results and New Trends in Computer Science. LNCS, vol. 555, pp. 359–370. Springer, Heidelberg (1991)
Yamashita, M., Suzuki, I.: Characterizing geometric patterns formable by oblivious anonymous mobile robots. Theoretical Computer Science (to appear, 2010)
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Dieudonné, Y., Petit, F., Villain, V. (2010). Leader Election Problem versus Pattern Formation Problem. In: Lynch, N.A., Shvartsman, A.A. (eds) Distributed Computing. DISC 2010. Lecture Notes in Computer Science, vol 6343. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15763-9_26
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DOI: https://doi.org/10.1007/978-3-642-15763-9_26
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