Abstract
In this paper, we consider the problem of formation of a series of geometric patterns by a network of oblivious mobile robots that communicate only through vision. So far, the problem has been studied in models where robots are either assumed to have distinct identifiers or to be completely anonymous. To generalize these results and to better understand how anonymity affects the computational power of robots, we study the problem in a new model in which n robots may share up to 1 ≤ h ≤ n different identifiers. We present necessary and sufficient conditions, relating symmetricity and homonymy, that makes the problem solvable. We also show that in the case where h = n, making the identifiers of robots invisible does not limit their computational power. This contradicts a recent result of Das et al. To present our algorithms, we use a function that computes the Weber point for many regular and symmetric configurations. This function is interesting in its own right, since the problem of finding Weber points has been solved up to now for only few other patterns.
This work is supported in part by the DIGITEO project PACTOLE and ANR SPADES.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Agmon, N., Peleg, D.: Fault-tolerant gathering algorithms for autonomous mobile robots. SODA 11(14), 1070–1078 (2004)
Anderegg, L., Cieliebak, M., Prencipe, G.: Efficient algorithms for detecting regular point configurations. In: Coppo, M., Lodi, E., Pinna, G.M. (eds.) ICTCS 2005. LNCS, vol. 3701, pp. 23–35. Springer, Heidelberg (2005)
Bouzid, Z., Lamani, A.: Robot networks with homonyms: The case of patterns formation. hal.inria.fr (2011)
Chandrasekaran, R., Tamir, A.: Algebraic optimization: the fermat-weber location problem. Mathematical Programming 46(1), 219–224 (1990)
Das, S., Flocchini, P., Santoro, N., Yamashita, M.: On the computational power of oblivious robots: forming a series of geometric patterns. In: PODC, pp. 267–276. ACM, New York (2010)
Delporte-Gallet, C., Fauconnier, H., Guerraoui, R., Kermarrec, A.M., Ruppert, E., Tran-The, H.: Byzantine agreement with homonyms. In: PODC (2011)
Flocchini, P., Ilcinkas, D., Pelc, A., Santoro, N.: Remembering without memory: Tree exploration by asynchronous oblivious robots. Theoretical Computer Science 411(14-15), 1583–1598 (2010)
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)
Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots: Formation of geometric patterns. SIAM Journal of Computing 28(4), 1347–1363 (1999)
Weiszfeld, E.: Sur le point pour lequel la somme des distances de n points donnes est minimum, t6hoku math. J 43, 355–386 (1937)
Yamashita, M., Kameda, T.: Leader election problem on networks in which processor identity numbers are not distinct. IEEE Trans. Parallel Distrib. Syst. 10(9), 878–887 (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bouzid, Z., Lamani, A. (2011). Robot Networks with Homonyms: The Case of Patterns Formation. In: Défago, X., Petit, F., Villain, V. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2011. Lecture Notes in Computer Science, vol 6976. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24550-3_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-24550-3_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24549-7
Online ISBN: 978-3-642-24550-3
eBook Packages: Computer ScienceComputer Science (R0)