Abstract
Self-stabilization is a versatile technique to withstand any transient fault in a distributed system. Mobile robots (or agents) are one of the emerging trends in distributed computing as they mimic autonomous biologic entities. The contribution of this paper is threefold. First, we present a new model for studying mobile entities in networks subject to transient faults. Our model differs from the classical robot model because robots have constraints about the paths they are allowed to follow, and from the classical agent model because the number of agents remains fixed throughout the execution of the protocol. Second, in this model, we study the possibility of designing self-stabilizing algorithms when those algorithms are run by mobile robots (or agents) evolving on a graph. We concentrate on the core building blocks of robot and agents problems: naming and leader election. Not surprisingly, when no constraints are given on the network graph topology and local execution model, both problems are impossible to solve. Finally, using minimal hypothesis with respect to impossibility results, we provide deterministic and probabilistic solutions to both problems, and show equivalence of these problems by an algorithmic reduction mechanism.
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. In: Proc. 15th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2004), pp. 1070–1078, New Orleans, LA, USA (January 2004)
Angluin, D.: Local and global properties in networks of processors (extended abstract). In: STOC, pp. 82–93. ACM (1980)
Angluin, D., Aspnes, J., Diamadi, Z., Fischer, M.J., Peralta, R.: Computation in networks of passively mobile finite-state sensors. In: PODC, pp. 290–299 (2004)
Angluin, D., Aspnes, J., Diamadi, Z., Fischer, M.J., Peralta, R.: Computation in networks of passively mobile finite-state sensors. Distributed Computing 235–253 (March 2006)
Angluin, D., Aspnes, J., Fischer, M.J., Jiang, H.: Self-stabilizing population protocols. In: Anderson, J.H., Prencipe, G., Wattenhofer, R. (eds.) OPODIS 2005. LNCS, vol. 3974, pp. 103–117. Springer, Heidelberg (2005)
Beauquier, J., Herault, T., Schiller, E.: Easy Stabilization with an Agent. In: Datta, A.K., Herman, T. (eds.) WSS 2001. LNCS, vol. 2194, pp. 35–51. Springer, Heidelberg (2001)
Défago, X., Gradinariu, M., Messika, S., Parvédy, P.R.: Fault-tolerant and self-stabilizing mobile robots gathering. In: DISC, pp. 46–60 (2006)
Dessmark, A., Fraigniaud, P., Kowalski, D.R., Pelc, A.: Deterministic rendezvous in graphs. Algorithmica 46(1), 69–96 (2006)
Dobrev, S., Flocchini, P., Prencipe, G., Santoro, N.: Searching for a black hole in arbitrary networks: optimal mobile agent protocols. In: PODC, pp. 153–161 (2002)
Dolev, S.: Self-stabilization. MIT Press, Cambridge (2000)
Dolev, S., Schiller, E., Welch, J.: Random walk for self-stabilizing group communication in ad-hoc networks.In: Reliable Distributed Systems, 2002. Proceedings. 21st IEEE Symposium on, pp. 70–79 (2002)
Feige, U.: A tight upper bound on the cover time for random walks on graphs. Random Struct. Algorithms 6(1), 51–54 (1995)
Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Distributed coordination of a set of autonomous mobile robots. IVS, 480–485, (2000)
Fomin, F.V., Fraigniaud, P., Nisse, N.: Nondeterministic Graph Searching: From Pathwidth to Treewidth. In: Jedrzejowicz, J., Szepietowski, A. (eds.) MFCS 2005. LNCS, vol. 3618, pp. 364–375. Springer, Heidelberg (2005)
Fraigniaud, P., Ilcinkas, D., Rajsbaum, S., Tixeuil, S.: The Reduced Automata Technique for Graph Exploration Space Lower Bounds. In: Goldreich, O., Rosenberg, A.L., Selman, A.L. (eds.) Theoretical Computer Science. LNCS, vol. 3895, pp. 1–26. Springer, Heidelberg (2006)
Ghosh, S.: Agents, distributed algorithms, and stabilization. In: Du, D.-Z., Eades, P., Sharma, A.K., Lin, X., Estivill-Castro, V. (eds.) COCOON 2000. LNCS, vol. 1858, pp. 242–251. Springer, Heidelberg (2000)
Herman, T., Masuzawa, T.: Self-Stabilizing Agent Traversal. In: Datta, A.K., Herman, T. (eds.) WSS 2001. LNCS, vol. 2194, pp. 152–166. Springer, Heidelberg (2001)
Prencipe, G.: Corda: Distributed coordination of a set of autonomous mobile robots.In: Proc. ERSADS, pp. 185–190, (May 2001)
Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots—formation and agreement problems.In: Proceedings of the 3rd International Colloquium on Structural Information and Communication Complexity (SIROCCO 1996), Siena, Italy, (June 1996)
Tetali, P., Winkler, P.: On a random walk problem arising in self-stabilizing token management. In: PODC, pp. 273–280 (1991)
Yamashita, M., Kameda, T.: Computing on anonymous networks: Part i-characterizing the solvable cases. IEEE Trans. Parallel Distrib. Syst. 7(1), 69–89 (1996)
Yamashita, M., Kameda, T.: Computing on Anonymous Networks: Part II-Decision and Membership Problems. IEEE Trans. Parallel Distrib. Syst. 7(1), 90–96 (1996)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Blin, L., Gradinariu Potop-Butucaru, M., Tixeuil, S. (2007). On the Self-stabilization of Mobile Robots in Graphs. In: Tovar, E., Tsigas, P., Fouchal, H. (eds) Principles of Distributed Systems. OPODIS 2007. Lecture Notes in Computer Science, vol 4878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77096-1_22
Download citation
DOI: https://doi.org/10.1007/978-3-540-77096-1_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77095-4
Online ISBN: 978-3-540-77096-1
eBook Packages: Computer ScienceComputer Science (R0)