Abstract
We consider the rendezvous problem which requires k mobile agents that are dispersed in a ring of size n, to gather at a single node of the network. The problem is difficult to solve when the agents are identical (i.e. indistinguishable), they execute the same deterministic algorithm, and the nodes of the ring are unlabelled (i.e. anonymous). In this case, rendezvous can be achieved by having each agent mark its starting location in the ring using a token. This paper focusses on fault tolerant solutions to the problem when tokens left by an agent may fail unexpectedly. Previous solutions to the problem had several limitations—they either assumed a completely synchronous setting or were restricted to few specific instances of the problem where the value of n is such that \(\gcd(n,k')=1\) ∀ k′ ≤ k. We improve on these results, solving rendezvous in asynchronous rings for arbitrary values of n and k, whenever it is solvable.
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References
Alpern, S., Gal, S.: The Theory of Search Games and Rendezvous. Kluwer, Dordrecht (2003)
Baston, V., Gal, S.: Rendezvous search when marks are left at the starting points. Naval Research Logistics 38, 469–494 (1991)
Chalopin, J., Das, S., Santoro, N.: Rendezvous of Mobile Agents in Unknown Graphs with Faulty Links. In: Pelc, A. (ed.) DISC 2007. LNCS, vol. 4731, pp. 108–122. Springer, Heidelberg (2007)
Dessmark, A., Fraigniaud, P., Pelc, A.: Deterministic rendezvous in graphs. In: Di Battista, G., Zwick, U. (eds.) ESA 2003. LNCS, vol. 2832, pp. 184–195. Springer, Heidelberg (2003)
Dobrev, S., Flocchini, P., Prencipe, G., Santoro, N.: Multiple agents rendezvous in a ring in spite of a black hole. In: Papatriantafilou, M., Hunel, P. (eds.) OPODIS 2003. LNCS, vol. 3144, pp. 34–46. Springer, Heidelberg (2004)
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)
Flocchini, P., Kranakis, E., Krizanc, D., Luccio, F.L., Santoro, N., Sawchuk, C.: Mobile Agents Rendezvous When Tokens Fail. In: Kralovic, R., Sýkora, O. (eds.) SIROCCO 2004. LNCS, vol. 3104, pp. 161–172. Springer, Heidelberg (2004)
Gasieniec, L., Kranakis, E., Krizanc, D., Zhang, X.: Optimal memory rendezvous of anonymous mobile agents in a unidirectional ring. In: Wiedermann, J., Tel, G., Pokorný, J., Bieliková, M., Štuller, J. (eds.) SOFSEM 2006. LNCS, vol. 3831, pp. 282–292. Springer, Heidelberg (2006)
Kranakis, E., Krizanc, D., Santoro, N., Sawchuk, C.: Mobile agent rendezvous in a ring. In: ICDCS 03. Int. Conf. on Distibuted Computing Systems, pp. 592–599 (2003)
Kranakis, E., Krizanc, D., Markou, E.: Mobile Agent Rendezvous in a Synchronous Torus. In: Correa, J.R., Hevia, A., Kiwi, M. (eds.) LATIN 2006. LNCS, vol. 3887, pp. 653–664. Springer, Heidelberg (2006)
De Marco, G., Gargano, L., Kranakis, E., Krizanc, D., Pelc, A., Vaccaro, U.: Asynchronous deterministic rendezvous in graphs. Theoretical Computer Science 355(3), 315–326 (2006)
Yu, X., Yung, M.: Agent rendezvous: A dynamic symmetry-breaking problem. In: Meyer auf der Heide, F., Monien, B. (eds.) ICALP 1996. LNCS, vol. 1099, pp. 610–621. Springer, Heidelberg (1996)
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Das, S. (2007). Mobile Agent Rendezvous in a Ring Using Faulty Tokens. In: Rao, S., Chatterjee, M., Jayanti, P., Murthy, C.S.R., Saha, S.K. (eds) Distributed Computing and Networking. ICDCN 2008. Lecture Notes in Computer Science, vol 4904. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77444-0_29
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DOI: https://doi.org/10.1007/978-3-540-77444-0_29
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