Abstract
We study a group of mobile agents operating on an arbitrary unknown distributed system. One of the nodes of the distributed system is extremely harmful and destroys any incoming agent without notification. The task of exploring the distributed system and locating the harmful node, Black hole search, has been studied with various modifications.
We are studying the effects of the knowledge of incoming link on the size of the optimal solution. When an agent enters a node, the information which port leads back can be given to it. We refer to this as to the knowledge of incoming link. In previous research, it was always assumed that the agent is given this information.
In this paper we study arbitrary, unknown distributed systems without the knowledge of incoming link. Agents are asynchronous and they communicate via whiteboards. We present a lower bound on the size of the optimal solution, proving that at least \(\frac{\Delta^2+\Delta}{2} + 1\) agents are necessary to locate the black hole, with respect to the degree of the black hole Δ. We provide an algorithm for black hole search without the knowledge of incoming link as well. We prove that this algorithm is correct, and that it uses \(\frac{\Delta^2+\Delta}{2} + 1\) agents, thus providing optimal solution.
Research supported by grant APVV 0433-06.
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References
Dobrev, S., Flocchini, P., Prencipe, G., Santoro, N.: Searching for a black hole in arbitrary networks: optimal mobile agent protocols. In: Proceedings of the twenty-first annual symposium on Principles of distributed computing (PODC 2002), pp. 153–162. ACM, New York (2002)
Czyzowicz, J., Dobrev, S., Královič, R., Miklík, S., Pardubská, D.: Black hole search in directed graphs. In: SIROCCO 2009. LNCS, Springer, Heidelberg (to appear, 2009)
Dobrev, S., Flocchini, P., Prencipe, G., Santoro, N.: Mobile search for a black hole in an anonymous ring. In: Welch, J.L. (ed.) DISC 2001. LNCS, vol. 2180, pp. 166–179. Springer, Heidelberg (2001)
Dobrev, S., Flocchini, P., Královič, R., Prencipe, G., Ružička, P., Santoro, N.: Black hole search in common interconnection networks. Networks 47(2), 61–71 (2006)
Dobrev, S., Flocchini, P., Santoro, N.: Improved bounds for optimal black hole search with a network map. In: Kralovic, R., Sýkora, O. (eds.) SIROCCO 2004. LNCS, vol. 3104, pp. 111–122. Springer, Heidelberg (2004)
Dobrev, S., Flocchini, P., Santoro, N.: Cycling through a dangerous network: A simple efficient strategy for black hole search. In: 26th IEEE International Conference on Distributed Computing Systems (ICDCS 2006), p. 57. IEEE Computer Society, Los Alamitos (2006)
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)
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)
Flocchini, P., Ilcinkas, D., Santoro, N.: Ping pong in dangerous graphs: Optimal black hole search with pure tokens. In: Taubenfeld, G. (ed.) DISC 2008. LNCS, vol. 5218, pp. 227–241. Springer, Heidelberg (2008)
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Glaus, P. (2009). Locating a Black Hole without the Knowledge of Incoming Link. In: Dolev, S. (eds) Algorithmic Aspects of Wireless Sensor Networks. ALGOSENSORS 2009. Lecture Notes in Computer Science, vol 5804. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05434-1_13
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DOI: https://doi.org/10.1007/978-3-642-05434-1_13
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