Hardness and Approximation Results for Black Hole Search in Arbitrary Graphs
A black hole is a highly harmful stationary process residing in a node of a network and destroying all mobile agents visiting the node, without leaving any trace. We consider the task of locating a black hole in a (partially) synchronous arbitrary network, assuming an upper bound on the time of any edge traversal by an agent. For a given graph and a given starting node we are interested in finding the fastest possible Black Hole Search by two agents (the minimum number of agents capable to identify a black hole). We prove that this problem is NP-hard in arbitrary graphs, thus solving an open problem stated in . We also give a 7/2-approximation algorithm, thus improving on the 4-approximation scheme observed in . Our approach is to explore the given input graph via some spanning tree. Even if it represents a very natural technique, we prove that this approach cannot achieve an approximation ratio better than 3/2.
Keywordsapproximation algorithm black hole search graph exploration mobile agent NP-hardness
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- 1.Czyzowicz, J., Kowalski, D., Markou, E., Pelc, A.: Complexity of searching for a black hole (2004) (manuscript)Google Scholar
- 3.Dobrev, S., Flocchini, P., Kralovic, R., Prencipe, G., Ruzicka, P., Santoro, N.: Black hole search by mobile agents in hypercubes and related networks. In: Proc. of 6th International Conference on Principles of Distributed Systems (OPODIS 2002), pp. 169–180 (2002)Google Scholar
- 5.Dobrev, S., Flocchini, P., Prencipe, G., Santoro, N.: Searching for a black hole in arbitrary networks: Optimal mobile agents protocols. In: Proc. 21st ACM Symposium on Principles of Distributed Computing (PODC 2002), pp. 153–161 (2002)Google Scholar
- 9.Hohl, F.: A framework to protect mobile agents by using reference states. In: Proc. 20th Int. Conf. on Distributed Computing Systems (ICDCS 2000), pp. 410–417 (2000)Google Scholar
- 10.Ng, S., Cheung, K.: Protecting mobile agents against malicious hosts by intention of spreading. In: Proc. Int. Conf. on Parallel and Distributed Processing and Applications (PDPTA 1999), pp. 725–729 (1999)Google Scholar
- 13.Vitek, J., Castagna, G.: Mobile computations and hostile hosts. In: Tsichritzis, D. (ed.) Mobile Objects, pp. 241–261. University of Geneva (1999)Google Scholar