Abstract
We consider synchronous and mobile entities that have to explore and make safe a network with faulty nodes, called black-holes, that destroy any entering entity. We are interested in the scenario where the destruction of an entity by means of a black-hole also affects all the entities within a fixed range r (in terms of hops), and we ask for the minimum number of synchronized steps needed to remove all the black-holes from that network. Clearly, if there are b black-holes in the network, then k ≥ b entities are necessary.
First, we show that the problem is NP-hard even for b = k = 1; second, we provide an asymptotical optimal solution for the case of r = 0 and a general lower bound for the case of r > 0; third, we propose two different strategies plus a refined heuristic for the case of r = 1, and we prove they are all asymptotically optimal; finally, we provide an experimental study to show the practical performance of the proposed strategies.
Research partially supported by the Research Grant 2010N5K7EB ’PRIN 2010’ ARS TechnoMedia (Algoritmica per le Reti Sociali Tecno-mediate)’ from the Italian Ministry of University and Research, and by “Fondazione Cassa di Risparmio della Provincia dell’Aquila”, project ARISE.
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D’Emidio, M., Frigioni, D., Navarra, A. (2013). Exploring and Making Safe Dangerous Networks Using Mobile Entities. In: Cichoń, J., Gȩbala, M., Klonowski, M. (eds) Ad-hoc, Mobile, and Wireless Network. ADHOC-NOW 2013. Lecture Notes in Computer Science, vol 7960. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39247-4_12
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DOI: https://doi.org/10.1007/978-3-642-39247-4_12
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