Abstract
In this paper, we deal with an error model in distributed networks. For a target t, every node is assumed to give an advice, ie. to point to a neighbour that take closer to the destination. Any node giving a bad advice is called a liar. Starting from a situation without any liar, we study the impact of topology changes on the number of liars.
More precisely, we establish a relationship between the number of liars and the number of distance changes after one edge deletion. Whenever ℓ deleted edges are chosen uniformly at random, for any graph with n nodes, m edges and diameter D, we prove that the expected number of liars and distance changes is \(O(\frac{\ell^2Dn}{m})\) in the resulting graph. The result is tight for ℓ = 1. For some specific topologies, we give more precise bounds.
This work is granted by the european project EULER.
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Glacet, C., Hanusse, N., Ilcinkas, D. (2011). The Impact of Edge Deletions on the Number of Errors in Networks. In: Fernàndez Anta, A., Lipari, G., Roy, M. (eds) Principles of Distributed Systems. OPODIS 2011. Lecture Notes in Computer Science, vol 7109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25873-2_26
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DOI: https://doi.org/10.1007/978-3-642-25873-2_26
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