The impact of edge deletions on the number of errors in networks

Authors:
Christian Glacet;Nicolas Hanusse;David Ilcinkas
Affiliations:
LaBRI, University of Bordeaux, CNRS, INRIA, France;LaBRI, University of Bordeaux, CNRS, INRIA, France;LaBRI, University of Bordeaux, CNRS, INRIA, France
Venue:
OPODIS'11 Proceedings of the 15th international conference on Principles of Distributed Systems
Year:
2011

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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.