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

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(ℓ 2Dn/m) in the resulting graph. The result is tight for ℓ = 1. For some specific topologies, we give more precise bounds. © 2011 Springer-Verlag.