The impact of dynamic events on the number of errors in networks
Résumé
In order to achieve routing in a graph, nodes need to store routing information.
In the case of shortest path routing, for a given destination, every node has to
store an \emph{advice} that is an outgoing link toward a neighbor.
If this neighbor does not belong to a shortest path then the advice is considered as an error and the node giving this advice will be qualified a \emph{liar}.
This article focuses on the impact of
graph dynamics on the advice set for a given destination. More precisely we show that, for
a weighted graph $G$ of diameter $D$ with $n$ nodes and $m$ edges, the
expected number of errors after $\mathcal{M}$ edge deletions is bounded by
$\mathcal{O}(n \cdot \mathcal{M} \cdot \frac{D}{m})$.
We also show that this bound is tight when $\mathcal{M} = {\scriptstyle\mathcal{O}}(n)$.
Moreover, for $\mathcal{M}'$ node deletions, the expected number of errors is
$\mathcal{O}(\mathcal{M}' \cdot D)$.
Finally we show that after a single edge addition the expected number of
liars can be $\Theta(n)$ for some families of graphs.
Origine : Fichiers produits par l'(les) auteur(s)
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