Scalable and Secure Aggregation in Distributed Networks

We consider the problem of computing an aggregation function in a \emph{secure} and \emph{scalable} way. Whereas previous distributed solutions with similar security guarantees have a communication cost of $O(n^3)$, we present a distributed protocol that requires only a communication complexity of $O(n\log^3 n)$, which we prove is near-optimal. Our protocol ensures perfect security against a computationally-bounded adversary, tolerates $(1/2-\epsilon)n$ malicious nodes for any constant $1/2 > \epsilon > 0$ (not depending on $n$), and outputs the exact value of the aggregated function with high probability

A distributed algorithm for computing and updating the process number of a forest

In this paper, we present a distributed algorithm to compute various parameters of a tree such as the process number, the edge search number or the node search number and so the pathwidth. This algorithm requires n steps, an overall computation time of O(n log(n)), and n messages of size log_3(n)+3. We then propose a distributed algorithm to update the process number (or the node search number, or the edge search number) of each component of a forest after adding or deleting an edge. This second algorithm requires O(D) steps, an overall computation time of O(D log(n)), and O(D) messages of size log_3(n)+3, where D is the diameter of the modified connected component. Finally, we show how to extend our algorithms to trees and forests of unknown size using messages of less than 2a+4+e bits, where a is the parameter to be determined and e=1 for updates algorithms

Reconfiguration dans les réseaux optiques

International audienceL'évolution permanente du trafic, les opérations de maintenance et l'existence de pannes dans les réseaux WDM, obligent à rerouter régulièrement des connexions. Les nouvelles demandes de connexions sont routées en utilisant les ressources disponibles et, si possible, sans modifier le routage des connexions existantes. Ceci peut engendrer une mauvaise utilisation des ressources disponibles. Il est donc préférable de reconfigurer régulièrement l'ensemble des routes des différentes connexions. Un objectif particulièrement important est alors de minimiser le nombre de requêtes simultanément interrompues lors de la reconfiguration. Nous proposons une heuristique pour résoudre ce problème dans les réseaux WDM. Les simulations montrent que cette heuristique réalise de meilleures performances que celle proposée par Jose et Somani (2003). Nous proposons également un modèle permettant de prendre en compte différentes classes de clients, avec notamment la contrainte que des requêtes, dites prioritaires, ne peuvent pas être interrompues. Une simple transformation permet de réduire le problème avec requêtes prioritaires au problème initial. De ce fait, notre heuristique s'applique également au cas autorisant des requêtes prioritaires

(ℓ,k)(\ell,k)-Routing on Plane Grids

The packet routing problem plays an essential role in communication networks. It involves how to transfer data from some origins to some destinations within a reasonable amount of time. In the $(\ell,k)$-routing problem, each node can send at most $\ell$ packets and receive at most $k$ packets. Permutation routing is the particular case $\ell=k=1$. In the $r$-central routing problem, all nodes at distance at most $r$ from a fixed node $v$ want to send a packet to $v$. In this article we study the permutation routing, the $r$-central routing and the general $(\ell,k)$-routing problems on plane grids, that is square grids, triangular grids and hexagonal grids. We use the \emph{store-and-forward} $\Delta$-port model, and we consider both full and half-duplex networks. The main contributions are the following: \begin{itemize} \item[1.] Tight permutation routing algorithms on full-duplex hexagonal grids, and half duplex triangular and hexagonal grids. \item[2.] Tight $r$-central routing algorithms on triangular and hexagonal grids. \item[3.] Tight $(k,k)$-routing algorithms on square, triangular and hexagonal grids. \item[4.] Good approximation algorithms (in terms of running time) for $(\ell,k)$-routing on square, triangular and hexagonal grids, together with new lower bounds on the running time of any algorithm using shortest path routing. \end{itemize} \noindent All these algorithms are completely distributed, i.e. can be implemented independently at each node. Finally, we also formulate the $(\ell,k)$-routing problem as a \textsc{Weighted Edge Coloring} problem on bipartite graphs

Algorithme générique pour les jeux de capture dans les arbres

National audienceNous présentons un algorithme distribué simple calculant le process number des arbres en n étapes, avec un nombre total d'opérations en O(nlog(n)) et un total de O(nlog(n)) bits échangés. De plus cet algorithme est facilement adaptable pour calculer d'autre paramètres sur l'arbre, dont le node search number

On the Pathwidth of Planar Graphs

Fomin and Thilikos in [5] conjectured that there is a constant $c$ such that, for every $2$-connected planar graph $G$, {pw}(G^*) \leq 2\text{pw}(G)+c$(the same question was asked simutaneously by Coudert, Huc and Sereni in [4]). By the results of Boedlander and Fomin [2] this holds for every outerplanar graph and actually is tight by Coudert, Huc and Sereni [4]. In [5], Fomin and Thilikos proved that there is a constant$c$such that the pathwidth of every 3-connected graph$G$satisfies:${pw}(G^*) \leq 6\text{pw}(G)+c$. In this paper we improve this result by showing that the dual a 3-connected planar graph has pathwidth at most$3$times the pathwidth of the primal plus two. We prove also that the question can be answered positively for$4$-connected planar graphs