MOATAZ , Fatima Zahra

We study in this thesis optimization problems with application in optical networks. The problems we consider are related to fault-tolerance and efficient resource allocation and the results we obtain are mainly related to the computational complexity of these problems. The first part of this thesis is devoted to finding paths and disjoint...

To face the explosion of the Internet trac, a new generation of optical networks is being developed; the Elastic Optical Networks (EONs). EONs use the optical spectrum eciently and flexibly, but that gives rise to more diculty in the resource allocation problems. In this article, we study the problem of Spectrum Assignment (SA) in Elastic...

To face the explosion of the Internet traffic, a new generation of optical networks is being developed; the Elastic optical Networks (EONs). The aim with EONs is to use the optical spectrum efficiently and flexibly. The benefit of the flexibility is, however, accompanied by more difficulty in the resource allocation problems. In this report, we...

L'augmentation du trafic Internet motive une évolution des réseaux WDM traditionnels vers les réseaux optiques élastiques (Elastic Optical Networks, EON). Les EONs sont conçus pour optimiser l'utilisation des ressources optiques; ils permettent l'attribution de bandes de largeurs quelconques et offrent ainsi plus de souplesse que les réseaux...

L'augmentation du trafic Internet motive une évolution des réseaux WDM traditionnels vers les réseaux optiques élastiques (Elastic Optical Networks, EON). Les EONs sont conçus pour optimiser l'utilisation des ressources optiques; ils permettent l'attribution de bandes de largeurs quelconques et offrent ainsi plus de souplesse que les réseaux...

Tree-Decompositions are the corner-stone of many dynamic programming algorithms for solving graph problems. Since the complexity of such algorithms generally depends exponentially on the width (size of the bags) of the decomposition, much work has been devoted to compute tree- decompositions with small width. However, practical algorithms...

We study in this paper the problem of computing a tree-decomposition of a graph with width at most k and minimum number of bags. More precisely, we focus on the following problem: given a fixed $k ≥ 1$, what is the complexity of computing a tree-decomposition of width at most k with minimum number of bags in the class of graphs with treewidth...

Tree-Decompositions are the corner-stone of many dynamic programming algorithms for solving graph problems. Since the complexity of such algorithms generally depends exponentially on the width (size of the bags) of the decomposition, much work has been devoted to compute tree-decompositions with small width. However, practical algorithms...

The notion of Shared Risk Link Groups (SRLG) has been introduced to capture survivability issues where a set of links of a network fail simultaneously. In this context, the \emph{diverse routing} problem is to find a set of SRLG-disjoint paths between a given pair of end nodes of the network. This problem has been proved $NP$-complete in...

Une transition dans un graphe est une paire d'arêtes incidentes à un même sommet. Etant donnés un graphe G = (V, E), deux sommets s,t ∈ V et un ensemble associé de transitions interdites F ⊆ E × E, le problème de chemin évitant des transitions interdites consiste à décider s'il existe un chemin élémentaire de s à t qui n'utilise aucune des...

The notion of Shared Risk Link Groups (SRLG) has been introduced to capture survivability issues where some links of a network fail simultaneously. In this context, the diverse routing problem is to find a set of pairwise SRLG-disjoint paths between a given pair of end nodes of the network. This problem has been proved NP-complete in general...

The notion of Shared Risk Link Group, SRLG has been intro- duced to capture multiple correlated failures in a network. A SRLG is a set of links that fail simultaneously if a given event (risk) occurs. In such multiple failures scenario, the problem of Diverse Routing consists in finding two SRLG- disjoint paths between a pair of nodes. We...

A transition in a graph is a pair of adjacent edges. Given a graph G = (V, E), a set of forbidden transitions F ⊆ E × E and two vertices s, t ∈ V , we study the problem of finding a path from s to t which uses none of the forbidden transitions of F. This means that it is forbidden for the path to consecutively use two edges forming a pair in F....

Une transition dans un graphe est une paire d'arêtes incidente a un même sommet. Etant donnés un graphe G = (V, E), deux sommets s, t ∈ V et un ensemble associé de transitions interdites F ⊆ E × E, le problème de chemin évitant des transitions interdites consiste à décider s'il existe un chemin élémentaire de s à t qui n'utilise aucune des...

La notion de groupe de liens partageant un risque (Shared Risk Link Group, SRLG) a été introduite pour modéliser des problèmes de tolérance aux pannes simultanées d'ensembles de liens d'un réseau. Dans ce contexte, le problème du routage diversifié est de trouver un ensemble de chemins SRLG-disjoints entre une paire donnée de noeuds du réseau....