L-distance-edge-coloring and clustering : studies and self-stabilizing algorithms

La coloration de graphes est un problème central de l’optimisation combinatoire. C’est un domaine très attractif par ses nombreuses applications. Différentes variantes et généralisations du problème de la coloration de graphes ont été proposées et étudiées. La coloration d’arêtes d’un graphe consiste à attribuer une couleur à chaque arête du graphe de sorte que deux arêtes ayant un sommet commun n’ont jamais la même couleur, le tout en utilisant le moins de couleurs possibles. Dans la première partie de cette thèse, nous étudions le problème de la coloration d’arêtes ℓ-distance, qui est une généralisation de la coloration d’arêtes classique. Nous menons une étude combinatoire et algorithmique du paramètre. L’étude porte sur les classes de graphes suivantes : les chaines, les grilles, les hypercubes, les arbres et des graphes puissances. Le paramètre de la coloration d’arêtes ℓ-distance permet de modéliser des problèmes dans des réseaux assez grands. Cependant, avec la multiplication du nombre de nœuds, les réseaux sont de plus en plus vulnérables aux défaillances (ou pannes). Dans la deuxième partie, nous nous intéressons aux algorithmes tolérants aux pannes et en particulier les algorithmes auto-stabilisants. Nous proposons un algorithme auto-stabilisant pour la coloration propre d’arêtes. Notre solution se base sur le résultat de vizing pour utiliser un minimum de couleurs possibles. Par la suite, nous proposons un algorithme auto-stabilisant de clustering destine a des applications dans le domaine de la sécurité dans les réseaux mobiles Ad hoc. La solution que nous proposons est un partitionnement en clusters base sur les relations de confiance qui existent entre nœuds. Nous proposons aussi un algorithme de gestion de clés de groupe dans les réseaux mobiles ad hoc qui s’appuie sur la topologie de clusters préalablement construite. La sécurité de notre protocole est renforcée par son critère de clustering qui surveille en permanence les relations de confiance et expulse les nœuds malveillants de la session de diffusion.Graph coloring is a famous combinatorial optimization problem and is very attractive for its numerous applications. Many variants and generalizations of the graph-coloring problem have been introduced and studied. An edge-coloring assigns a color to each edge so that no two adjacent edges share the same color. In the first part of this thesis, we study the problem of the ℓ-distance-edge-coloring, which is a generalization of the classical edge-coloring. The study focuses on the following classes of graphs : paths, grids, hypercubes, trees and some power graphs. We are conducting a combinatorial and algorithmic study of the parameter. We give a sequential coloring algorithm for each class of graph. The ℓ-distance-edge-coloring is especially considered in large-scale networks. However, with the increasing number of nodes, networks are increasingly vulnerable to faults. In the second part, we focus on fault-tolerant algorithms and in particular self-stabilizing algorithms. We propose a self-stabilizing algorithm for proper edge-coloring. Our solution is based on Vizing’s result to minimize number of colors. Subsequently, we propose a selfstabilizing clustering algorithm for applications in the field of security in mobile ad hoc networks. Our solution is a partitioning into clusters based on trust relationships between nodes. We also propose a group key-management algorithm in mobile ad hoc networks based on the topology of clusters previously built. The security of our protocol is strengthened by its clustering criterion which constantly monitors trust relationships and expels malicious nodes out of the multicast session

Coloration d’arêtes ℓ-distance et clustering : études et algorithmes auto-stabilisants

Graph coloring is a famous combinatorial optimization problem and is very attractive for its numerous applications. Many variants and generalizations of the graph-coloring problem have been introduced and studied. An edge-coloring assigns a color to each edge so that no two adjacent edges share the same color. In the first part of this thesis, we study the problem of the ℓ-distance-edge-coloring, which is a generalization of the classical edge-coloring. The study focuses on the following classes of graphs : paths, grids, hypercubes, trees and some power graphs. We are conducting a combinatorial and algorithmic study of the parameter. We give a sequential coloring algorithm for each class of graph. The ℓ-distance-edge-coloring is especially considered in large-scale networks. However, with the increasing number of nodes, networks are increasingly vulnerable to faults. In the second part, we focus on fault-tolerant algorithms and in particular self-stabilizing algorithms. We propose a self-stabilizing algorithm for proper edge-coloring. Our solution is based on Vizing’s result to minimize number of colors. Subsequently, we propose a selfstabilizing clustering algorithm for applications in the field of security in mobile ad hoc networks. Our solution is a partitioning into clusters based on trust relationships between nodes. We also propose a group key-management algorithm in mobile ad hoc networks based on the topology of clusters previously built. The security of our protocol is strengthened by its clustering criterion which constantly monitors trust relationships and expels malicious nodes out of the multicast session.La coloration de graphes est un problème central de l’optimisation combinatoire. C’est un domaine très attractif par ses nombreuses applications. Différentes variantes et généralisations du problème de la coloration de graphes ont été proposées et étudiées. La coloration d’arêtes d’un graphe consiste à attribuer une couleur à chaque arête du graphe de sorte que deux arêtes ayant un sommet commun n’ont jamais la même couleur, le tout en utilisant le moins de couleurs possibles. Dans la première partie de cette thèse, nous étudions le problème de la coloration d’arêtes ℓ-distance, qui est une généralisation de la coloration d’arêtes classique. Nous menons une étude combinatoire et algorithmique du paramètre. L’étude porte sur les classes de graphes suivantes : les chaines, les grilles, les hypercubes, les arbres et des graphes puissances. Le paramètre de la coloration d’arêtes ℓ-distance permet de modéliser des problèmes dans des réseaux assez grands. Cependant, avec la multiplication du nombre de nœuds, les réseaux sont de plus en plus vulnérables aux défaillances (ou pannes). Dans la deuxième partie, nous nous intéressons aux algorithmes tolérants aux pannes et en particulier les algorithmes auto-stabilisants. Nous proposons un algorithme auto-stabilisant pour la coloration propre d’arêtes. Notre solution se base sur le résultat de vizing pour utiliser un minimum de couleurs possibles. Par la suite, nous proposons un algorithme auto-stabilisant de clustering destine a des applications dans le domaine de la sécurité dans les réseaux mobiles Ad hoc. La solution que nous proposons est un partitionnement en clusters base sur les relations de confiance qui existent entre nœuds. Nous proposons aussi un algorithme de gestion de clés de groupe dans les réseaux mobiles ad hoc qui s’appuie sur la topologie de clusters préalablement construite. La sécurité de notre protocole est renforcée par son critère de clustering qui surveille en permanence les relations de confiance et expulse les nœuds malveillants de la session de diffusion

Coloration d’arêtes ℓ-distance et clustering : études et algorithmes auto-stabilisants

Graph coloring is a famous combinatorial optimization problem and is very attractive for its numerous applications. Many variants and generalizations of the graph-coloring problem have been introduced and studied. An edge-coloring assigns a color to each edge so that no two adjacent edges share the same color. In the first part of this thesis, we study the problem of the ℓ-distance-edge-coloring, which is a generalization of the classical edge-coloring. The study focuses on the following classes of graphs : paths, grids, hypercubes, trees and some power graphs. We are conducting a combinatorial and algorithmic study of the parameter. We give a sequential coloring algorithm for each class of graph. The ℓ-distance-edge-coloring is especially considered in large-scale networks. However, with the increasing number of nodes, networks are increasingly vulnerable to faults. In the second part, we focus on fault-tolerant algorithms and in particular self-stabilizing algorithms. We propose a self-stabilizing algorithm for proper edge-coloring. Our solution is based on Vizing’s result to minimize number of colors. Subsequently, we propose a selfstabilizing clustering algorithm for applications in the field of security in mobile ad hoc networks. Our solution is a partitioning into clusters based on trust relationships between nodes. We also propose a group key-management algorithm in mobile ad hoc networks based on the topology of clusters previously built. The security of our protocol is strengthened by its clustering criterion which constantly monitors trust relationships and expels malicious nodes out of the multicast session.La coloration de graphes est un problème central de l’optimisation combinatoire. C’est un domaine très attractif par ses nombreuses applications. Différentes variantes et généralisations du problème de la coloration de graphes ont été proposées et étudiées. La coloration d’arêtes d’un graphe consiste à attribuer une couleur à chaque arête du graphe de sorte que deux arêtes ayant un sommet commun n’ont jamais la même couleur, le tout en utilisant le moins de couleurs possibles. Dans la première partie de cette thèse, nous étudions le problème de la coloration d’arêtes ℓ-distance, qui est une généralisation de la coloration d’arêtes classique. Nous menons une étude combinatoire et algorithmique du paramètre. L’étude porte sur les classes de graphes suivantes : les chaines, les grilles, les hypercubes, les arbres et des graphes puissances. Le paramètre de la coloration d’arêtes ℓ-distance permet de modéliser des problèmes dans des réseaux assez grands. Cependant, avec la multiplication du nombre de nœuds, les réseaux sont de plus en plus vulnérables aux défaillances (ou pannes). Dans la deuxième partie, nous nous intéressons aux algorithmes tolérants aux pannes et en particulier les algorithmes auto-stabilisants. Nous proposons un algorithme auto-stabilisant pour la coloration propre d’arêtes. Notre solution se base sur le résultat de vizing pour utiliser un minimum de couleurs possibles. Par la suite, nous proposons un algorithme auto-stabilisant de clustering destine a des applications dans le domaine de la sécurité dans les réseaux mobiles Ad hoc. La solution que nous proposons est un partitionnement en clusters base sur les relations de confiance qui existent entre nœuds. Nous proposons aussi un algorithme de gestion de clés de groupe dans les réseaux mobiles ad hoc qui s’appuie sur la topologie de clusters préalablement construite. La sécurité de notre protocole est renforcée par son critère de clustering qui surveille en permanence les relations de confiance et expulse les nœuds malveillants de la session de diffusion

ECGK: an Efficient Clustering Scheme for Group Key Management in MANETs

International audienceMobile Ad hoc NETworks (or MANETs) are flexible networks that are expected to support emerging group applications such as spontaneous collaborative activities and rescue operations. In order to provide secrecy to these applications, a common encryption key has to be established between group members of the application. This task is critical in MANETs because these networks have no fixed infrastructure, frequent node and link failures and a dynamic topology. The proposed approaches to cope with these characteristics aim to avoid centralized solutions and organize the network into clusters. However, the clustering criteria used in the literature are not always adequate for key management and security. In, this paper, we propose, a group key management framework based on a trust oriented clustering scheme. We show that trust is a relevant clustering criterion for group key management in MANETs. Trust information enforce authentication and is disseminated by the mobility of nodes. Furthermore, it helps to evict malicious nodes from the multicast session even if they are authorized members of the group. Simulation results show that our solution is efficient and typically adapted to mobility of nodes

A Self-Stabilizing (delta+1)- Edge-Coloring Algorithm of Arbitrary Graphs.

International audienceGiven a graph G = (V,E), an edge-coloring of G is a function from the set of edges E to colors {1, 2, · · ·, k} such that any two adjacent edges are assigned different colors. In this paper, we propose a self-stabilizing edge-coloring algorithm in a polynomial number of moves. The protocol assumes the unfair central dæmon and the coloring is a (delta + 1)-edge-coloring of G, where delta is the maximum degree in G. To our knowledge, we give the first self-stabilizing edge-coloring algorithm using (delta+ 1) colors of arbitrary graphs

Distance-edge-coloring of trees

International audienceFor a given bounded nonnegative integer ℓ, an ℓ-distance-edge-coloring of a graph G = (V (G),E(G)) is a function from the edges E to colors {1, 2, · · · , k} such that any two edges within distance ℓ of each other are assigned different colors. In this paper, we propose an algorithm to compute the minimum value of k for trees

Topologie dynamique virtuelle pour le routage dans les réseaux mobiles Ad hoc

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Distance edge coloring and collision-free communication in wireless sensor networks

International audienceMotivated by the problem of link scheduling in wireless sensor networks where differentsensors have different transmission and interference ranges and may be mobile, we study theproblem of distance edge coloring of graphs which is a generalization of proper edge coloring.Let G be a graph modeling a sensor network. An ℓ-distance edge coloring of G is a coloringof the edges of G such that any two edges within distance ℓ of each other are assigneddifferent colors. The parameter ℓ is chosen so that the links corresponding to two edges thatare assigned the same color do not interfere. We investigate the ℓ-distance edge coloringproblem on several families of graphs which can be used as topologies in sensor deployment.We focus on determining the minimum number of colors needed and on optimal coloringalgorithms

Distance-edge-coloring of power graphs

International audienceThe \ell-distance-edge-coloring is a generalization of the edge-coloring that tries to assign a color from 1 to k to each edge such that any two edges of distance at most \ell have distinct colors. The minimum number of colors used to color a graph with an \ell-distance-edge-coloring is called the \ell-chromatic index. Solving the \ell-distance-edge-coloring problem is different from determining the chromatic index, by Vizing's theorem, for its power graph. The \ell-distance-edge-coloring is thus an original problem which is NP-hard in general. We study the \ell-distance-edge-coloring problem in some classes of graphs in order to bring a new insight on the relative difficulties of this problem. We focus on the \ell-chromatic index for some classes of p-th power graphs. We present, for any integer \ell\geq0, the exact values for the \ell-chromatic index for power graphs of paths and complete k-ary trees, and bounds and exact values for the \ell-chromatic index for power graphs of cycles and general trees. Furthermore, we propose a polynomial-time coloring algorithm, for each studied class of graph, that satisfies the \ell-distance-edge-coloring

Distance edge coloring and collision-free communication in wireless sensor networks

International audienceMotivated by the problem of link scheduling in wireless sensor networks where differentsensors have different transmission and interference ranges and may be mobile, we study theproblem of distance edge coloring of graphs which is a generalization of proper edge coloring.Let G be a graph modeling a sensor network. An ℓ-distance edge coloring of G is a coloringof the edges of G such that any two edges within distance ℓ of each other are assigneddifferent colors. The parameter ℓ is chosen so that the links corresponding to two edges thatare assigned the same color do not interfere. We investigate the ℓ-distance edge coloringproblem on several families of graphs which can be used as topologies in sensor deployment.We focus on determining the minimum number of colors needed and on optimal coloringalgorithms