Impact of Obstacles on the Degree of Mobile Ad Hoc Connection Graphs

What is the impact of obstacles on the graphs of connections between stations in Mobile Ad hoc Networks? In order to answer, at least partially, this question, the first step is to define both an environment with obstacles and a mobility model for the stations in such an environment. The present paper focuses on a new way of considering the mobility within environments with obstacles, while keeping the core ideas of the well-known Random WayPoint mobility model (a.k.a RWP). Based on a mesh-partitioning of the space, we propose a new model called RSP-O-G for which we compute the spatial distribution of stations and analyse how the presence of obstacles impacts this distribution compared to the distribution when no obstacles are present. Coupled with a simple model of radio propagation, and according to the density of stations in the environment, we study the mean degree of the connection graphs corresponding to such mobile ad hoc networks

GraphStream: A Tool for bridging the gap between Complex Systems and Dynamic Graphs

The notion of complex systems is common to many domains, from Biology to Economy, Computer Science, Physics, etc. Often, these systems are made of sets of entities moving in an evolving environment. One of their major characteristics is the emergence of some global properties stemmed from local interactions between the entities themselves and between the entities and the environment. The structure of these systems as sets of interacting entities leads researchers to model them as graphs. However, their understanding requires most often to consider the dynamics of their evolution. It is indeed not relevant to study some properties out of any temporal consideration. Thus, dynamic graphs seem to be a very suitable model for investigating the emergence and the conservation of some properties. GraphStream is a Java-based library whose main purpose is to help researchers and developers in their daily tasks of dynamic problem modeling and of classical graph management tasks: creation, processing, display, etc. It may also be used, and is indeed already used, for teaching purpose. GraphStream relies on an event-based engine allowing several event sources. Events may be included in the core of the application, read from a file or received from an event handler

DynamicScore: a Novel Metric for Quantifying Graph Dynamics

This study introduces a new metric called ''DynamicScore'' to evaluate the dynamics of graphs. It can be applied to both vertices and edges. Unlike traditional metrics, DynamicScore not only measures changes in the number of vertices or edges between consecutive time steps, but also takes into account the composition of these sets. To illustrate the possible contributions of this metric, we calculate it for increasing networks of preferential attachment (Barab{\'a}si-Albert model) and Edge-Markovian graphs. The results improve our understanding of the dynamics inherent in these generated evolving graphs

Dynamic Graphs Generators Analysis : an Illustrative Case Study

In this work, we investigate the analysis of generators for dynamic graphs, which are defined as graphs whose topology changes over time. We introduce a novel concept, called ''sustainability,'' to qualify the long-term evolution of dynamic graphs. A dynamic graph is considered sustainable if its evolution does not result in a static, empty, or periodic graph. To measure the dynamics of the sets of vertices and edges, we propose a metric, named ''Nervousness,'' which is derived from the Jaccard distance.As an illustration of how the analysis can be conducted, we design a parametrized generator, named D3G3 (Degree-Driven Dynamic Geometric Graphs Generator), which generates dynamic graph instances from an initial geometric graph. The evolution of these instances is driven by two rules that operate on the vertices based on their degree. By varying the parameters of the generator, different properties of the dynamic graphs can be produced.Our results show that in order to ascertain the sustainability of the generated dynamic graphs, it is necessary to study both the evolution of the order and the Nervousness for a given set of parameters

A Metapopulation Model for Chikungunya Including Populations Mobility on a Large-Scale Network

In this work we study the influence of populations mobility on the spread of a vector-borne disease. We focus on the chikungunya epidemic event that occurred in 2005-2006 on the R\'eunion Island, Indian Ocean, France, and validate our models with real epidemic data from the event. We propose a metapopulation model to represent both a high-resolution patch model of the island with realistic population densities and also mobility models for humans (based on real-motion data) and mosquitoes. In this metapopulation network, two models are coupled: one for the dynamics of the mosquito population and one for the transmission of the disease. A high-resolution numerical model is created out from real geographical, demographical and mobility data. The Island is modeled with an 18 000-nodes metapopulation network. Numerical results show the impact of the geographical environment and populations' mobility on the spread of the disease. The model is finally validated against real epidemic data from the R\'eunion event.Comment: Accepted in Journal of Theoretical biolog

Modélisation et traitement décentralisé des graphes dynamiques<br />Application aux réseaux mobiles ad hoc

Dynamic graphs are being used to a large extent in the modeling of lots of dynamically changing and uncertain environments such as complex networks or mobile ad hoc networks. These models are specialized and dedicated to the application they handle. To your knowledge no unified model handles the ideas of dynamic graphs regardless of any applicative background. Moreover, problem solving in these dynamic environments is a key problem. In this work a unified formulation of dynamic graph is proposed. We then study the resolution of problems in these dynamic graphs with the naturally dynamic and distributed methods that are Swarm Intelligence approaches. The proposed models are validated in the field of mobile ad hoc networks. We propose an original approach aimed at constructing and maintaining communication paths under several constraints. Another problem successfully addressed is the construction and the maintaining of a spanning forest in a mobile ad hoc network.Les graphes dynamiques sont un outil de plus en plus utilisé dans des contextes variés où il s'avère nécessaire de modéliser des environnements changeants ou incertains. Les modèles aujourd'hui proposés sont dédiés à ces applications précises. Il n'existe pas de modèle général reprenant, hors de tout contexte applicatif, ces caractéristiques. D'autre part la résolution de problèmes liés à ces environnements dynamiques et incertains est problématique. Nous proposons, ici, la formalisation d'un modèle général de graphe dynamique. Nous étudions la résolution de problèmes dans ces graphes à l'aide de méthodes inspirées de mécanismes d'intelligence collective. Les modèles proposés sont validés dans le contexte applicatif des réseaux mobiles ad hoc. Une approche originale de construction et de maintien de chemins de communication sous plusieurs contraintes est proposée. Le problème de la construction et du maintien d'une forêt couvrante dans un réseau mobile ad hoc est également étudié

Mobilité dans les graphes dynamiques: Mémoire d'Habilitation à Diriger des Recherches

This work presents and synthesizes the scientific activity and research conducted throughout my academic career. Spanning from the completion of my thesis in 2008 to the end of 2022, the central focus of this work is the concept of graphs, with a particular emphasis on dynamic graphs. This model of representation is pervasive throughout the presented research, including investigations into vehicle networks, computation of connected components, or maritime traffic. The document is organized around three primary themes: mobility, analysis, and algorithmic in the field of dynamic graphs. Each theme encompasses the corresponding research and also spans a specific time frame, with some overlap. The theme of mobility primarily covers the research conducted in the early period (approximately 2009 to 2015). The first chapter, "Vehicle Mobility," revisits the research conducted during my postdoctoral work in Luxembourg, which focused on network simulation and traffic modeling. The second chapter presents research on the representation of obstacles in mobile ad-hoc networks. The third chapter discusses results obtained in epidemiology. The theme of analysis pertains to the research conducted in the mid-period (approximately 2014 to 2018). The first chapter examines collaborative efforts with researchers in environmental science and focuses on life cycle analysis (LCA). The second chapter investigates maritime transportation networks. The theme of algorithmic pertains to the most recent research (approximately 2018 to 2022). The first chapter of this theme examines flows, and the second chapter addresses connectivity, both applied to dynamic graphs.Ce travail a pour objet de présenter et de synthétiser l'activité scientifique et les travaux de recherche menés durant ma carrière académique. Il couvre une période allant de la fin de ma thèse en 2008 à fin 2022. La notion de graphe, et en particulier celle de graphe dynamique, est transversale à mon champ de recherche. Ce modèle de représentation est omniprésent dans tout ce qui est présenté ici, allant des réseaux de véhicules aux calculs de composantes connexes, en passant par le trafic maritime. Le document est organisé autour de trois axes principaux, à savoir la mobilité, l’analyse et l’algorithmique dans le domaine des graphes dynamiques. Chacun de ces axes regroupe les travaux correspondants et couvre également une fenêtre temporelle spécifique, avec des recouvrements possibles. L'axe mobilité couvre principalement les travaux menés au début de la période (environ 2009 à 2015). Le premier chapitre, intitulé "Mobilité des véhicules", revient sur les travaux menés lors de mon post-doctorat au Luxembourg, portant sur la simulation de réseau et la modélisation de trafic routier. Le deuxième chapitre présente un travail sur la représentation des obstacles dans les réseaux mobiles ad hoc. Le troisième chapitre discute des résultats obtenus en épidémiologie. L'axe analyse concerne les travaux réalisés au milieu de la période (environ 2014 à 2018). Le premier chapitre examine la collaboration avec des chercheurs en sciences de l'environnement et concerne l'analyse du cycle de vie. Le deuxième chapitre examine les réseaux de transport maritimes. L'axe algorithmique concerne les travaux les plus récents (environ 2018 à 2022). Dans cet axe, les deux chapitres, le premier portant sur les flux, le second sur la connectivité, s'intéressent à ces notions classiques, appliquées au cas dynamique

Modélisation et traitement décentralisé des graphes dynamiques<br />Application aux réseaux mobiles ad hoc

Dynamic graphs are being used to a large extent in the modeling of lots of dynamically changing and uncertain environments such as complex networks or mobile ad hoc networks. These models are specialized and dedicated to the application they handle. To your knowledge no unified model handles the ideas of dynamic graphs regardless of any applicative background. Moreover, problem solving in these dynamic environments is a key problem. In this work a unified formulation of dynamic graph is proposed. We then study the resolution of problems in these dynamic graphs with the naturally dynamic and distributed methods that are Swarm Intelligence approaches. The proposed models are validated in the field of mobile ad hoc networks. We propose an original approach aimed at constructing and maintaining communication paths under several constraints. Another problem successfully addressed is the construction and the maintaining of a spanning forest in a mobile ad hoc network.Les graphes dynamiques sont un outil de plus en plus utilisé dans des contextes variés où il s'avère nécessaire de modéliser des environnements changeants ou incertains. Les modèles aujourd'hui proposés sont dédiés à ces applications précises. Il n'existe pas de modèle général reprenant, hors de tout contexte applicatif, ces caractéristiques. D'autre part la résolution de problèmes liés à ces environnements dynamiques et incertains est problématique. Nous proposons, ici, la formalisation d'un modèle général de graphe dynamique. Nous étudions la résolution de problèmes dans ces graphes à l'aide de méthodes inspirées de mécanismes d'intelligence collective. Les modèles proposés sont validés dans le contexte applicatif des réseaux mobiles ad hoc. Une approche originale de construction et de maintien de chemins de communication sous plusieurs contraintes est proposée. Le problème de la construction et du maintien d'une forêt couvrante dans un réseau mobile ad hoc est également étudié