PhD defense of Fionn Mc Inerney

PhD Fionn Mc Inerney

    • Title: “Domination and Identification Games in Graphs”
    • When: July 8, 2019 — 14:00
    • Where: Inria Sophia Antipolis, Euler violet
    • Committee:
      • Steve Alpern, Warwick Business School, The University of Warwick, Coventry West Midlands, UK
      • Victor Chepoi, Laboratoire d’Informatique et Systèmes, Aix-Marseille Université, Marseille, France
      • Paul Dorbec (Rapporteur), Université de Caen Normandie, Caen, France
      • Sylvain Gravier (Rapporteur), Université Grenoble Alpes, Institut Fourier, Grenoble, France
      • Nicolas Nisse (Directeur), Université Côte d’Azur, Inria, CNRS, I3S, Sophia Antipolis, France
      • Aline Parreau, Laboratoire LIRIS, Université Claude Bernard Lyon 1, Lyon, France
    • Abstract: In this thesis, 2-player games on graphs and their algorithmic and structural aspects are studied. First, we investigate two dynamic dominating set games: the eternal domination game and its generalization, the spy game. In these two games, a team of guards pursue a fast attacker or spy in a graph with the objective of staying close to him eternally and one wants to calculate the eternal domination number (guard number in the spy game) which is the minimum number of guards needed to do this. Secondly, the metric dimension of digraphs and a sequential version of the metric dimension of graphs are then studied. These two problems are those of finding a minimum subset of vertices that uniquely identify all the vertices of the graph by their distances from the vertices in the subset. In particular, in the latter, one can probe a certain number of vertices per turn which return their distances to a hidden target and the goal is to minimize the number of turns in order to ensure locating the target. These games and problems are studied in particular graph classes and their computational complexities are also studied.

      Precisely, the NP-hardness of the spy game and the guard numbers of paths and cycles are first presented. Then, results for the spy game on trees and grids are presented. Notably, we show an equivalence between the fractional variant and the “integral” version of the spy game in trees which allowed us to use Linear Programming to come up with what we believe to be the first exact algorithm using the fractional variant of a game to solve the “integral” version. Asymptotic bounds on the eternal domination number of strong grids are then presented. This is followed by results on the NP-completeness of the Localization game under different conditions (and a variant of it) and the game in trees. Notably, we show that the problem is NP-complete in trees, but despite this, we come up with a polynomial-time (+1)-approximation algorithm in trees. We consider such an approximation to be rare as we are not aware of any other such approximation in games on graphs. Lastly, results on the metric dimension of oriented graphs are presented. In particular, the orientations which maximize the metric dimension are investigated for graphs of bounded degree, tori, and grids.

    • Titre: “Jeux de Domination et d’Identification dans les Graphes”
    • Résumé: Dans cette thèse, les jeux à 2 joueurs dans les graphes et leurs aspects algorithmiques et structurels sont étudiés. Nous explorons tout d’abord le jeu de domination éternelle ainsi que sa généralisation, le jeu de l’espion, deux jeux qui reposent sur les ensembles dominants dynamiques. Dans ces deux jeux, une équipe de gardes poursuit un attaquant ou espion rapide dans un graphe, avec l’objectif de rester près de lui éternellement. Le but est de calculer le nombre de domination éternelle (nombre de gardes pour le jeu de l’espion) qui est le nombre minimum de gardes nécessaires pour réaliser l’objectif. La dimension métrique des digraphes et une version séquentielle de la dimension métrique des graphes sont aussi étudiées. Ces deux problèmes ont pour objectif de trouver un sous-ensemble de sommets de taille minimum tel que tous les sommets du graphe sont identifiés uniquement par leurs distances aux sommets du sous-ensemble. En particulier, dans ce dernier problème, on peut “interroger” un certain nombre de sommets par tour. Les sommets interrogés retournent leurs distances à une cible cachée. Le but est de minimiser le nombre de tours nécessaires pour localiser la cible. Ces jeux et problèmes sont étudiés pour des classes de graphe particulières et leurs complexités temporelles sont aussi étudiées.

      Précisément, il est démontré que le jeu de l’espion est NP-difficile et les nombres de gardes des chemins et des cycles sont présentés. Ensuite, des résultats sur le jeu de l’espion dans les arbres et les grilles sont présentés. Notamment, nous démontrons une équivalence entre la variante fractionnaire et la variante “intégrale” du jeu de l’espion dans les arbres qui nous a permise d’utiliser la programmation linéaire pour concevoir ce que nous pensons être le premier algorithme exact qui utilise la variante fractionnaire d’un jeu pour résoudre sa variante “intégrale”. Des bornes asymptotiques sur le nombre de domination éternelle de la grille du roi sont aussi présentées. Ensuite, des résultats sur la NP-complétude du jeu de Localisation sous différentes conditions (et une variante de ce jeu) sont présentés. Notamment, nous démontrons que le problème est NP-complet dans les arbres. Malgré cela, nous concevons un (+1)-algorithme d’approximation qui résout le problème en temps polynomial. Autant que nous sachions, il n’existe pas d’autres telles approximations pour les jeux dans les graphes. Finalement, des résultats sur la dimension métrique des graphes orientés sont présentés. En particulier, les orientations qui maximisent la dimension métrique sont explorées pour les graphes de degré borné, les tores et les grilles.

PhD defense of Andrea Tomassilli

PhD Andrea Tomassilli

    • Title: “Towards Next Generation Networks with SDN and NFV”
    • When: June 24, 2019 — 14:30
    • Where: Inria Sophia Antipolis, Euler violet
    • Committee:
      • Mathieu Bouet (Referee), Thales, Paris, France
      • Stefano Secci (Referee), Cedric – CNAM, Pairs, France
      • Stéphane Pérennes (Supervisor), COATI, Université Côte d’Azur, CNRS, I3S, Inria, Sophia Antipolis, France
      • Frédéric Giroire (Supervisor), COATI, Université Côte d’Azur, CNRS, I3S, Inria, Sophia Antipolis, France
      • Michele Flammini, Dipartimento di Ingegneria e Scienze dell’Informazione e Matematica, Università degli Studi dell’Aquila, L’Aquila, Italy
      • Thierry Turletti, Inria, Sophia Antipolis, France
      • Brigitte Jaumard, Concordia University, Montréal, Québec, Canada
    • Abstract: Recent advances in networks, such as Software Defined Networking (SDN) and Network Function Virtualization (NFV), are changing the way network operators deploy and manage Internet services.
      On one hand, SDN introduces a logically centralized controller with a global view of the network state.
      On the other hand, NFV enables the complete decoupling of network functions from proprietary appliances and runs them as software applications on general–purpose servers. In such a way, network operators can dynamically deploy Virtual Network Functions (VNFs).
      SDN and NFV benefit network operators by providing new opportunities for reducing costs, enhancing network flexibility and scalability, and shortening the time-to-market of new applications and services.
      Moreover, the centralized routing model of SDN jointly with the possibility of instantiating VNFs on–demand, may open the way for an even more efficient operation and resource management of networks. For instance, an SDN/NFV-enabled network may simplify the Service Function Chain (SFC) deployment and provisioning by making the process easier and cheaper.
      In this study, we aim at investigating how to leverage both SDN and NFV in order to exploit their potential benefits.
      We took steps to address the new opportunities offered in terms of network design, network resilience, and energy savings, and the new problems that arise in this new context, such as the optimal network function placement in the network.
      We show that a symbiosis between SDN and NFV can improve network performance and significantly reduce the network’s Capital Expenditure (CapEx) and Operational Expenditure (OpEx).

    • Titre: “Vers les Réseaux de Nouvelle Génération avec SDN et NFV”
    • Résumé: Les progrès récents dans le domaine des réseaux, tels que les réseaux logiciel (SDN) et la virtualisation des fonctions réseaux (NFV), modifient la façon dont les opérateurs de réseaux déploient et gèrent les services Internet.
      D’une part, SDN introduit un contrôleur logiquement centralisé avec une vue globale de l’état du réseau. D’autre part, NFV permet le découplage complet des fonctions réseaux des appareils propriétaires et les exécute en tant qu’applications logicielles sur des serveurs génériques. De cette façon, les opérateurs de réseaux peuvent déployer dynamiquement des fonctions réseaux virtuelles (VNF).
      SDN et NFV, tous deux séparément, offrent aux opérateurs de nouvelles opportunités pour réduire les coûts, améliorer la flexibilité et le passage à l’échelle des réseaux et réduire les délais de mise sur le marché des nouveaux services et applications. De plus, le modèle de routage centralisé du SDN, associé à la possibilité d’instancier les VNF à la demande, peut ouvrir la voie à une gestion encore plus efficace des ressources réseaux. Par exemple, un réseau SDN/NFV peut simplifier le déploiement des chaînes de fonctions de services (SFC) en rendant le processus plus facile et moins coûteux.
      Dans cette thèse, notre objectif était d’examiner comment tirer parti des avantages potentiels de combiner SDN et NVF. En particulier, nous avons étudié les nouvelles possibilités offertes en matière de conception de réseau, de résilience et d’économies d’énergie, ainsi que les nouveaux problèmes qui surgissent dans ce nouveau contexte, comme l’emplacement optimal des fonctions réseaux.
      Nous montrons qu’une symbiose entre le SDN et le NFV peut améliorer la performance des réseaux et réduire considérablement les dépenses d’investissement (CapEx) et les dépenses opérationnelles (OpEx) du réseau.

HDR defense of Frédéric Giroire

HDR Frédéric Giroire

  • Title: “Optimisation des infrastructures réseaux. Un peu de vert dans les réseaux et autres problèmes de placement et de gestion de ressources
  • When: October 23, 2018 — 10:30
  • Where: Room Euler Violet, Inria Sophia Antipolis Méditerranée
  • Committee:
  • Abstract: In this thesis, I present a set of solutions to optimize network infrastructures. Pushed by the new sensitivity of the society, politics, and companies to energy costs and global warming, I investigated the question of how to build green networks. I first studied some practical scenarios to answer the question: how much energy could be saved for Internet Service Providers by putting into practice energy efficient protocols? It led me to study fundamental problems of graph theory.

    At the core of these energy efficient methods, there is a dynamic adaptation to the changes of demands, which is impossible to do in legacy networks which are mostly manually operated. The emergence of two new paradigms, software defined networking (SDN) and network function virtualization (NFV), leads to a finer control of networks and thus bears the promise to to put energy efficient solutions into practice. I thus studied how to use SDN to implement dynamic routing.

    My approach has been to use theoretical tools to solve problems raised by the introduction of new technologies or new applications. My tools come mainly from combinatorics and in particular from graph theory, algorithmics, optimization and probabilities. When I was able to propose new methods of resolution, I then tried to evaluate their practical impact by numerical evaluation, simulation or experimentation with realistic scenarios.

PhD defense of William Lochet

PhD William Lochet

    • Title: “Sub-structures in digraphs”
    • When: July 19, 2018 — 14:00
    • Where: Inria Sophia Antipolis, Euler violet
    • Committee:
    • Abstract: The main purpose of the thesis was to exhibit sufficient conditions on digraphs to find subdivisions of complex structures. While this type of question is pretty well understood in the case of (undirected) graphs, few things are known for the case of directed graphs (also called digraphs). The most notorious conjecture is probably the one due to Mader in 1985. He asked if there exists a function f such that every digraph with minimum outdegree at least f(k) contains a subdivision of the transitive tournament on k vertices. The conjecture is still wide open as even the existence of f(5) remains open. This thesis presents some weakening ofthis conjecture. Among other results, we prove that digraphs with large minimum outdegree contain large in-arborescences. We also prove that digraphs with large minimum outdegree contain large transitive tournaments as immersions, which was conjectured by DeVos et al. in 2011. Changing the parameter, we also prove that large chromatic number can force subdivision of cycles and other structures in strongly connected digraphs.
      This thesis also presents the proof of the Erdős-Sands-Sauer-Woodrow conjecture that states that the domination number of tournaments whose arc set can be partitioned into k transitive digraphs only depends on k. The conjecture, asked in 1982, was still open for k=3.
      Finally this thesis presents proofs for two results, one about orientation of hypergraphs and the other about AVD colouring using the recently developed probabilistic technique of entropy compression.

    • Titre: “Sous-structure dans les digraphes”
    • Résumé: Le but principal de cette thèse est de présenter des conditions suffisantes pour garantir l’existence de subdivisions dans les graphes dirigés. Bien que ce genre de questions soit assez bien maitrisé dans le cas des graphes non orientés, très peu de résultats sont connus sur le sujet des graphes dirigés. La conjecture la plus célèbre du domaine est sans doute celle attribuée à Mader en 1985 qui dit qu’il existe une fonction f tel que tout graphe dirigé de degré sortant minimal supérieur à f(k) contient le tournoi transitif sur k sommets comme subdivision. Cette question est toujours ouverte pour k=5. Cette thèse présente quelques résultats intermédiaires tendant vers cette conjecture. Il y est d’abords question de montrer l’existence de subdivisions de graphes dirigés autre que les tournois, en particulier les arborescences entrantes. Il y a aussi la preuve que les graphes dirigés de grand degré sortant contiennent des immersions de grand tournois transitifs, question qui avait été posée en 2011 par DeVos et al. En regardant un autre paramètre, on montre aussi qu’un grand nombre chromatique permet de forcer des subdivisions de certains cycles orientés, ainsi que d’autre structures, pour des graphes dirigés fortement connexes.
      Cette thèse présente également la preuve de la conjecture de Erdős-Sands-Sauer-Woodrow qui dit que les tournois dont les arcs peuvent être partitionnés en k graphes dirigés transitifs peuvent être dominé par un ensemble de sommet dont la taille dépend uniquement de k.
      Pour finir, cette thèse présente la preuve de deux résultats, un sur l’orientation des hypergraphes et l’autre sur la coloration AVD, utilisant la technique de compression d’entropie.

PhD defense of Nicolas Huin

PhD Nicolas Huin

    • Title: “Energy Efficient Software Defined Networks”
    • When: September 28, 2017 — 14:30
    • Where: Inria Sophia Antipolis, amphi Kahn
    • Committee:
    • Abstract: In the recent years, the growth of the architecture of telecommunication networks has been quickly increasing to keep up with a booming traffic. Moreover, the energy consumption of these infrastructures is becoming a growing issue, both for its economic and ecological impact. Multiple approaches were proposed to reduce the networks’ power consumption such as decreasing the number of active elements. Indeed, networks are designed to handle high traffic, e.g., during the day, but are over-provisioned during the night. In this thesis, we focus on disabling links and routers inside the network while keeping a valid routing. This approach is known as Energy Aware Routing (EAR).

      However current networks are not adapted to support the deployment of network-wide green policies due to their distributed management and the black-box nature of current network devices.The SDN and NFV paradigms bear the promise of bringing green policies to reality.The first one decouples the control and data plane and thus enable a centralized control of the network.The second one proposes to decouple the software and hardware of network functions and allows more flexibility in the creation and management of network services.

      In this thesis, we focus on the challenges brought by these two paradigms for the deployment of EAR policies. We dedicated the first two parts to the SDN paradigm. We first study the forwarding table size constraints due to an increased complexity of rules. We then study the progressive deployment of SDN devices alongside legacy ones. We focus our attention on the NFV paradigm in the last part, and more particularly, we study the Service Function Chaining problem.

      All the publications at the core of this thesis are available online here


PhD Nicolas Huin

PhD defense of Guillaume Ducoffe

PhD Guillaume Ducoffe

  • Title: “Metric properties of large graphs”
  • When: December 9, 2016 — 14:30
  • Where: Inria Sophia Antipolis, amphi Kahn
  • Committee:
  • Abstract: Large scale communication networks are everywhere, ranging from data centers with millions of servers to social networks with billions of users. This thesis is devoted to the fine-grained complexity analysis of combinatorial problems on these networks.

    In the first part, we focus on the embeddability of communication networks to tree topologies. This property has been shown to be crucial in the understanding of some aspects of network traffic (such as congestion). More precisely, we study the computational complexity of Gromov hyperbolicity and of tree decomposition parameters in graphs – including treelength and treebreadth. On the way, we give new bounds on these parameters in several graph classes of interest, some of them being used in the design of data center interconnection networks. The main result in this part is a relationship between treelength and treewidth: another well-studied graph parameter, that gives a unifying view of treelikeness in graphs and has algorithmic applications. This part borrows from graph theory and recent techniques in complexity theory.

    The second part of the thesis is on the modeling of two privacy concerns with social networking services. We aim at analyzing information flows in these networks, represented as dynamical processes on graphs. First, a coloring game on graphs is studied as a solution concept for the dynamic of communities. We give a fine-grained complexity analysis for computing Nash and strong Nash equilibria in this game, thereby answering open questions from the literature. On the way, we propose new directions in algorithmic game theory and parallel complexity, using coloring games as a case example. Finally, we introduce a new learning problem that is motivated by the need for users to uncover any misuse of their personal data online. We give positive and negative results on the tractability of this problem.

    All the publications at the core of this thesis are available online here

  • Keywords: Graph theory, Hyperbolicity, tree-decomposition, complexity, privacy.

  • Manuscript: Core of the thesis, appendix, all in one file
  • Slides of the presentation

PhD defense of Fatima Zahra Moataz

PhD Fatima Zahra Moataz

  • Title: “Towards Efficient and Fault-Tolerant Optical Networks: Complexity and Algorithms”
  • When: October 30, 2015 — 14:30
  • Where: Inria Sophia Antipolis, salle Euler Violet
  • Committee:
  • Abstract: 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 paths. Finding a path is crucial in all types of networks in order to set up connections and finding disjoint paths is a common approach used to provide some degree of protection against failures in networks. We study these problems under different settings. We first focus on finding paths and vertex or link-disjoint paths in networks with asymmetric nodes, which are nodes with restrictions on their internal connectivity. Afterwards, we consider networks with star Shared Risk Link Groups (SRLGs) which are groups of links that might fail simultaneously due to a localized event. In these networks, we investigate the problem of finding SRLG-disjoint paths.
    The second part of this thesis focuses on the problem of Routing and Spectrum Assignment (RSA) in Elastic Optical Networks (EONs). EONs are proposed as the new generation of optical networks and they aim at an efficient and flexible use of the optical resources. RSA is the key problem in EONs and it deals with allocating resources to requests under multiple constraints. We first study the static version of RSA in tree networks. Afterwards, we examine a dynamic version of RSA in which a non-disruptive spectrum defragmentation technique is used.
    Finally, we present in the appendix another problem that has been studied during this thesis. It is a graph-theoretic problem referred to as minimum size tree-decomposition and it deals with the decomposition of graphs in a tree-like manner with the objective of minimizing the size of the tree.

  • Keywords: Asymmetric nodes, forbidden transitions, shared risk link group, routing and spectrum assignment, tree-decomposition, complexity.

PhD defense of Mohamed Bergach

PhD Mohamed Bergach

  • Title: “Adaptation of the Fast Fourier Transform processing on hybride integrated CPU/GPU architecture”
  • When: October 2, 2015 — 10:30
  • Where: Inria Sophia Antipolis, salle Euler Violet
  • Committee:
  • Abstract: Multicore architectures Intel Core (IvyBridge, Haswell, etc.) contain both general purpose CPU cores (4) and dedicated GPU cores embedded on the same chip (16 and 40 respectively). As part of the activity of Kontron (the company partially funding this CIFRE scholarship), an important objective is to efficiently compute arrays and sequences of fast Fourier transforms (FFT) such as one finds in radar applications, on this architecture. While native (but proprietary) libraries exist for Intel CPU, nothing is currently available for the GPU part.
    The aim of the thesis was to define the efficient placement of FFT modules, and to study theoretically the optimal form for grouping computing stages of such FFT according to data locality on a single computing core. This choice should allow processing efficiency, by adjusting the memory size available to the required application data size.
    Then the multiplicity of cores is exploitable to compute several FFT in parallel, without interference (except for possible bus contention between the CPU and the GPU). We have achieved significant results, both in the implementation of an FFT (1024 points) on a SIMD CPU core, expressed in C, and in the implementation of a FFT of the same size on a GPU SIMT core, then expressed in OpenCL.
    In addition, our results allow to define rules to automatically synthesize such solutions, based solely on the size of the FFT (more specifically its number of stages), and the size of the local memory for a given computing core. The performances obtained are better than the native Intel library for CPU, and demonstrate a significant gain in consumption on GPU. All these points are detailed in the thesis document.
    These results should lead to exploitation of the code as library by the Kontron company.

  • Keywords: FFT, GPU, multicores.