La première partie de cette thèse s'intéresse au groupage de trafic dans les réseaux de télécommunications. La notion de groupage de trafic correspond à l'agrégation de flux de faible débit dans des conduits de plus gros débit. Cependant, à chaque insertion ou extraction de trafic sur une longueur d'onde il faut placer dans le noeud du réseau un multiplexeur à insertion/extraction (ADM). De plus il faut un ADM pour chaque longueur d'onde utilisée dans le noeud, ce qui représente un coût d'équipements important. Les objectifs du groupage de trafic sont d'une part le partage efficace de la bande passante et d'autre part la réduction du coût des équipements de routage. Nous présentons des résultats d'inapproximabilité, des algorithmes d'approximation, un nouveau modèle qui permet au réseau de pouvoir router n'importe quel graphe de requêtes de degré borné, ainsi que des solutions optimales pour deux scénarios avec trafic all-to-all: l'anneau bidirectionnel et l'anneau unidirectionnel avec un facteur de groupage qui change de manière dynamique. La deuxième partie de la thèse s'intéresse aux problèmes consistant à trouver des sous-graphes avec contraintes sur le degré. Cette classe de problèmes est plus générale que le groupage de trafic, qui est un cas particulier. Il s'agit de trouver des sous-graphes d'un graphe donné avec contraintes sur le degré, tout en optimisant un paramètre du graphe (très souvent, le nombre de sommets ou d'arêtes). Nous présentons des algorithmes d'approximation, des résultats d'inapproximabilité, des études sur la complexité paramétrique, des algorithmes exacts pour les graphes planaires, ainsi qu'une méthodologie générale qui permet de résoudre efficacement cette classe de problèmes (et de manière plus générale, la classe de problèmes tels qu'une solution peut être codé avec une partition d'un sous-ensemble des sommets) pour les graphes plongés dans une surface. Finalement, plusieurs annexes présentent des résultats sur des problèmes connexes.

We consider the problem of maximizing the second smallest eigenvalue of the weighted Laplacian of a (simple) graph over all nonnegative edge weightings with bounded total weight. We generalize this problem by introducing node significances and edge lengths. We give a formulation of this generalized problem as a semidefinite program. The dual program can be equivalently written as embedding problem. This is fifinding an embedding of the n nodes of the graph in n-space so that their barycenter is at the origin, the distance between adjacent nodes is bounded by the respective edge length, and the embedded nodes are spread as much as possible. (The sum of the squared norms is maximized.) We proof the following necessary condition for optimal embeddings. For any separator of the graph at least one of the components fulfills the following property: Each straight-line segment between the origin and an embedded node of the component intersects the convex hull of the embedded nodes of the separator. There exists always an optimal embedding of the graph whose dimension is bounded by the tree-width of the graph plus one. We defifine the rotational dimension of a graph. This is the minimal dimension k such that for all choices of the node significances and edge lengths an optimal embedding of the graph can be found in k-space. The rotational dimension of a graph is a minor monotone graph parameter. We characterize the graphs with rotational dimension up to two.

Recently, graph mining approaches have become very popular, especially in certain domains such as bioinformatics, chemoinformatics and social networks. One of the most challenging tasks in this setting is frequent subgraph discovery. This task has been highly motivated by the tremendously increasing size of existing graph databases. Due to this fact, there is urgent need of efficient and scaling approaches for frequent subgraph discovery especially with the high availability of cloud computing environments. This thesis deals with distributed frequent subgraph mining in the cloud. First, we provide the required material to understand the basic notions of our two research fields, namely graph mining and cloud computing. Then, we present the contributions of this thesis. In the first axis, we propose a novel approach for large-scale subgraph mining, using the MapReduce framework. The proposed approach provides a data partitioning technique that consider data characteristics. It uses the densities of graphs in order to partition the input data. Such a partitioning technique allows a balanced computational loads over the distributed collection of machines and replace the default arbitrary partitioning technique of MapReduce. We experimentally show that our approach decreases significantly the execution time and scales the subgraph discovery process to large graph databases. In the second axis, we address the multi-criteria optimization problem of tuning thresholds related to distributed frequent subgraph mining in cloud computing environments while optimizing the global monetary cost of storing and querying data in the cloud. We define cost models for managing and mining data with a large scale subgraph mining framework over a cloud architecture. We present an experimental validation of the proposed cost models in the case of distributed subgraph mining in the cloud.

Graph partitioning is a fundamental optimization problem that has been intensively studied. Many graph partitioning formulations are important as building blocks for divide-and-conquer algorithms on graphs as well as to many applications such as VLSI layout, packet routing in distributed networks, clustering and image segmentation. Unfortunately such problems are notorious for the huge gap between known best known approximation algorithms and hardness of approximation results. In this thesis, we study approximation algorithms for graph partitioning problems using a strong hierarchy of relaxations based on semi-definite programming, called Lasserre Hierachy. Our main contribution in this thesis is a propagation based rounding framework for solutions arising from such relaxations. We present a novel connection between the quality of solutions it outputs and column based matrix reconstruction problem. As part of our work, we derive optimal bounds on the number of columns necessary together with efficient randomized and deterministic algorithms to find such columns. Using this framework, we derive approximation schemes for many graph partitioning problems with running times dependent on how fast the graph spectrum grows. Our final contribution is a fast SDP solver for this rounding framework: Even though SDP relaxation has nO(r) many variables, we achieve running times of the form 2O(r) poly(n) by only partially solving the relevant part of relaxation. In order to achieve this, we present a new ellipsoid algorithm that returns certificate of infeasibility.

L'analyse et la prévision du comportement des réseaux de transport sont aujourd'hui des éléments cruciaux pour la mise en place de politiques de gestion territoriale. La simulation informatique du trafic routier est un outil puissant permettant de tester des stratégies de gestion avant de les déployer dans un contexte opérationnel. La simulation du trafic à l'échelle d'un ville requiert cependant une puissance de calcul très importante, dépassant les capacité d'un seul ordinateur.Dans cette thèse, nous étudions des méthodes permettant d'effectuer des simulations de trafic multi-agent à large échelle. Nous proposons des solutions permettant de distribuer l'exécution de telles simulations sur un grand nombre de coe urs de calcul. L'une d'elle distribue directement les agents sur les coeurs disponibles, tandis que la seconde découpe l'environnement sur lequel les agents évoluent. Les méthodes de partitionnement de graphes sont étudiées à cet effet, et nous proposons une procédure de partitionnement spécialement adaptée à la simulation de trafic multi-agent. Un algorithme d'équilibrage de charge dynamique est également développé, afin d'optimiser les performances de la distribution de la simulation microscopique.Les solutions proposées ont été éprouvées sur un réseau réel représentant la zone de Paris-Saclay.Ces solutions sont génériques et peuvent être appliquées sur la plupart des simulateurs existants.Les résultats montrent que la distribution des agents améliore grandement les performances de la simulation macroscopique, tandis que le découpage de l'environnement est plus adapté à la simulation microscopique. Notre algorithme d'équilibrage de charge améliore en outre significativement l'efficacité de la distribution de l'environnement / Nowadays, analysis and prediction of transport network behavior are crucial elements for the implementation of territorial management policies. Computer simulation of road traffic is a powerful tool for testing management strategies before deploying them in an operational context. Simulation of city-wide traffic requires significant computing power exceeding the capacity of a single computer.This thesis studies the methods to perform large-scale multi-agent traffic simulations. We propose solutions allowing the distribution of such simulations on a large amount of computing cores.One of them distributes the agents directly on the available cores, while the second splits the environment on which the agents evolve. Graph partitioning methods are studied for this purpose, and we propose a partitioning procedure specially adapted to the multi-agent traffic simulation. A dynamic load balancing algorithm is also developed to optimize the performance of the microscopic simulation distribution.The proposed solutions have been tested on a real network representing the Paris-Saclay area.These solutions are generic and can be applied to most existing simulators.The results show that the distribution of the agents greatly improves the performance of the macroscopic simulation, whereas the environment distribution is more suited to microscopic simulation. Our load balancing algorithm also significantly improves the efficiency of the environment based distribution

In this thesis, we introduce the Partitioning-Hub Location-Routing problem (PHLRP), which can be classified as a variant of the hub location problem.<p>PHLRP consists of partitioning a network into sub-networks, locating at least one hub in each subnetwork and routing the traffic within the network such that all inter-subnetwork traffic is routed through the hubs and all intra-subnetwork traffic stays within the sub-networks all the way from the source to the destination. Obviously, besides the hub location component, PHLRP also involves a graph partitioning component and a routing component. PHLRP finds applications in the strategic planning or deployment of the Intermediate System-Intermediate System (ISIS) Internet Protocol networks and the Less-than-truck load freight distribution systems.<p><p>First, we introduce three IP formulations for solving PHLRP. The hub location component and the graph partitioning components of PHLRP are<p>modeled in the same way in all three formulations. More precisely, the hub location component is represented by the p-median variables and constraints; and the graph partitioning component is represented by the size-constrained graph partitioning variables and constraints. The formulations differ from each other in the way the peculiar routing requirements of PHLRP are modeled.<p><p>We then carry out analytical and empirical comparisons of the three IP<p>formulations. Our thorough analysis reveals that one of the formulations is<p>provably the tightest of the three formulations. We also show analytically that the LP relaxations of the other two formulations do not dominate each other. On the other hand, our empirical comparison in a standard branch-and-cut framework that is provided by CPLEX shows that not the tightest but the most compact of the three formulations yield the best performance in terms of solution time. <p><p>From this point on, based on the insight gained from detailed analysis of the formulations, we focus our attention on a common sub-problem of the three formulations: the so-called size-constrained graph partitioning problem. We carry out a detailed polyhedral analysis of this problem. The main benefit from this polyhedral analysis is that the facets we identify for the size-constrained graph partitioning problem constitute strong valid inequalities for PHLRP.<p><p>And finally, we wrap up our efforts for solving PHLRP. Namely, we present<p>the results of our computational experiments, in which we employ some facets<p>of the size-constrained graph partitioning polytope in a branch-and-cut algorithm for solving PHLRP. Our experiments show that our approach brings<p>significant improvements to the solution time of PHLRP when compared with<p>the default branch-and-cut solver of XPress. <p><p>/<p><p>Dans cette thèse, nous introduisons le problème Partitionnement-Location des Hubs et Acheminement (PLHA), une variante du problème de location de hubs. Le problème PLHA partitionne un réseau afin d'obtenir des sous-réseaux, localise au moins un hub dans chaque sous-réseau et achemine le traffic dans le réseau de la maniére suivante :le traffic entre deux<p>sous-réseaux distincts doit être éxpedié au travers des hubs tandis que le traffic entre deux noeuds d'un même sous-réseau ne doit pas sortir de celui-ci. PLHA possède des applications dans le planning stratégique, ou déploiement, d'un certain protocole de communication utilisé<p>dans l'Internet, Intermediate System - Intermediate System, ainsi que dans la distribution des frets.<p><p>Premièrement, nous préesentons trois formulations linéaires en variables entières pour résoudre PLHA. Le partitionnement du graphe et la localisation des hubs sont modélisées de la même maniére dans les trois formulations. Ces formulations diffèrent les unes des autres dans la maniére dont l'acheminement du traffic est traité.<p><p>Deuxièmement, nous présentons des comparaisons analytiques et empiriques des trois formulations. Notre comparaison analytique démontre que l'une des formulations est plus forte que les autres. Néanmoins, la comparaison empirique des formulations, via le solveur CPLEX, montre que la formulation la plus compacte (mais pas la plus forte) obtient les meilleures performances en termes de temps de résolution du problème.<p><p>Ensuite, nous nous concentrons sur un sous-problème, à savoir, le partitionnement des graphes sous contrainte de taille. Nous étudions le polytope des solutions réalisables de ce sous-problème. Les facettes de ce polytope constituent des inégalités valides fortes pour<p>PLHA et peuvent être utilisées dans un algorithme de branch-and-cut pour résoudre PLHA.<p><p>Finalement, nous présentons les résultats d'un algorithme de branch-and-cut que nous avons développé pour résoudre PLHA. Les résultats démontrent que la performance de notre méthode est meilleure que celle de l'algorithme branch-and-cut d'Xpress.<p> / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

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In recent years, neural networks have seen increased interest from both the cognitive computing and computation neuroscience fields. Neuromorphic computing systems simulate neural network efficiently, but have not yet reached the amount of neurons that a mammal has. Increasing this quantity is an aspiration, but more neurons will also increase the traffic load of the system. The placement of the neurons onto the neuromorphic computing system has a significant effect on the network load. This thesis introduces algorithms for placing a large amount of neurons in an efficient and agile way. First, an analysis of placement algorithms for very large scale integration design is done, displaying that computing complexity of these algorithms is high. When using the predefined underlying structure of the neural network, more rapid algorithms can be used. The results show that the population placement algorithm has high computing speed as well as providing exceptional result.

Considérons un graphe G = (V,E,w) non orienté dont les sommets sont pondérés et un entier k. Le problème à étudier consiste à la construction des algorithmes afin de déterminer le nombre minimum de nœuds qu’il faut enlever au graphe G pour que toutes les composantes connexes restantes contiennent chacune au plus k-sommets. Ce problème nous l’appelons problème de k-Séparateur et on désigne par k-séparateur le sous-ensemble recherché. Il est une généralisation du Vertex Cover qui correspond au cas k = 1 (nombre minimum de sommets intersectant toutes les arêtes du graphe) / Let G be a vertex-weighted undirected graph. We aim to compute a minimum weight subset of vertices whose removal leads to a graph where the size of each connected component is less than or equal to a given positive number k. If k = 1 we get the classical vertex cover problem. Many formulations are proposed for the problem. The linear relaxations of these formulations are theoretically compared. A polyhedral study is proposed (valid inequalities, facets, separation algorithms). It is shown that the problem can be solved in polynomial time for many special cases including the path, the cycle and the tree cases and also for graphs not containing some special induced sub-graphs. Some (k + 1)-approximation algorithms are also exhibited. Most of the algorithms are implemented and compared. The k-separator problem has many applications. If vertex weights are equal to 1, the size of a minimum k-separator can be used to evaluate the robustness of a graph or a network. Another application consists in partitioning a graph/network into different sub-graphs with respect to different criteria. For example, in the context of social networks, many approaches are proposed to detect communities. By solving a minimum k-separator problem, we get different connected components that may represent communities. The k-separator vertices represent persons making connections between communities. The k-separator problem can then be seen as a special partitioning/clustering graph problem

Big data processing frameworks utilizing distributed frameworks to parallelize the computing of datasets have become a staple part of the data engineering and data science pipelines. One of the more known frameworks is Dask, a widely utilized distributed framework used for parallelizing data processing jobs. In Dask, the main component that traverses and plans out the execution of the job is the scheduler. Dask utilizes a centralized scheduling approach, having a single server node as the scheduler. With no failover mechanism implemented for the scheduler, the work in progress is potentially lost if the scheduler fails. As a consequence, jobs that might have been executed for hours or longer need to be restarted. In this thesis, a highly available scheduler is designed, based on Dask. We introduce a highly-available scheduler that replicates the state of the job on a distributed key-value store. The replicated schedulers allow us to design an architecture where the schedulers are able to take over the job in case of a scheduler failure. To reduce the performance overhead of replication, we further explore optimizations based on partitioning typical task graphs and sending each partition to its own scheduler. The results show that the replicated scheduler is able to tolerate server failures and is able to complete the job without restarting but at a cost of reduced throughput due to the replication. This is mitigated by our partitioning, which achieves almost linear performance gains relative to our baseline fault-tolerant scheduler, through the utilization of a parallelized scheduling architecture. / Dataprocesseringsramverk av stora datamängder har blivit en viktig del inom Data Engineering och Data Science pipelines. Ett av de mer kända ramverken är Dask som används för att parallelisera jobb inom data processering. En av huvudkomponenterna i Dask är dess schemaläggare som traverserar och planerar exekveringen av av arbete. Dask använder en centraliserad schemaläggning, med en enda server nod som schemaläggare. Utan en implementerad felhanteringsmekanism innebär det att allt arbete är förlorat ifall schemaläggaren kraschar. I denna uppsats så skapar vi en schemaläggare baserad på Dask. Vi introducerar hög tillgänglighet till schemaläggaren genom att replikera statusen av ett jobb till en distribuerad Key-Value store. För att reducera kostnaden av replikationen så utforskas optimeringar genom att partitionera typiska uppgifts-grafer för att sedan skicka dem till varsin schemaläggare. Resultaten visar att en replikerad schemaläggare tolererar att schemaläggningsservarna kraschar, och att den kan slutföra ett jobb utan att behöva starta om, på en kostnad av reducerad schemaläggningseffektivitet på grund av replikationen. Denna reduktion av effektivitet mitigeras av vår partitioningsstrategi, som genom att använda en paralliserad schemaläggningsarkitektur, uppnår nästan linjära prestandaökningar jämfört med den simpla feltoleranta schemaläggaren.