Community detection in graphs has been an important research topic for many fields. The aim of community detection is to extract from graphs those groups of nodes that present more connections between them than with the rest of the network. Detecting such groups at different scales can help understanding the global behaviour of the system. However, recent studies have shown that realworld graphs follow power-law distributions for degree and community sizes. Specifically, these graphs present many small communities but just a few large ones. This unbalanced community size distribution poses a great challenge for community detection algorithms.Most of the existing methods are based on global approaches that require information about the network to be processed as a whole. Thus, those techniques can not be applied when the graph is too big to fit into one single machine, or in distributed setting when the graph is partitioned among multiple machines. To solve this limitations, a completely decentralized community detection algorithm is presented. It is based on diffusion, following a vertex-centric approach that allows each node to decide the diffusion rates based on local information. It adds as well a mechanism for controlling the diffusion speed through a customizable function.We evaluate the algorithm with a variety of graphs with different levels of imbalance and community structures. Our algorithm is able to detect (almost) perfectly the communities when the imbalance between community sizes is not extreme. We show as well how the sizes of the detected communities can be controlled by the diffusion strategy, allowing for better detection of finer or coarser resolutions in hierarchical graphs. The algorithm is also compared to other two well-known existing methods, achieving similar results in most of the cases though with a higher computation time. / Gemenskap detektering i grafer har varit ett viktigt forsknings ämne förmånga områden. Gemenskapsdetekterings syftet är att extrahera ur grafernade grupper av noder som har mer kopplingar mellan varandra än med restenav nätverket. Att upptäcka sådana grupper i olika skaler kan hjälpa till att förstå systemets globala beteende. Däremot har nyliga studier visat att verkliga grafers grad och gemenskap storlek följer en potenslagen fördelning. Specifikt,dessa grafer uppvisar många små gemenskaper men bara några stora. Denhär obalanserade gemenskaps storleks fördelningen utgör en stor utmaning för gemenskapsdetekterings algoritmer.De flesta av de befintliga metoderna är baserade på globala tillvägagångssätt som kräver att information om nätverket behandlas som helhet. Således kan dessa tekniker inte tillämpas när grafen är för stor för att passa in i en enda maskin, eller på distribuerat sätt när grafen är uppdelad bland flera maskiner. För att lösa dessa begränsningar, uppvisas en helt decentraliserad gemenskapsdetekterings algoritm.Denär baserad pådiffusion som följer en vertex-centrerad tillvägagångssätt.Varje node valder diffusionshastigheten baserad på lokal information. Deninnehåller även en mekanism som kontrollerar diffusionens hastighet genom en anpassningsbar funktion.Vi utvärderar algoritmen genom flera olika grafer med olika nivåer av obalans och gemenskaps strukurer. Vår algoritm kan (nästan) felfritt upptäcka gemenskaper där obalansen mellan dem inte är för stor. Vi visar även hur storlekenpå de hittade gemenskaperna kan kontrolleras genom diffusions strategin, somtillåter bättre uptäckt av finare eller grövre resolution av hierarkiska grafer. Algoritmen kan också jämföras med två befintliga, välkända metoder, vilka ger liknande resultat i de flesta fallen men tar längre tid att genomföra.

Diploma thesis deals with usage of artificial coordinate systems used for localization of a station on the internet and prediction of delay between the stations. There are described and compared basic properties of centralized and decentralized algorithms providing station localization on the internet and RTT prediction. More in depth are presented main representatives of both types of algorithms such as GNP, IDMAPS or Lighthouse. Central part of thesis is aimed at getting to know Vivaldi distributed algorithm. Basic principle of the algorithm for constant and variable time step, using two dimensional coordinate system with 3rd parameter height, is here outlined. Further more implementation of this algorithm as a library Vivaldi-lib in the environment of Java is implemented. Part of the thesis are simulations of behaviour of this algorithm for both variations realized on artificial networks and data obtained from PlanetLab experimental network, using simulation created program VIVALDIMONITOR.

Depuis quelques années, la thématique de la localisation a connu un regain d’intérêt,motivé en grande partie par le développement des réseaux de capteurs sans fil. Lespropositions ayant pour objectif d’apporter une réponse à cette problématique peuvent êtreclassées en deux catégories : les méthodes range-based, retenues pour cette thèse, dont lacaractéristique est de se fonder sur des mesures en temps réel du signal pour générer uneestimation relativement fiable de la distance, et les solutions range-free, économes enressources car se limitant à l’exploitation d’hypothèses concernant la connectivité des noeudsdans le réseau. Les contributions peuvent se focaliser sur l’un des trois aspects fondamentauxde la question : le développement d’une couche physique performante, la proposition d’unalgorithme de calcul permettant des résultats plus précis, et la mise en place d’un protocole decollecte de mesures.La contribution de cette thèse est par conséquent multiple : en premier lieu, nousproposons un nouveau protocole de mesure du temps de vol, nommé Parallel SymmetricDouble-Sided Two-Way Ranging (PSDS-TWR), dont l’objectif est la réduction de la chargeprotocolaire du service. Deuxièmement, nous avons mis en place un algorithme de calcul dela position désigné par interRing Localization Algorithm (iRingLA). Basé sur une recherchelinéaire, iRingLA accepte des données inexactes et en extrait une estimation de la positiondont l’erreur est inférieure à 2m dans 70% des cas, ceci en s’exécutant directement sur unnoeud mobile léger. Les données concernant l’algorithme ont été collectées grâce à unprototype utilisant la technologie Chirp Spread Spectrum tandis que l’étude de performancedu protocole a impliqué la conception d’un simulateur nommé DokoSim / The development of Wireless Sensor Networks has given a new life to research in thefield of localization. Many proposals have been made which can be classified as either rangefreeor range-based solutions. The range-free category relies on a priori knowledge of thenetwork while the latter uses the available hardware to measure signal characteristics fromwhich distance information can be derived. Although the information origin can vary, allproposals either introduce a new protocol, a novel algorithm or a new and improved physicallayer.Our work led to the definition of a new protocol and an efficient algorithm. Aside fromallowing the nodes to collect Time Of Flight related data, the Parallel Symmetric Double-Sided Two-Way Ranging protocol (PSDS-TWR) reduces overhead and energy consumption,making the localization service affordable for the network. The performance of this protocol,in terms of duration, has been studied using a homemade simulator named DokoSim. We alsointroduce an algorithm based on rings and linear search. This inter-Ring LocalizationAlgorithm (iRingLA) achieves a localization error of less than 2m in 70% of the cases whilebeing tested on our Chirp Spread Sprectrum based prototype