Graph decompositions have useful applications in optimization problems that are categorized as NP-Hard. Modular Decomposition of a graph is a technique to decompose the graph into non-overlapping modules. A module M of an undirected graph G = (V, E) is commonly defined as a set of vertices such that any vertex outside of M is either adjacent or non-adjacent to all vertices in M . By the theory of modular decomposition, the modules can be categorized as parallel, series or prime modules. Series modules which are maximal and are also cliques are termed as simple series modules or critical cliques. There are modular decomposition algorithms that can be used to decompose the graph into modules and obtain critical cliques. In this current research, we present a new algorithm to decompose the graph into critical cliques without applying the process of modular decomposition. Given a simple, undirected graph G = (V, E), the runtime complexity of our proposed algorithm is O(|V| + |E|) under certain input constraints. Thus, one of our main contributions is to propose a novel algorithm for decomposing a simple, undirected graph directly into critical cliques. We apply the idea of critical cliques to propose a new way for solving the influence maximization problem in online social networks. Influence maximization in online social networks is the problem of identifying a small, initial set of influential individuals which can influence the maximum number of individuals in the network. In this research, we propose a new model of online social networks based on the notion of critical cliques. We utilize the properties of critical cliques to assign parameters for our proposed model and select an initial set of activation nodes. We then simulate the influence propagation process in the online social network using our proposed model and experimentally compare our approach to the greedy algorithm proposed by Kempe, Kleinberg and Tardos. Our main contribution in the influence maximization research is to propose a new model of online social network taking into account the structural properties of the social network graph and a new, faster algorithm for determining the initial set of influential individuals in the online social network.

One goal of persistent homology is to recover meaningful information from point-cloud data by examining long-lived topological features of filtered simplicial complexes built over the point-cloud. Motivated by real-world applications, the classic setting for this approach has been on finite metric spaces where many suitable complexes can be defined, and a natural filtration exists via sublevel sets of the metric. We consider the extension of persistent homology to dissimilarity networks equipped with a relaxed metric that does not assume symmetry nor the triangle inequality, by computing persistent homology on the directed clique complex defined over weighted directed graphs induced from a dissimilarity network and filtered by an adapted Rips filtration. We characterize digraph maps that induce maps on homology, describe a procedure to lift any digraph map to one that does induce maps on homology, and present a homotopy classification that provides a condition for two such digraph maps to induce the same map at the homology level. We also prove functoriality of directed clique homology and describe filtrations of digraphs induced by digraph maps. We then prove stability of persistent directed clique homology by showing that the persistence modules of a digraph and that of an admissible perturbation are interleaved. These admissible perturbations include perturbing dissimilarity measures in the network that either preserve the digraph structure or collapse series of arrows. We also explore similar constructions for maps between digraphs that allow reversal of arrows and show that while such maps, in general, produce unstable persistence barcodes, one can recover stability by inducing a reverse filtration and truncating at an appropriate threshold. Finally, we present an application of persistent directed clique homology to trace patterns and shapes embedded in migration and remittance networks.

Parallel computing has long been an area of research interest because exploiting parallelism in difficult problems has promised to deliver orders of magnitude speedups. Processors are now both powerful and cheap, so that systems incorporating tens, hundreds or even thousands of powerful processors need not be prohibitively expensive. The weak link in exploiting parallelism is the means of communication between the processors. Shared memory systems are fundamentally limited in the number of processors they can utilise. To achieve high levels of parallelism it is still necessary to use distributed memory and some form of interconnection network. But interconnection networks can be costly, slow, difficult to build and expand, vulnerable to faults and limited in the range of problems they can be used to solve effectively. As a result there has been extensive research into developing interconnection networks which overcome some or all of these difficulties. In this thesis it is argued that a new interconnection network, Hierarchical Cliques (HiC), and a derivative, FatHiC, possesses many desirable properties and are worthy of consideration for use in building parallel computers. A fundamental element of an interconnection network is its topology. After defining the topology of HiC, expressions are derived for the various parameters which define its underlying limits of performance and fault tolerance. A second element of an interconnection network is an addressing and routing scheme. The addressing scheme and routing algorithms of HiC are described. The flexibility of HiC is demonstrated by developing embeddings of popular, regular interconnection networks. Some embeddings into HiC suffer from high congestion, however the FatHiC network is shown to have low congestion for those embeddings. The performance of some important, regular, data parallel problems on HiC and ++ / FatHiC are determined by analysis and simulation, using the 2D-mesh as a means of comparison. But performance alone does not tell the whole story. Any parallel computer system must be cost effective. In order to analyse the cost effectiveness of HiCs an existing measure was expanded to provide a more realistic model and a more accurate means of comparison. One aim of this thesis is to demonstrate the suitability of HiC for parallel computing systems which execute irregular algorithms requiring dynamic load balancing. A new dynamic load balancing algorithm is proposed which takes advantage of the hierarchical structure of the HiC to reduce communication overheads incurred when distributing work. To demonstrate performance of an irregular problem, a novel parallel algorithm was developed to detect subgraph isomorphism from many model graphs to a single input graph. The use of the new load balancing algorithm in conjunction with the subgraph isomorphism algorithm is discussed.

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The main focus of this thesis is to evaluate .k_r(n,\delta)., the minimal number of $r$-cliques in graphs with $n$ vertices and minimum degree~$\delta$. A fundamental result in Graph Theory states that a triangle-free graph of order $n$ has at most $n 2/4$ edges. Hence, a triangle-free graph has minimum degree at most $n/2$, so if $k_3(n,\delta) =0$ then $\delta \le n/2$. For $n/2 \leq \delta \leq 4n/5$, I have evaluated $k_r(n,\delta)$ and determined the structures of the extremal graphs. For $\delta \ge 4n/5$, I give a conjecture on $k_r(n,\delta)$, as well as the structures of these extremal graphs. Moreover, I have proved various partial results that support this conjecture. Let $k_r �(n, \delta)$ be the analogous version of $k_r(n,\delta)$ for regular graphs. Notice that there exist $n$ and $\delta$ such that $k_r(n, \delta) =0$ but $k_r �(n, \delta) >0$. For example, a theorem of Andr{\'a}sfai, Erd{\H}s and S{\'o}s states that any triangle-free graph of order $n$ with minimum degree greater than $2n/5$ must be bipartite. Hence $k_3(n, \lfloor n/2 \rfloor) =0$ but $k_3 �(n, \lfloor n/2 \rfloor) >0$ for $n$ odd. I have evaluated the exact value $k_3 �(n, \delta)$ for $\delta$ between $2n/5+12 \sqrt{n}/5$ and $n/2$ and determined the structure of these extremal graphs. At the end of the thesis, I investigate a question in Ramsey Theory. The Ramsey number $R_k(G)$ of a graph $G$ is the minimum number $N$, such that any edge colouring of $K_N$ with $k$ colours contains a monochromatic copy of $G$. The constrained Ramsey number $f(G,T)$ of two graphs $G$ and $T$ is the minimum number $N$ such that any edge colouring of $K_N$ with any number of colours contains a monochromatic copy of $G$ or a rainbow copy of $T$. It turns out that these two quantities are closely related when $T$ is a matching. Namely, for almost all graphs $G$, $f(G,tK_2) =R_{t-1}(G)$ for $t \geq 2$.

Cette thèse vise à la mise en œuvre et à l'évaluation de techniques d'extraction de relations sémantiques à partir d'un corpus multilingue aligné. Ces relations seront extraites par transitivité de l'équivalence traductionnelle, deux lexèmes possédant les mêmes équivalents dans une langue cible étant susceptibles de partager un même sens. D'abord, nos observations porteront sur la comparaison sémantique d'équivalents traductionnels dans des corpus multilingues alignés. A partir des équivalences, nous tâcherons d'extraire des "cliques", ou sous-graphes maximaux complets connexes, dont toutes les unités sont en interrelation, du fait d'une probable intersection sémantique. Ces cliques présentent l'intérêt de renseigner à la fois sur la synonymie et la polysémie des unités, et d'apporter une forme de désambiguïsation sémantique. Elles seront créées à partir de l'extraction automatique de correspondances lexicales, basée sur l'observation des occurrences et cooccurrences en corpus. Le recours à des techniques de lemmatisation sera envisagé. Ensuite nous tâcherons de relier ces cliques avec un lexique sémantique (de type Wordnet) afin d'évaluer la possibilité de récupérer pour les unités arabes des relations sémantiques définies pour des unités en anglais ou en français. Ces relations permettraient de construire automatiquement un réseau utile pour certaines applications de traitement de la langue arabe, comme les moteurs de question-réponse, la traduction automatique, les systèmes d'alignement, la recherche d'information, etc. / This study aims at the implementation and evaluation of techniques for extracting semantic relations from a multilingual aligned corpus. Firstly, our observations will focus on the semantic comparison of translational equivalents in multilingual aligned corpus. From these equivalences, we will try to extract "cliques", which ara maximum complete related sub-graphs, where all units are interrelated because of a probable semantic intersection. These cliques have the advantage of giving information on both the synonymy and polysemy of units, and providing a form of semantic disambiguation. Secondly, we attempt to link these cliques with a semantic lexicon (like WordNet) in order to assess the possibility of recovering, for the Arabic units, a semantic relationships already defined for English, French or Spanish units. These relations would automatically build a semantic resource which would be useful for different applications of NLP, such as Question Answering systems, machine translation, alignment systems, Information Retrieval…etc.

Vi vill med denna studie bidra till att förstå hur barns status och popularitet påverkas av kläder i grundskolan. Våra resultat visar att kläder påverkar popularitet och status i ett komplext samspel med andra faktorer, såsom beteende och umgänge. Kläder börjar bli viktigt för status och popularitet någon gång under mellanstadiet. Det är då barnen börjar bry sig om sin egen, och andras, klädsel. De måste förhålla sig till ett socialt spel där bl.a. kläder påverkar barnets position i statushierarkin på skolan. Hur barnen gör detta kan variera och vissa försöker ställa sig utanför ”popularitetstjafset”, medan andra tar till förtryckande taktiker för att själva stiga i status. Vi har undersökt detta genom att intervjua sju ungdomar i åldrarna 15-18 år om deras upplevelser i mellan- och högstadiet. Dessa intervjuer har vi sedan tolkat med en fenomenologisk analysmetod för att kunna förstå hur barnen upplever att kläder påverkat dem. För att tolka våra resultat har vi använt Goffmans dramaturgiska perspektiv och Adler & Adlers beskrivning av klickar. En artikel som betytt väldigt mycket för oss under planerandet av denna studie är Jon Swains artikel The Right Stuff som utforskar hur klädsel påverkar barnen i en brittisk mellanstadieskola. / The purpose of this stydy is to contribute to the understanding of how clothing affects the popularity among children. Our results show that clothing affects popularity and status i a complex interaction with other factors, such as behaviour and associates. Clothing becomes an important factor for popularity sometime during the ages middle school. This is when the children begin to care about theirs, and others, clothing. They have to relate to a social game where clothing affects their position in the status hierarchy. How they relate to this game may vary and some of them try not to compete for popularity, while others act opressively in order to gain status. We have studied this by interviewing youths ages 15-18, on their experiences during junior school. We have interpreted these interviews with an phenomenological method of analysis in order to understand how the youths experience the effects of clothing. We have used Goffmans dramaturgical perspective and Adler & Adlers description of clique dynamics in order to better understand this phenomenon. Jon Swains article The Right Stuff has proven to be of great aid during the planing of our stydy. In his article he explores how clothing affects the children in a junior school in england.

Dans cette thèse nous étudierons des problématiques de graphes. Nous proposons deux études théoriques sur la recherche et l'énumération de cliques et quasi-cliques. Ensuite nous proposons une étude appliquée sur la propagation d'information dans un graphe d'entités nommées. Premièrement, nous étudierons la recherche de cliques dans des graphes compressés. Les problèmes MCE et MCP sont des problèmes rencontrés dans l'analyse des graphes. Ce sont des problèmes difficiles, pour lesquels des solutions adaptées doivent être conçues pour les grands graphes. Nous proposons de travailler sur une version compressée du graphe. Nous montrons les bons résultats obtenus par notre méthode pour l'énumération de cliques maximales. Secondement, nous étudierons l'énumération de quasi-cliques maximales. Nous proposons un algorithme distribué qui énumère l'ensemble des quasi-cliques maximales. Nous proposons aussi une heuristique qui liste des quasi-cliques plus rapidement. Nous montrons l'intérêt de l'énumération de ces quasi-cliques par une évaluation des relations en regardant la co-occurrence des noeuds dans l'ensemble des quasi-cliques énumérées. Troisièmement, nous travaillerons sur la diffusion d'événements dans un graphe d'entités nommées. De nombreux modèles existent pour simuler des problèmes de diffusion de rumeurs ou de maladies dans des réseaux sociaux ou des problèmes de propagation de faillites dans les milieux bancaires. Nous proposons de répondre au problème de diffusion d'événements dans des réseaux hétérogènes représentant un environnement économique du monde. Nous proposons un problème de diffusion, nommé problème de classification de l'infection, qui consiste à déterminer quelles entités sont concernées par un événement. Pour ce problème, nous proposons deux modèles inspirés du modèle de seuil linéaire auxquels nous ajoutons différentes fonctionnalités. Finalement, nous testons et validons nos modèles sur un ensemble d'événements / In this thesis we will study graph problems. We will study theoretical problems in pattern research and applied problems in information diffusion. We propose two theoretical studies on the identification/detection and enumeration of dense subgraphs, such as cliques and quasi-cliques. Then we propose an applied study on the propagation of information in a named entities graph. First, we will study the identification/detection of cliques in compressed graphs. The MCE and MCP are problems that are encountered in the analysis of data graphs. These problem are difficult to solve (NP-Hard for MCE and NP-Complete for MCP), and adapted solutions must be found for large graphs. We propose to solve these problems by working on a compressed version of the initial graph. We show the correct results obtained by our method for the enumeration of maximal cliques on compressed graphs. Secondly, we will study the enumeration of maximal quasi-cliques. We propose a distributed algorithm that enumerates the set of maximal quasi-cliques of the graph. We show that this algorithm lists the set of maximal quasi-cliques of the graph. We also propose a heuristic that lists a set of quasi-cliques more quickly. We show the interest of enumerating these quasi-cliques by an evaluation of relations by looking at the co-occurrence of nodes in the set of enumerated quasi-cliques. Finally, we work on the event diffusion in a named entities graph. Many models exist to simulate diffusion problems of rumors or diseases in social networks and bankruptcies in banking networks. We address the issue of significant events diffusion in heterogeneous networks, representing a global economic environment. We propose a diffusion problem, called infection classification problem, which consists to dertemine which entities are concerned by an event. To solve this problem we propose two models inspired by the linear threshold model to which we add different features. Finally, we test and validate our models on a set of events

Large graph-based datasets are common to many applications because of the additional structure provided to data by graphs. Patterns extracted from graphs must adhere to these structural properties, making them a more complex class of patterns to identify. The role of graph mining is to efficiently extract these patterns and quantify their significance. In this thesis, we focus on two application domains and demonstrate the design of graph mining algorithms in these domains. First, we investigate the use of graph grammar mining as a tool for diagnosing potential memory leaks from Java heap dumps. Memory leaks occur when memory that is no longer in use fails to be reclaimed, resulting in significant slowdowns, exhaustion of available storage, and eventually application crashes. Analyzing the heap dump of a program is a common strategy used in memory leak diagnosis, but our work is the first to employ a graph mining approach to the problem. Memory leaks accumulate in the heap as classes of subgraphs and the allocation paths from which they emanate can be explored to contextualize the leak source. We show that it suffices to mine the dominator tree of the heap dump, which is significantly smaller than the underlying graph. We demonstrate several synthetic as well as real-world examples of heap dumps for which our approach provides more insight into the problem than state-of-the-art tools such as Eclipse's MAT. Second, we study the problem of multipartite graph clustering as an approach to database summarization on an integrated biological database. Construction of such databases has become a common theme in biological research, where heterogeneous data is consolidated into a single, centralized repository that provides a structured forum for data analysis. We present an efficient approximation algorithm for identifying clusters that form multipartite cliques spanning multiple database tables. We show that our algorithm computes a lossless compression of the database by summarizing it into a reduced set of biologically meaningful clusters. Our algorithm is applied to data from C. elegans, but we note its applicability to general relational databases. / Master of Science

Cette thèse porte sur des aspects structuraux et algorithmiques des graphes. Elle est divisée en deux parties, qui comportent deux études différentes : une partie sur des algorithmes centralisés-séquentiels, et une autre sur des algorithmes distribués. Dans la première partie, on étudie des aspects algorithmiques de deux structures de graphes appelés séparateurs minimaux et cliques maximales potentielles. Ces deux objets sont au coeur d'un méta-théorème dû à Fomin, Todinca and Villanger (SIAM J. Comput. 2015), qui affirme qu'une grande famille des problèmes d'optimisation peut être résolue en temps polynomial, si le graphe d'entrée contient un nombre polynomial de séparateurs minimaux. La contribution de cette partie consiste à prolonger le méta-théorème de Fomin et al. de deux manières : d'un côté, on l'adapte pour qu'il soit valide pour une plus grande famille des problèmes ; de l'autre, on étend ces résultats à des version paramétrées, pour certains paramètres des graphes. La deuxième partie de la thèse correspond à une étude du modèle appelé « Diffusion dans une Clique Congestionnée ». Dans ce modèle, les sommets d'un graphe communiquent entre eux dans des rondes synchrones, en diffusant un message de petite taille, visible par tout autre sommet. L'objectif ici est d'élaborer des protocoles qui reconnaissent des classes de graphes, en minimisant la taille des messages et le nombre de rondes. La contribution de cette partie est l'étude du rôle du hasard dans ce modèle, et la conception de protocoles pour la reconnaissance et la reconstruction des certaines classes des graphes. / This thesis is about structural and algorithmic aspects of graphs. It is divided in two parts, which are about two different studies: one part is about centralized-sequential algorithms, and the other part is about distributed algorithms. In the first part of the thesis we study algorithmic applications of two graph structures called minimal separators and potential maximal cliques. These two objects are in the core of a meta-theorem due to Fomin, Todinca and Villanger (SIAM J. Comput. 2015), which states that a large family of graph optimization problems can be solved in polynomial time, when the input is restricted to the family of graphs with polynomially many minimal separators. The contribution of this part of the thesis is to extend the meta-theorem of Fomin et al. in two ways. On one hand, we adapt it to be valid into a larger family of problems. On the other hand, we extend it into a parameterized version, for several graph parameters. In the second part of this thesis we study the broadcast congested clique model. In this model, the nodes of a graph communicate in synchronous rounds, broadcasting a message of small size visible to every other node. The goal is to design protocols that recognize graph classes minimizing the number of rounds and the message sizes. The contribution of this part is to explore the role of randomness on this model, and provide protocols for the recognition and reconstruction of some graph classes.