Dissertations / Theses on the topic 'Graphe ordonné'
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Buchwalder, Xavier. "Sur l'algèbre et la combinatoire des sous-graphes d'un graphe." Phd thesis, Université Claude Bernard - Lyon I, 2009. http://tel.archives-ouvertes.fr/tel-00441324.
Full textGatse, Franchel. "Spectre ordonné et branches analytiques d'une surface qui dégénère sur un graphe." Electronic Thesis or Diss., Orléans, 2020. http://www.theses.fr/2020ORLE3205.
Full textIn this work, we give a general framework of Riemannian surfaces that can degenerate on metric graphs and that we call surfaces made from cylinders and connecting pieces. The latter depend on a parameter t that describes the degeneration. When t goes to 0, the waists of the cylinders go to 0 but their lengths stay fixed. We thus obtain the edges of the limiting graph. The connecting pieces are squeezed in all directions and degenerate on the vertices of the limiting graph. We then study the asymptotic behaviour of the spectrum of these surfaces when t varies from two different points of view, considering the spectrum either as a sequence of ordered eigenvalues or as a collection of analytic eigenbranches. In the case of ordered eigenvalues, we recover a rather classical statement, and prove that the spectrum converges to the spectrum of the limiting object. The study of the analytic eigenbranches is more original. We prove that any such eigenbranch converges and we give a characterisation of the possible limits. These results apply to translation surfaces on which there is a completely periodic direction
Pitois, François. "Recherche de régularités et représentations succinctes de graphes." Electronic Thesis or Diss., Bourgogne Franche-Comté, 2024. http://www.theses.fr/2024UBFCK021.
Full textIn this thesis, we investigate regularities in graphs and succinct representations of graphs.A regularity, or structure, is a generic term that refers to a set of vertices in a graph with certain properties.Among the most well-known regularities, we can mention cliques, dense subgraphs, communities, modules, and splits.A succinct representation of a graph is a way of describing it that is more efficient than simply listing the different edges of the graph.Searching for regularities enables obtaining succinct representations.Thus, in a first step, we developed a graph compression algorithm that searches for different graph regularities, selects a portion of them, and partitions the graph based on the selected structures.This algorithm provides a succinct description of the graph that is better than some benchmark algorithms.In a second step, we created our own structures, so they are suitable for compression and are easy enough to search for.To do this, we started from a known structure, the split, and generalized it to create the r-split, where r is a fixed integer parameter.We then showed that the set of r-splits of a graph has a global coherence, in the sense that only a polynomial number of them is sufficient to describe all r-splits of the graph.This generalizes a well-known property of splits, for which only a linear number of them is sufficient to recover all the others.We also demonstrated that r-splits can be computed in polynomial time using submodular function optimization algorithms.In a third step, we focused on searching for particular regularities: patterns in ordered graphs.An ordered graph is a graph in which the vertices are ordered from 1 to n.A pattern is a partial ordered subgraph, in the sense that each pair of vertices can be connected either by an edge, a non-edge, or neither.The goal is to fix a pattern P and build an algorithm capable of detecting if P is in any ordered graph given as an input.This problem is polynomial in the size of the graph via exhaustive search.However, is it possible to do better?We were able to show that yes: most three-vertex patterns can be detected in linear time while exhaustive search requires cubic time.Regarding larger patterns, we exhibited classes of patterns that can be detected in subcubic time: outerplanar patterns.By adding additional constraints, we exhibited a class of patterns that can be detected in linear time: these are outerplanar patterns without cycles and non-edges
Rexhep, Selim. "Combinatorics of finite ordered sets: order polytopes and poset entropy." Doctoral thesis, Universite Libre de Bruxelles, 2016. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/231859.
Full textLe but de la thèse est d'étudier deux problèmes ouverts sur les ensembles ordonnés finis: la structure des polytopes d'ordre et l'approximation du nombre d'extensions linéaires d'un ordre partiel au moyen de la notion d'entropie de graphe. Les polytopes considérés sont le polytope des ordres totaux, le polytope des semiordres, le polytope des ordres d'intervalles, le polytope des ordres partiels, ainsi qu'une généralisation du polytope des ordres totaux: le polytope des extensions linéaires d'un ensemble ordonné fixé P. Des résultats sur la structure de ces polytopes sont présentés dans la première partie de la thèse. Dans la deuxième partie de la thèse, nous améliorons les bornes existantes liant l'entropie du graphe d'incomparabilité d'un ordre partiel et son nombre d'extensions linéaires.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished
Retoré, Christian. "Réseaux et séquents ordonnés." Phd thesis, Université Paris-Diderot - Paris VII, 1993. http://tel.archives-ouvertes.fr/tel-00585634.
Full textLécuyer, Fabrice. "Ordonner les nœuds pour passer à l'échelle sur les grands réseaux réels." Electronic Thesis or Diss., Sorbonne université, 2023. http://www.theses.fr/2023SORUS172.
Full textThis thesis focuses on using theoretical tools of computer science to improve algorithms in practice, specifically algorithms that process data in the form of graphs. A graph represents elements (nodes) and their interactions (edges). Computer scientists have designed theoretical algorithms for arbitrary graphs, such as finding shortest paths or identifying inter-connected nodes. However, real-world networks have specific properties that are unknown in advance due to the situations from which they arise. They can be very large, which presents a challenge for processing them in reasonable time. To help design scalable algorithms for real-world networks, we focus on the technique of node ordering, which consists in processing the nodes in a specific order that depends on local or global properties of the network. We provide a review on the different mechanisms and methods that have been used to design orderings across various application domains. Then, we present three contributions that use node orderings to make algorithms more efficient. First, we replicate a paper that designs an ordering to make cache systems more effective, which accelerates different graph algorithms. Second, we create new orderings that diminish the number of operations in an existing algorithm for triangle listing. Third, we use greedy algorithms with certain orderings to bound the size of a minimum vertex cover on a specific instance, which allows us to certify the quality of approximate values. These findings insist on scalability issues, time measurements, mathematical grounding and validation by experiments. Finally, we present a collaboration on network analysis that consists in describing the mobility of researchers within the space of knowledge
Hilali, Abdelmajid. "Ordres de contiguïté." Lyon 1, 1993. http://www.theses.fr/1993LYO10264.
Full textBoneva, Iovka. "Expressivité, satisfiabilité et model checking d'une logique spatiale pour arbres non ordonnés." Lille 1, 2006. https://ori-nuxeo.univ-lille1.fr/nuxeo/site/esupversions/dffac6b2-50d6-4e6d-9e4c-f8f5731c75e2.
Full textJanaqi, Stefan. "Quelques éléments de la géométrie des graphes : graphes médians, produits d'arbres, génération convexe des graphes de Polymino." Université Joseph Fourier (Grenoble), 1994. http://www.theses.fr/1995GRE10093.
Full textRoux, Bernard. "Une approche relationnelle des automates et de l'ordonnancement." Lyon 1, 2000. http://www.theses.fr/2000LYO10255.
Full textDelhommé, Christian. "Propriétés de projection." Lyon 1, 1995. http://www.theses.fr/1995LYO10159.
Full textDelanoue, Nicolas. "Algorithmes numériques pour l'analyse topologique : Analyse par intervalles et théorie des graphes." Phd thesis, Université d'Angers, 2006. http://tel.archives-ouvertes.fr/tel-00340999.
Full textDe nombreux problèmes, comme l'étude de l'espace des configurations d'un robot, se ramènent à une étude qualitative d'ensembles. Ici, la ``taille'' de l'ensemble importe peu, ce qui compte, c'est sa ``topologie''. Les méthodes proposées calculent des invariants topologiques d'ensembles. Les ensembles considérés sont décrits à l'aide d'inégalités $\mathcal{C}^{\infty}$. L'idée maîtresse est de décomposer un ensemble donné en parties contractiles et d'utiliser l'homologie de \v Cech.
La seconde partie de la thèse concerne l'étude de point
asymptotiquement stables des systèmes dynamiques (linéaires ou non). Plus largement, on propose une méthode pour approcher le bassin d'attraction d'un point asymptotiquement stable. Dans un premier temps, on utilise la théorie de Lyapunov et le calcul par intervalle
pour trouver effectivement un voisinage inclus dans le bassin d'attraction d'un point prouvé asymptotiquement stable. Puis, on combine, une fois de plus, la théorie des graphes et les méthodes d'intégration d'équations différentielles ordinaires pour améliorer ce voisinage et ainsi construire un ensemble inclus dans le bassin
d'attraction de ce point.
Daniel-Vatonne, Marie-Christine. "Les termes : un modèle de représentation et structuration de données symboliques." Montpellier 2, 1993. http://www.theses.fr/1993MON20031.
Full textMorvan, Michel. "Algorithmes linéaires et invariants d'ordres." Montpellier 2, 1991. http://www.theses.fr/1991MON20022.
Full textMoller, Pierre. "Théorie algébrique des systèmes à évènements discrets." Phd thesis, École Nationale Supérieure des Mines de Paris, 1988. http://pastel.archives-ouvertes.fr/pastel-00654163.
Full textMarmol, Bruno. "Contribution à l'évaluation d'attributs et l'optimisation mémoire sur machines multiprocesseurs." Phd thesis, Université d'Orléans, 1995. http://tel.archives-ouvertes.fr/tel-00005806.
Full textVo, Thi Quynh Trang. "Algorithms and Machine Learning for fair and classical combinatorial optimization." Electronic Thesis or Diss., Université Clermont Auvergne (2021-...), 2024. http://www.theses.fr/2024UCFA0035.
Full textCombinatorial optimization is a field of mathematics that searches for an optimal solution in a finite set of objects. It has crucial applications in many fields, including applied mathematics, software engineering, theoretical computer science, and machine learning. extit{Branch-and-cut} is one of the most widely-used algorithms for solving combinatorial optimization problems exactly. In this thesis, we focus on the computational aspects of branch-and-cut when studying two critical dimensions of combinatorial optimization: extit{the fairness of solutions} and extit{the integration of machine learning}.In Partef{part:1} (Chaptersef{chap:bnc-btsp} andef{chap:owa}), we study two common approaches to deal with the issue of fairness in combinatorial optimization, which has gained significant attention in the past decades. The first approach is extit{balanced combinatorial optimization}, which finds a fair solution by minimizing the difference between the largest and smallest components used. Due to the difficulties in bounding these components, to the best of our knowledge, no general exact framework based on mixed-integer linear programming (MILP) has been proposed for balanced combinatorial optimization. To address this gap, in Chapteref{chap:bnc-btsp}, we present a branch-and-cut algorithm and a novel class of local cutting planes tailored for balanced combinatorial optimization problems. We demonstrate the effectiveness of the proposed framework in the Balanced Traveling Salesman Problem. Additionally, we introduce bounding algorithms and mechanisms to fix variables to accelerate performance further.The second approach to handling the issue of fairness is extit{Ordered Weighted Average (OWA) combinatorial optimization}, which integrates the OWA operator into the objective function. Due to the ordering operator, OWA combinatorial optimization is nonlinear, even if its original constraints are linear. Two MILP formulations of different sizes have been introduced in the literature to linearize the OWA operator. However, which formulation performs best for OWA combinatorial optimization remains uncertain, as integrating the linearization methods may introduce additional difficulties. In Chapteref{chap:owa}, we provide theoretical and empirical comparisons of the two MILP formulations for OWA combinatorial optimization. In particular, we prove that the formulations are equivalent in terms of the linear programming relaxation. We empirically show that for OWA combinatorial optimization problems, the formulation with more variables can be solved faster with branch-and-cut.In Partef{part:2} (Chapteref{chap:mlbnc}), we develop methods for applying machine learning to enhance fundamental decision problems in branch-and-cut, with a focus on cut generation. Cut generation refers to the decision of whether to generate cuts or to branch at each node of the search tree. We empirically demonstrate that this decision significantly impacts branch-and-cut performance, especially for combinatorial cuts that exploit the facial structure of the convex hull of feasible solutions. We then propose a general framework combining supervised and reinforcement learning to learn effective strategies for generating combinatorial cuts in branch-and-cut. Our framework has two components: a cut detector to predict cut existence and a cut evaluator to choose between generating cuts and branching. Finally, we provide experimental results showing that the proposed method outperforms commonly used strategies for cut generation, even on instances larger than those used for training