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International audience; In this talk, we will present a recent variant of the graph embedding problem on labeled graphs. Given a graph G=(V,E), a k-labeled embedding of G is a vertex labeling of G with k colors such that there exists an edge-disjoint placement of two copies of G into the complete graph $K_|V|$, preserving the labeling function. The objective is the maximization of the parameter k. We will present upper bounds in the general case, exact values for some families of graphs, and extensions for the placement of more than two copies of G.

In this thesis, we investigate some problems in graph theory, namelythe graph coloring problem, the graph packing problem and tree pattern matchingfor XML query processing. The common point between these problems is that theyuse labeled graphs.In the first part, we study a new coloring parameter of graphs called the gapvertex-distinguishing edge coloring. It consists in an edge-coloring of a graph G whichinduces a vertex distinguishing labeling of G such that the label of each vertex isgiven by the difference between the highest and the lowest colors of its adjacentedges. The minimum number of colors required for a gap vertex-distinguishing edgecoloring of G is called the gap chromatic number of G and is denoted by gap(G).We will compute this parameter for a large set of graphs G of order n and we evenprove that gap(G) 2 fn E 1; n; n + 1g.In the second part, we focus on graph packing problems, which is an area ofgraph theory that has grown significantly over the past several years. However, themajority of existing works focuses on unlabeled graphs. In this thesis, we introducefor the first time the packing problem for a vertex labeled graph. Roughly speaking,it consists of graph packing which preserves the labels of the vertices. We studythe corresponding optimization parameter on several classes of graphs, as well asfinding general bounds and characterizations.The last part deal with the query processing of a core subset of XML query languages:XML twig queries. An XML twig query, represented as a small query tree,is essentially a complex selection on the structure of an XML document. Matching atwig query means finding all the occurrences of the query tree embedded in the XMLdata tree. Many holistic twig join algorithms have been proposed to match XMLtwig pattern. Most of these algorithms find twig pattern matching in two steps. Inthe first one, a query tree is decomposed into smaller pieces, and solutions againstthese pieces are found. In the second step, all of these partial solutions are joinedtogether to generate the final solutions. In this part, we propose a novel holistictwig join algorithm, called TwigStack++, which features two main improvementsin the decomposition and matching phase. The proposed solutions are shown to beefficient and scalable, and should be helpful for the future research on efficient queryprocessing in a large XML database., Cette thèse se situe dans le domaine de graphes et de leurs applications, Elleest constitué de trois grandes parties, la première est consacrée à l’étude d’unnouveau type de coloration sommets distinguantes, les arête-colorations sommetsdistinguantespar écarte. Il consiste de trouver une valuation des arêtes qui permettede distinguer les sommets de graphes telle que chaque sommet v du graphe est identifiéde façon unique par la différence entre la plus grande et la plus petite des valeursincidentes à v. Le plus entier pour lequel le graphe G admet une arête-colorationsommets-distinguantes par écarte est le nombre chromatique par écart de G, notégap(G). Nous avons étudié ce paramètre pour diverses familles de graphes. Uneconjecture intéressante, proposée dans cette partie, suggère que le nombre chromatiquepar écart de tout graphe connexe d’ordre n > 2 vaut n - 1, n ou n + 1.La deuxième partie du manuscrit concerne le problème du placement de graphes.Nous proposons un état de l’art des problèmes de placement de graphes, puis nousintroduisons la nouvelle notion de placement de graphes étiquetés. Il s’agit d’unplacement de graphes qui préserve les étiquettes des sommets. Ensuite, nous proposonsdes encadrements de ce nouveau paramètre pour plusieurs classes de graphes.La troisième partie de la thèse s’intéresse au problème d’appariement d’arbres dansle cadre de la recherche d’information dans des documents structurés de type XML.Les algorithmes holistique de jointure structurelle est l’une des premières méthodesproposées pour résoudre l’appariement exact des documents XML. Ces algorithmessont souvent divisés en deux grandes étapes. La première étape permet de décomposerl’arbre de la requête en un ensemble de petites composantes connexes. Ensuite,des solutions intermédiaires pour chaque composante de la requête sont trouvées, cesrésultats intermédiaires sont joints pour obtenir la solution finale. Nous proposonsdans cette partie un nouvel algorithme appelé TwigStack++ qui vise principalementà diminuer le coût de la jointure et le calcule inutile recherche. Notre algorithmeobtient de meilleurs résultats en comparaison avec deux autres méthodes de l’étatde l’art.

International audience; Finding all occurrences of a twig pattern in an XML document is a core operation for XML query processing. Many holistic twig join algorithms have been proposed to match XML twig pattern. Most of these algorithms find twig pattern matching in two phases. In the first phase, a query tree is decomposed into smaller pieces, and solutions against these pieces are found. In the second phase, all of these partial solutions are joined together to generate the final solutions. In this paper, we propose a novel holistic twig join algorithm, called TwigStack++, which features two main improvements in the decomposition and matching phase. Experimental results on various datasets show that our algorithm outperforms the existing approaches.