Query equivalence is a fundamental problem within database theory. The correctness of all forms of logical query rewriting—join minimization, view flattening, rewriting over materialized views, various semantic optimizations that exploit schema dependencies, federated query processing and other forms of data integration—requires proving that the final executed query is equivalent to the original user query. Hence, advances in the theory of query equivalence enable advances in query processing and optimization. In this thesis we address the problem of deciding query equivalence between conjunctive SQL queries containing aggregation operators that may be nested. Our focus is on understanding the interaction between nested aggregation operators and the other parts of the query body, and so we model aggregation functions simply as abstract collection constructors. Hence, the precise language that we study is a conjunctive algebraic language that constructs complex objects from databases of flat relations. Using an encoding of complex objects as flat relations, we reduce the query equivalence problem for this algebraic language to deciding equivalence between relational encodings output by traditional conjunctive queries (not containing aggregation). This encoding-equivalence cleanly unifies and generalizes previous results for deciding equivalence of conjunctive queries evaluated under various processing semantics. As part of our study of aggregation operators that can construct empty sub-collections—so-called “scalar” aggregation—we consider query equivalence for conjunctive queries extended with a left outer join operator, a very practical class of queries for which the general equivalence problem has never before been analyzed. Although we do not completely solve the equivalence problem for queries with outer joins or with scalar aggregation, we do propose useful sufficient conditions that generalize previously known results for restricted classes of queries. Overall, this thesis offers new insight into the fundamental principles governing the behaviour of nested aggregation.

Query equivalence is a fundamental problem within database theory. The correctness of all forms of logical query rewriting—join minimization, view flattening, rewriting over materialized views, various semantic optimizations that exploit schema dependencies, federated query processing and other forms of data integration—requires proving that the final executed query is equivalent to the original user query. Hence, advances in the theory of query equivalence enable advances in query processing and optimization. In this thesis we address the problem of deciding query equivalence between conjunctive SQL queries containing aggregation operators that may be nested. Our focus is on understanding the interaction between nested aggregation operators and the other parts of the query body, and so we model aggregation functions simply as abstract collection constructors. Hence, the precise language that we study is a conjunctive algebraic language that constructs complex objects from databases of flat relations. Using an encoding of complex objects as flat relations, we reduce the query equivalence problem for this algebraic language to deciding equivalence between relational encodings output by traditional conjunctive queries (not containing aggregation). This encoding-equivalence cleanly unifies and generalizes previous results for deciding equivalence of conjunctive queries evaluated under various processing semantics. As part of our study of aggregation operators that can construct empty sub-collections—so-called “scalar” aggregation—we consider query equivalence for conjunctive queries extended with a left outer join operator, a very practical class of queries for which the general equivalence problem has never before been analyzed. Although we do not completely solve the equivalence problem for queries with outer joins or with scalar aggregation, we do propose useful sufficient conditions that generalize previously known results for restricted classes of queries. Overall, this thesis offers new insight into the fundamental principles governing the behaviour of nested aggregation.

La popularisation de la technologie a permis d'implanter des dispositifs et des applications de plus en plus développés à la portée d'utilisateurs non experts. Ces systèmes produisent des flux ainsi que des données persistantes dont les schémas et les dynamiques sont hétérogènes. Cette thèse s'intéresse à pouvoir observer les données de ces systèmes pour aider à les comprendre et à les diagnostiquer. Nous proposons tout d'abord un modèle algébrique Astral capable de traiter sans ambiguïtés sémantiques des données provenant de flux ou relations. Le moteur d'exécution Astronef a été développé sur l'architecture à composants orientés services pour permettre une grande adaptabilité. Il est doté d'un constructeur de requête permettant de choisir un plan d'exécution efficace. Son extension Asteroid permet de s'interfacer avec un SGBD pour gérer des données persistantes de manière intégrée. Nos contributions sont confrontées à la pratique par la mise en œuvre d'un système d'observation du réseau domestique ainsi que par l'étude des performances. Enfin, nous nous sommes intéressés à la mise en place de la personnalisation des résultats dans notre système par l'introduction d'un modèle de préférences top-k. / Due to the popularization of technology, non-expert people can now use more and more advanced devices and applications. Such systems produce data streams as well as persistent data with heterogeneous schemas and dynamics. This thesis is focused on monitoring data coming from those systems to help users to understand and to perform diagnosis on them. We propose an algebraic model Astral able to treat data coming from streams or relations without semantic ambiguity. The engine Astronef has been developed on top of a service-oriented component framework to enable a large adaptability. It embeds a query builder which can select a composition of components to provide an efficient query plan. Its extension Asteroid interfaces with a DBMS in order to manage persistent data in an integrated manner. Our contributions have been confronted to practice with the deployment of a monitoring system for the digital home and with a performance study. Finally, we extend our approach with an operator to personalize the results by introducing a top-k preference model.