Views and Queries: Determinacy and Rewriting

International audienceWe investigate the question of whether a query Q can be answered using a set V of views. We first define the problem in information-theoretic terms: we say that V determines Q if V provides enough information to uniquely determine the answer to Q . Next, we look at the problem of rewriting Q in terms of V using a specific language. Given a view language V and query language Q , we say that a rewriting language R is complete for V -to- Q rewritings if every Q ∈ Q can be rewritten in terms of V ∈ V using a query in R , whenever V determines Q . While query rewriting using views has been extensively investigated for some specific languages, the connection to the information-theoretic notion of determinacy, and the question of completeness of a rewriting language have received little attention. In this article we investigate systematically the notion of determinacy and its connection to rewriting. The results concern decidability of determinacy for various view and query languages, as well as the power required of complete rewriting languages. We consider languages ranging from first-order to conjunctive queries

Automatic physical database design : recommending materialized views

This work discusses physical database design while focusing on the problem of selecting materialized views for improving the performance of a database system. We first address the satisfiability and implication problems for mixed arithmetic constraints. The results are used to support the construction of a search space for view selection problems. We proposed an approach for constructing a search space based on identifying maximum commonalities among queries and on rewriting queries using views. These commonalities are used to define candidate views for materialization from which an optimal or near-optimal set can be chosen as a solution to the view selection problem. Using a search space constructed this way, we address a specific instance of the view selection problem that aims at minimizing the view maintenance cost of multiple materialized views using multi-query optimization techniques. Further, we study this same problem in the context of a commercial database management system in the presence of memory and time restrictions. We also suggest a heuristic approach for maintaining the views while guaranteeing that the restrictions are satisfied. Finally, we consider a dynamic version of the view selection problem where the workload is a sequence of query and update statements. In this case, the views can be created (materialized) and dropped during the execution of the workload. We have implemented our approaches to the dynamic view selection problem and performed extensive experimental testing. Our experiments show that our approaches perform in most cases better than previous ones in terms of effectiveness and efficiency

Equivalence of Queries with 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

On the content of materialized aggregate views

We consider the problem of answering queries using only materialized views. We rst show that if the views subsume the query from the point of view of the information content, then the query can be answered using only the views, but the resulting query might be extremely ine cient. We then focus on aggregate views and queries over a single relation, which are fundamental in many applications such as data warehousing. We show that in this case, it is possible to guarantee that as soon as the views subsume the query, it can be completely rewritten in terms of the views in a simple query language. Our main contribution is the conception of various rewriting algorithms which run in polynomial time, and the proof of their completeness which relies on combinatorial arguments. Finally, we discuss the choice of materializing or not ratio views such asaverage and percentage, important for the design of materialized views. We show that it has an impact on the information content, which can be used to protect data, as well as on the maintenance of views. 1