Vassia Pavlaki

Data exchange in the presence of arithmetic comparisons

Data exchange is the problem of transforming data structured under a schema (called source) into data structured under a different schema (called target). The emphasis of data exchange is to materialize a target instance (called solution) that satisfies the relationship between the schemas. Universal solutions were shown to be the most suitable solutions, mainly because they can be used to answer conjunctive queries posed over the target schema. Trying to extend this result to more expressive query languages fails, even if we only add inequalities (≠) to conjunctive queries. In this work we study data exchange in the presence of general arithmetic comparisons (<, ≤, >, ≥, =, ≠): (a) We consider queries posed over the target schema that belong to the class of unions of conjunctive queries with arithmetic comparisons (in short CQACs). (b) We exploit arithmetic comparisons to define more expressive data exchange settings, called DEAC settings. In particular, DEAC settings consist of constraints that involve arithmetic comparisons. For that, two new classes of dependencies (tgd-ACs and acgds) are introduced, to capture the need of arithmetic comparisons in source-to-target and target constraints. We show that in DEAC settings the existence of solution problem is in NP. We define a novel chase procedure called AC-chase which is a tree and we prove that it produces a universal solution (appropriately defined to deal with arithmetic comparisons). We show that the new concept of universal solution is the right tool for query answering in the case of unions of CQACs. The complexity of computing certain answers for unions of CQACs is shown to be coNP-complete. Moreover, we identify polynomial cases for a) computing a universal solution and b) computing certain answers. For that, we introduce the succinct AC-chase which is a sequence instead of a tree, but its result is not necessarily a solution. We identify cases where succinct AC-chase returns indeed a universal solution and we investigate the syntactic conditions of the query under which query answering takes polynomial time. We show that the latter is feasible even in cases where the result of chase is not a universal solution.

On rewriting XPath queries using views

The problem of rewriting a query using a materialized view is studied for a well known fragment of XPath that includes the following three constructs: wildcards, descendant edges and branches. In earlier work, determining the existence of a rewriting was shown to be coNP-hard, but no tight complexity bound was given. While it was argued that Σ3p is an upper bound, the proof was based on results that have recently been refuted. Consequently, the exact complexity (and even decidability) of this basic problem has been unknown, and there have been no practical rewriting algorithms if the query and the view use all the three constructs mentioned above. It is shown that under fairly general conditions, there are only two candidates for rewriting and hence, the problem can be practically solved by two containment tests. In particular, under these conditions, determining the existence of a rewriting is coNP-complete. The proofs utilize various novel techniques for reasoning about XPath patterns. For the general case, the exact complexity remains unknown, but it is shown that the problem is decidable.

Data exchange: query answering for incomplete data sources

Data exchange is the problem of transforming data structured under a schema, called the source schema, into data structured under another schema, called the target schema. Existing work on data exchange considers settings where the source instance does not contain incomplete information. In this paper we study semantics and address algorithmic issues for data exchange settings where the source instance may contain incomplete data. We investigate the query answering problem in such data exchange settings. First we give two different meaningful semantics to certain answers: One via the certain answers in the corresponding complete data exchange problems and the other via the set of all solutions of the corresponding complete data exchange problems. We use the chase to compute a universal instance which is materialized over the target schema and is used to compute the certain answers to unions of conjunctive queries. We prove that computing certain answers (under both semantics) for unions of conjunctive queries can be done in polynomial time when the schema mapping contains constraints that consist of a weakly acyclic set of tuple-generating dependencies and equality-generating dependencies.

Finding equivalent rewritings in the presence of arithmetic comparisons

The problem of rewriting queries using views has received significant attention because of its applications in a wide variety of data-management problems. For select-project-join SQL (a.k.a. conjunctive) queries and views, there are efficient algorithms in the literature, which find equivalent and maximally contained rewritings. In the presence of arithmetic comparisons (ACs) the problem becomes more complex. We do not know how to find maximally contained rewritings in the general case. There are algorithms which find maximally contained rewritings only for special cases such as when ACs are restricted to be semi-interval. However, we know that the problem of finding an equivalent rewriting (if there exists one) in the presence of ACs is decidable, yet still doubly exponential. This complexity calls for an efficient algorithm which will perform better on average than the complete enumeration algorithm. In this work we present such an algorithm which is sound and complete. Its efficiency lies in that it considers fewer candidate rewritings because it includes a preliminary test to decide for each view whether it is potentially useful in some rewriting.

View selection for real conjunctive queries

Given a query workload, a database and a set of constraints, the view-selection problem is to select views to materialize so that the constraints are satisfied and the views can be used to compute the queries in the workload efficiently. A typical constraint, which we consider in the present work, is to require that the views can be stored in a given amount of disk space. Depending on features of SQL queries (e.g., the DISTINCT keyword) and on whether the database relations on which the queries are applied are sets or bags, the queries may be computed under set semantics, bag-set semantics, or bag semantics. In this paper we study the complexity of the view-selection problem for conjunctive queries and views under these semantics. We show that bag semantics is the “easiest to handle” (we show that in this case the decision version of view selection is in NP), whereas under set and bag-set semantics we assume further restrictions on the query workload (we only allow queries without self-joins in the workload) to achieve the same complexity. Moreover, while under bag and bag-set semantics filtering views (i.e., subgoals that can be dropped from the rewriting without impacting equivalence to the query) are practically not needed, under set semantics filtering views can reduce significantly the query-evaluation costs. We show that under set semantics the decision version of the view-selection problem remains in NP only if filtering views are not allowed in the rewritings. Finally, we investigate whether the cgalg algorithm for view selection introduced in Chirkova and Genesereth (Linearly bounded reformulations of conjunctive databases, pp. 987–1001, 2000) is suitable in our setting. We prove that this algorithm is sound for all cases we examine here, and that it is complete under bag semantics for workloads of arbitrary conjunctive queries and under bag-set semantics for workloads of conjunctive queries without self-joins.

Designing views to efficiently answer real SQL queries

The problem of optimizing queries in the presence of materialized views and the related view-design problem have recently attracted a lot of attention. Significant research results have been reported, and materialized views are increasingly used in query evaluation in commercial data-management systems. At the same time, most results in the literature assume set-theoretic semantics, whereas SQL queries have bag-theoretic semantics (duplicates are not eliminated unless explicitly requested). This paper presents results on selecting views to answer queries in relational databases under set, bag, and bag-set semantics. The results can be used under each of the three assumptions, to find sound and complete algorithms for designing views and rewriting queries efficiently.

From CTL to datalog

We provide a translation from CTL to DatalogSucc. The translation has the following advantages: a) It is natural. b) It provides intuition to the expressive power of CTL and its various fragments. c) It uses a fragment of DatalogSucc which is close to the expressive power of CTL.