Algebraic optimization of recursive queries

Over the past few years, much attention has been paid to deductive databases. They offer a logic-based interface, and allow formulation of complex recursive queries. However, they do not offer appropriate update facilities, and do not support existing applications. To overcome these problems an SQL-like interface is required besides a logic-based interface.\ud \ud In the PRISMA project we have developed a tightly-coupled distributed database, on a multiprocessor machine, with two user interfaces: SQL and PRISMAlog. Query optimization is localized in one component: the relational query optimizer. Therefore, we have defined an eXtended Relational Algebra that allows recursive query formulation and can also be used for expressing executable schedules, and we have developed algebraic optimization strategies for recursive queries. In this paper we describe an optimization strategy that rewrites regular (in the context of formal grammars) mutually recursive queries into standard Relational Algebra and transitive closure operations. We also describe how to push selections into the resulting transitive closure operations.\ud \ud The reason we focus on algebraic optimization is that, in our opinion, the new generation of advanced database systems will be built starting from existing state-of-the-art relational technology, instead of building a completely new class of systems

Data fragmentation for parallel transitive closure strategies

Addresses the problem of fragmenting a relation to make the parallel computation of the transitive closure efficient, based on the disconnection set approach. To better understand this design problem, the authors focus on transportation networks. These are characterized by loosely interconnected clusters of nodes with a high internal connectivity rate. Three requirements that have to be fulfilled by a fragmentation are formulated, and three different fragmentation strategies are presented, each emphasizing one of these requirements. Some test results are presented to show the performance of the various fragmentation strategie

Complex transitive closure queries on a fragmented graph

In this paper we study the reformulation of transitive closure queries on a fragmented graph. We split a query into several subqueries, each requiring only a fragment of the graph. We prove this reformulation to be correct for shortest path and bill of material queries. Here we describe the reformulation for an abstract graph, elsewhere we have described an actual implementation of our approach and some promising simulation results.\ud \ud We view the study of distributed computation of transitive closure queries as a result of the trend towards distributed computation. First selections were distributed to fragments of a relation, then fragmentation was used to compute joins in a distributed way, and now we are studying distributed computation of transitive closure queries. This should result in a deeper insight into the use and possible benefit of parallelism. Our work may be used in ordinary distributed databases as well as advanced multiprocessor database machines, such as PRISMA.\ud \ud Although this research was started to efficiently use distributed computation, it turns out to be beneficiary in a central environment as well. This is due to the introduction of extra selections, stemming from an appropriate fragmentation. This leads to extra focus on relevant data

An overview of parallel strategies for transitive closure on algebraic machines

An important feature of database technology of the nineties is the use of distributed computation for speeding up the execution of complex queries. Today, the use of parallelism is tested in several experimental database architectures and a few commercial systems for conventional select-project-join queries. In particular, hash-based fragmentation is used to distribute data to disks under the control of different processors, in multi-processor architectures without shared memory, in order to perform selections and joins in parallel.\ud With the development of new (logic) query languages and deductive databases, the new dimension of recursion has been added to query processing. Transitive closure queries, such as bill-of-material, allow important database problems to be solved by the database system itself; and more general logic programming queries allow us to study queries not considered before. Although recursive queries are very complex, their regular structure makes them particularly suited for parallel execution. Well-considered use of parallelism can give a high efficiency gain when processing recursive queries.\ud In this paper, we give an overview of approaches to parallel execution of recursive queries as they have been presented in recent literature. After showing that the most typical Datalog queries have exactly the same expressive power as the transitive closure of simple algebraic expressions, we focus on describing algebraic approaches to recursion.\ud To give a good overview of the problems that are inherent to parallel computation, we introduce a graphical formalism to describe parallel execution. This formalism enables us to clearly show the behaviour of parallel execution strategies. We first review algorithms developed in the framework of algebraic transitive closures that operate on entire relations; then we introduce fragmentation, distinguishing between hash-based and semantic fragmentation.\ud This research is partially supported by the LOGIDATA + Project of the National Research Council of Ital

Data fragmentation for parallel transitive closure strategies

A topic that is currently inspiring a lot of research is parallel (distributed) computation of transitive closure queries. In [lo] the disconnection set approach has been introduced as an effective strategy for such a computation. It involves reformulating a transitive closure query on a relation into a number of transitive closure queries on smaller fragments; these queries can then execute independently on the fragments, without need for communication and without computing the same tuples at more than one processor. Now that effective strategies as just mentioned have been developed, the next problem is that of developing adequate data fragmentation strategies for these approaches. This is a dificult problem, but of paramount importance to the success of these approaches. We discuss the issues that influence data fragmentation. We present a number of algorithms, each focusing on one of the important issues. We discuss the pros and cons of the algorithms, and we give some results of applying the algorithms to different types of graphs. This last aspect shows to what respect the algorithms indeed conform to the goals we set out

A Semantic Data Model for Integration of Data and Knowledge

In this paper we present the Data and Knowledge Model (DK-model) that integrates the representation of data and certain types of knowledge in a semantic data model. The ER model is used as a basis for the DK-model. The main features of the DK-model are modularity of modelling, generalization/specialization hierarchies, deductive capabilities in the form of so-called virtual attributes, and inheritance of attributes and knowledge rules. Virtual attributes do not have a static value, but an associated knowledge rule that states how to compute their value. These knowledge rules are specified declaratively in a Datalog-like way. Because virtual attributes are subject to inheritance they allow for a modular, non-redundant definition of knowledge rules. The mapping of knowledge rules, which describe virtual attributes, onto Relational Algebra is also described. This leads to an efficient, set-oriented way of solving queries. 1 Reflections on Databases and Knowledge The need for semantic dat..