A survey of parallel execution strategies for transitive closure and logic programs

An important feature of database technology of the nineties is the use of parallelism for speeding up the execution of complex queries. This technology is being 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 order to perform selections and joins in parallel. With the development of new query languages, and in particular with the definition of transitive closure queries and of more general logic programming queries, the new dimension of recursion has been added to query processing. Recursive queries are complex; at the same time, their regular structure is particularly suited for parallel execution, and parallelism may give a high efficiency gain. We survey the approaches to parallel execution of recursive queries that have been presented in the recent literature. We observe that research on parallel execution of recursive queries is separated into two distinct subareas, one focused on the transitive closure of Relational Algebra expressions, the other one focused on optimization of more general Datalog queries. Though the subareas seem radically different because of the approach and formalism used, they have many common features. This is not surprising, because most typical Datalog queries can be solved by means of the transitive closure of simple algebraic expressions. We first analyze the relationship between the transitive closure of expressions in Relational Algebra and Datalog programs. We then review sequential methods for evaluating transitive closure, distinguishing iterative and direct methods. We address the parallelization of these methods, by discussing various forms of parallelization. Data fragmentation plays an important role in obtaining parallel execution; we describe hash-based and semantic fragmentation. Finally, we consider Datalog queries, and present general methods for parallel rule execution; we recognize the similarities between these methods and the methods reviewed previously, when the former are applied to linear Datalog queries. We also provide a quantitative analysis that shows the impact of the initial data distribution on the performance of methods

Solving equations in the relational algebra

Enumerating all solutions of a relational algebra equation is a natural and powerful operation which, when added as a query language primitive to the nested relational algebra, yields a query language for nested relational databases, equivalent to the well-known powerset algebra. We study \emph{sparse} equations, which are equations with at most polynomially many solutions. We look at their complexity, and compare their expressive power with that of similar notions in the powerset algebra.Comment: Minor revision, accepted for publication in SIAM Journal on Computin

An Inflationary Fixed Point Operator in XQuery

We introduce a controlled form of recursion in XQuery, inflationary fixed points, familiar in the context of relational databases. This imposes restrictions on the expressible types of recursion, but we show that inflationary fixed points nevertheless are sufficiently versatile to capture a wide range of interesting use cases, including the semantics of Regular XPath and its core transitive closure construct. While the optimization of general user-defined recursive functions in XQuery appears elusive, we will describe how inflationary fixed points can be efficiently evaluated, provided that the recursive XQuery expressions exhibit a distributivity property. We show how distributivity can be assessed both, syntactically and algebraically, and provide experimental evidence that XQuery processors can substantially benefit during inflationary fixed point evaluation.Comment: 11 pages, 10 figures, 2 table

CrocoPat 2.1 Introduction and Reference Manual

CrocoPat is an efficient, powerful and easy-to-use tool for manipulating relations of arbitrary arity, including directed graphs. This manual provides an introduction to and a reference for CrocoPat and its programming language RML. It includes several application examples, in particular from the analysis of structural models of software systems.Comment: 19 pages + cover, 2 eps figures, uses llncs.cls and cs_techrpt_cover.sty, for downloading the source code, binaries, and RML examples, see http://www.software-systemtechnik.de/CrocoPat

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

Automatic view schema generation in object-oriented databases

An object-oriented data schema is a complex structure of classes interrelated via generalization and property decomposition relationships. We define an object-oriented view to be a virtual schema graph with possibly restructured generalization and decomposition hierarchies - rather than just one individual virtual class as proposed in the literature. In this paper, we propose a methodology, called MultiView, for supporting multiple such view schemata. MultiView is anchored on the following complementary ideas: (a) the view definer derives virtual classes and then integrates them into one consistent global schema graph and (b) the view definer specifies arbitrarily complex view schemata on this augmented global schema. The focus of this paper is, however, on the second, less explored, issue. This part of the view definition is performed using the following two steps: (1) view class selection and (2) view schema graph generation. For the first, we have developed a view definition language that can be used by the view definer to specify the selection of the desired view classes from the global schema. For the second, we have developed two algorithms that automatically augment the set of selected view classes to generate a complete, minimal and consistent view class generalization hierarchy. The first algorithm has linear complexity but it assumes that the global schema graph is a tree. The second algorithm overcomes this restricting assumption and thus allows for multiple inheritance, but it does so at the cost of a higher complexity