We describe set-oriented algorithms for mining association rules. Such algorithms imply performing multiple joins and may appear to be inherently less escient than special-purpose algorithms. W e develop new algorithms that can be expressed as SQL queries, and discuss optimization of these algorithms. After analytical evaluation, an algorithm named S E T M emerges as the algorithm of choice. Algorithm S E T M uses only simple database primitives, viz., sorting and merge-scan join. Algorithm S E T M is simple, fast, and stable over the mnge of pammeter values. The major contribution of this paper is that it shows that at least some aspects of data mining can be cam'ed out by using general query languages such as SQL, mther than by developing specialized black box algorithms. The set-oriented nature of Algorithm S E T M facilitates the development of extensions.

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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.

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