Algebraic optimization of recursive queries

Abstract

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.In the PRISMA project we have developed a tightly-coupled distributed database, on a multiprocessor machine, with two user interfaces: SQL and PRISMAIog. 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. 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.

Incorporating an implicit time dimension into the relational model and algebra

“…This form of recursion is called linear temporal recursion. There are recursive extensions of the relational algebra [13], but, to the best of our knowledge, recursion has not been explored in the context of temporal algebras. The algebras of Tuzhilin and Clifford [32] and Gabbay and McBrien [10] each offers two linear recursive operators, but no recursive équations.…”

Teaching Structured Design of Network Algorithms in Enhanced Versions of SQL

“…In several database (and other) applications, structures such as trees, graphs, and networks play a prominent role; see for instance Aho, Hopcroft, and Ullman (1983), Houtsma and Apers (1992), Küng, Wagner, and Wöβ (1995), and Ullman (1989) as well as their references among (many) others. There are many well-known examples of such application areas: bills of material, genealogical trees, organization charts, holding structures, networks of railroads, networks of conduit pipes, and telecom networks, to name a few.…”