Converting nested algebra expressions into flat algebra expressions

Reviewer: Ferdi W. J. Put

Nested relations can be obtained by removing the first normal form assumption in the relational model. As a consequence, tuple values can be either atomic or set-valued. During the 1980s, a lot of research was conducted on nested relations as an extension of the basic relational model. This paper does not consider nested relations as such, but rather a nested algebra in combination with the classical flat relational model. Both the operands and the result are flat relations (ff-expressions). The key problem addressed in this paper is the following. If we consider flat relations, is it possible to write queries in nested algebra that cannot be expressed in regular relational algebra__?__ The algebra (introduced in S<__?__Pub Caret>ection 2) consists of nine operators: union, difference, product, projection, selection, nest, unnest, empty, and renaming. Not included is the powerset operator. In Section 3, the authors indicate how the algebra must be translated into a nested calculus. This translation is used as an intermediate step in the translation of ff-expressions of the nested algebra into equivalent expressions of the flat algebra, because finding a completely algebraic strategy to obtain the same result remains an open problem. This translation (Section 4) is the main part of the paper (20 pages, of which 6 are occupied by the central proof of constructiveness). The main result is that every ff-expression of the nested algebra can be translated into an equivalent expression in the flat algebra. Without the powerset operator, it is not possible to express recursive queries. In this case, the regular flat algebra is rich enough to extract the same information from a database. The authors claim, however, that user queries, which are still expressed in a flat query language, can be optimized by using properties of the nested algebra. The intention of this paper is completely different from other research in this field. For example, Kitagawa and Kunii use nested relations to represent complex objects, such as office forms [1]. The associated algebra not only operates on the contents of the database, as in the flat relational model, but allows one to modify the structure of the nested relations dynamically. This ability is essential for the manipulation of complex user objects in an office environment.