Nest and Unnest Operators in Nested Relations

Abstract

By distinguishing nested attributes as Decomposable and Non-Decomposable, it is proved that for all nested relations, unnesting and then renesting on the same attribute yields the original relation subject only to the elimination of duplicate data. Therefore, the statement that was popular in nested relations research: "Unnesting and then nesting on the same attribute of a nested relation does not always yield the original relation" is reconsidered.Keywords: Non-First Normal Form database, Nested relation, Decomposable nested attribute INTRODUCTIONThe Nested or Non-First Normal Form (N1NF) data model was first introduced by Makinouchi (1997), in an effort to relax the first normal form (1NF) assumption, i.e. attributes must contain only atomic values. In contrast, in the N1NF data model, relations are allowed to have both atomic and non-atomic attributes that is the value of an attribute can be a relation itself, which can be considered as a subrelation of the relation. The N1NF data model allows each such subrelation to have relation-valued attributes, thus allowing nesting of relations or embedding of one relation within another. In this paper, relations that contain relation-valued attributes are called nested relations, whereas relations that do not contain relation valued attributes are called flat relations.The N1NF data model has been widely investigated since 1977, as it has offered good solutions for a number of applications, such as engineering design and textual data (Hernández, 1993). The major advantage claimed for nested relations over flat relations is that they minimise data fragmentation (Garani, 2006). The nested structure of the relation makes the semantics of the stored data clear. In addition, redundancy and update anomalies can be minimised and less storage is needed as one relation in non-first normal form can represent many relations in first normal form representation (Gyssens, Suciu & Van Gucht, 2001;Liu, Vincent & Mohania, 1999). As a result, query processing can be faster because a smaller number of join operations may be required (Despande & Larson, 1991).This paper is structured as follows. In Section 2 definitions of nested relations are given and two different categories of nested attributes are distinguished based on the semantics of the data they hold. In Section 3, this distinction is used to demonstrate that unnesting and then nesting on the same attribute of a nested relation R returns the original relation R, subject to the elimination of duplicate tuples. Therefore, the proposition that unnesting a nested relation R and then nesting it on the same attribute does not, necessarily, give the original R relation at all times, which is mentioned in Fischer & Thomas (1983), Jaeschke & Schek (1982), Schek & Scholl (1986) and Thomas & Fischer (1986), is reconsidered. It is shown that this is only a theoretical issue because a case such as that discussed in the earlier papers either cannot exist in the real world or if it does, that no information is lost by unnesting a nes...

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