Properties of Embedded Multivalued Dependencies in Relational Databases

Katsumi TANAKA, Yahiko KAMBAYASHI, Shuzo YAJIMA

Summary :

In Codd's relational data model, several dependencies have been introduced to specify the intensional properties of a relation. Fagin and independently, Zaniolo introduced the notion of a multivalued dependency (MVD). The definition of MVD's refers to an underlying set of attributes of a relation. The embedded multivalued dependency (EMVD), which is also introduced by Fagin, is an MVD that holds for a projection of an original relation on the subset of attributes of the relation. The properties of EMVD's are not well known although EMVD's play an important role in designing relation schemata by Fagin's decomposition approach. Our study in this paper is motivated from the following problems: (a) Since the validity of an MVD depends on an underlying set of attributes, it is not so easy to specify valid" MVD's for a relation with many attributes. (b) There has not been a useful tool to analyze whether or not a set of relation schemata obtained by Fagin's decomposition approach can represent the same data and the same dependencies of an initial relation schema. Our standpoint is to handle these problems by studying the properties of EMVD's. The main results of this paper are the following: (1) A basic theorem about the interaction between MVD's and EMVD's is provided. Several useful inference rules for MVD's and EMVD's are derived from this theorem. (2) A marked Hasse diagram called a dependency diagram is introduced to investigate the interections between MVD's and EMVD's. (3) We provide some conditions for an MVD or a set of MVD's to be invariant under the addition or deletion of attributes. (4) Some useful equivalence relationships between two dependency sets including MVD's and EMVD's are provided. We also provide some conditions to represent a given dependency set in a reduced form.

• Publication: IEICE TRANSACTIONS on transactions Vol.E62-E No.8 pp.536-543
• Publication Date: 1979/08/25
• Type of Manuscript: PAPER
• Category: Data Processing

Authors

Katsumi TANAKA
Yahiko KAMBAYASHI
Shuzo YAJIMA

Keyword