On representing relationships in object oriented databases

Abstract

Things in the real world, which surrounds us, do not come as singularity, rather we find them associated. These relationships occur in various forms, for example a person and a car owned by that very person are things associated via the ownership association. When designing a database for an application, we have to identify and model things pertaining to the application and their relationships. To ease this task, an object­ oriented data model o#ers to model identified things as objects. We model relationships between things as attributes of the corresponding objects. So we introduce for instance for a person and its car objects and define for the ``person'' object an attribute ``owns'' holding an reference to the ``car'' object, or the other way round, i. e., the ``car'' object receives an attribute holding a reference to the person object. This modelling technique finds its limits when three or more things are associated. In this work we give a solution to this problem by using first a data model that directly supports relationships, namely the entity­relationship data model, and then by translating results into an object­oriented data model. We propose a transformation called pivoting to derive di#erent representations from the initial translation results in a systematic way, and we compare the di#erent representations with respect to their quality. To measure the quality, we give rigorous and precise quality measurements. To do so, we need and subsequently define a formal object­oriented data model and a formal way to tell whether two representations represent the same section of the real world. Two quality indicators are used, redundancy and enforcement costs. Redundancy means that we cannot remove any data from a model instance without losing informa­ tion, while enforcement costs are the costs that entail from the enforcement of semantic constraints.