An algorithm for horizontal decompositions

Abstract

In the study of the Relational Database Model, the vertical decomposition of relations into projections of these relations has been emphasized ever since its introduction in [3]. The presence (in the ‘real world’) of a constraint, e.g., a functional dependency, is indispensable for the use of vertical decompositions. However, in many applications it is necessary to allow violation of the desired constraints. In this paper an ‘exception handling mechanism’ is described which is based on the horizontal decomposition of a relation into restrictions of this relation, using the union as composition operator. By separating the ‘exceptions’ from the main part of the relation, the desired functional dependency is preserved in this main part. Hence, vertical decomposition of (part of) the relation becomes possible after performing the horizontal decomposition. To illustrate the use of horizontal decompositions consider a (small part of a) database PARKING (E, PB, C), representing Employees hiring Parking Boxes for their Car(s). Most employees only have one car and only hire one parking box. This, however, is not a constraint that might be used for any optimization of the database. The horizontal decomposition, described below, selects a (large) subrelation in which every employee only has one car and only hires one box. The latter constraint (a functional dependency) is very useful for optimizing the database structure.