Degrees of Monotonicity of Spatial Transformations

We consider spatial databases that can be defined in terms of polynomial inequalities, and we are interested in monotonic transformations of spatial databases. We investigate a hierarchy of monotonicity classes of spatial transformations that is determined by the number of degrees of freedom of the transformations. The result of a monotonic transformation with k degrees of freedom on a spatial database is completely determined by its result on subsets of cardinality at most k of the spatial database. The result of a transformation in the largest class of the hierarchy on a spatial database is determined by its result on arbitrary large subsets of the database. The latter is the class of all the monotonic spatial transformations. We give a sound and complete language for the monotonic spatial transformations that can be expressed in the relational calculus augmented with polynomial inequalities and that belong to a class with a finite number of degrees of freedom. In particular, we sh...

• Type: Conference
• Year: 1997
• Where: DBPL
• Authors: Bart Kuijpers
• Keywords: Database, DBPL 1997, Spatial, Spatial Database, Spatial Transformations