Manipulating spatial data in constraint databases

Abstract

Constraint databases have recently been proposed as a powerful framework to model and retrieve spatial data. In a constraint database, a spatial object is represented as a quantifier free conjunction of (usually linear) constraints, called generalized tuple. The set of solutions of such quantifier free formula represents the set of points belonging to the extension of the object. The relational algebra can be easily extended to deal with generalized relations. However, such algebra has some limitations when it is used for modeling spatial data. First of all, there is no explicit way to deal with the set of points representing a spatial object as a whole. Rather, only point-based computations can be performed using this algebra. Second, practical constraint database languages typically use linear constraints. This allows to use efficient algorithms but, at the same time, some interesting queries cannot be represented (for example, the distance between two objects cannot be computed). Finally, no update language for spatial constraint databases has been defined yet. The aim of this paper is to overcome some of the previous limitations. In particular, we extend the model and the algebra to directly deal with the set of points represented by a generalized tuple (a spatial object), retaining at the same time the ability of expressing all computations that can be expressed by other constraint database languages. Moreover, we discuss the introduction of external functions in the proposed algebra, in order to cover all the functionalities that cannot be expressed in the chosen logical theory. Finally, we propose an update language for spatial constraint databases, based on the same principles of the algebra.