Region-Based Query Languages for Spatial Databases in the Topological Data Model

Abstract

We consider spatial databases in the topological data model, i.e., databases that consist of a finite number of labeled regions in the real plane. Such databases partition the plane further into elementary regions. We propose a first-order language, which uses elementary-region variables and label variables, to query spatial databases. All queries expressible in this first-order logic are topological\/ and they can be evaluated in polynomial time. Furthermore, the proposed language is powerful enough to distinguish between any two spatial databases that are not topologically equivalent. This language does not allow the expression of all computable topological queries, however, as is illustrated by the connectivity query. We also study some more powerful extensions of this first-order language, e.g., with a while-loop. In particular, we describe an extension that is sound and computationally complete for the topological queries on spatial databases in the topological data model.