Linearization and completeness results for terminating transitive closure queries on spatial databases

Abstract

We study queries to spatial databases, where spatial data are modelled as semialgebraic sets, using the relational calculus with polynomial inequalities as a basic query language. We work with the extension of the relational calculus with terminating transitive closures. The main result is that this language can express the linearization of semi-algebraic databases. We also show that the sublanguage with linear inequalities only can express all computable queries on semi-linear databases. As a consequence of these results, we obtain a completeness result for topological queries on semi-algebraic databases.