Constraint database query evaluation with approximation

Considers the problem of solving a large number of simple systems of linear constraints. This problem occurs in the context of constraint databases. The developed methodology is based on a hierarchical evaluation of the constraints, which are first simplified and replaced by approximations. We focus on systems of linear constraints over the reals, which model spatial objects, and we consider both geometric and topological approximations, defined with very simple constraints. We show that these constraints can be used either to solve the initial systems, or at least to filter out unsatisfiable systems. The main contribution of the paper is the development of a set of rewriting rules that allow the transformation of spatial object queries into equivalent ones that make use of the approximation, reducing the query evaluation cost.