Hierarchical Optimization of Linear Constraint Processing

. We consider the problem of solving a large number of simple systems of constraints. This problem occurs in the context of databases with very large collections of data while the constraints are over a small number of variables. The methodology we develop is based on a hierarchical evaluation of the constraints which are first simplified, and replaced by constraints approximating the initial ones. We focus on systems of linear constraints over the reals, which model spatial objects, and 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. More generally, we consider the manipulation of the spatial objects with first-order queries. We show how the queries can be evaluated by taking advantage of the approximations. In general, it is undecidable if a query can be completely answered on approximated data. The ..