Uniform generation in spatial constraint databases and applications

We study the efficient approximation of queries in linear constraint databases using sampling techniques. We define the notion of an almost uniform generator for a generalized relation and extend the classical generator of Dyer, Frieze and Kannan for convex sets to the union and the projection of relations. For the intersection and the difference, we give sufficient conditions for the existence of such generators. We show how such generators give relative estimations of the volume and approximations of generalized relations as the composition of convex hulls obtained from the samples.