Uniform generation in spatial constraint databases and applications (Extended abstract)

Abstract

We study the e cient approximation of queries in linear constraint databases using sampling techniques. We de ne 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 di erence, we give su cient conditions for the existence of such generators. We show h o w such generators give relative estimations of the volume and approximations of generalized relations as the composition of convex hulls obtained from the samples.