The problem of selectivity estimation for queries of nontraditional databases is still an open issue. In this article, we examine the problem of selectivity estimation for some types of spatial queries in databases containing real data. We have shown earlier [Faloutsos and Kamel 1994] that real point sets typically have a nonuniform distribution, violating consistently the uniformity and independence assumptions. Moreover, we demonstrated that the theory of fractals can help to describe real point sets. In this article we show how the concept of fractal dimension, i.e., (noninteger) dimension, can lead to the solution for the selectivity estimation problem in spatial databases. Among the infinite family of fractal dimensions, we consider here the Hausdorff fractal dimension D 0 and the "Correlation" fractal dimension D 2 . Specifically, we show that (a) the average number of neighbors for a given point set follows a power law, with D 2 as exponent, and (b) the average number of nonempty range queries follows a power law with E Ϫ D 0 as exponent (E is the dimension of the embedding space). We present the formulas to estimate the selectivity for "biased" range queries, for self-spatial joins, and for the average number of nonempty range queries. The result of some experiments on real and synthetic point sets are shown. Our formulas achieve very low relative errors, typically about 10%, versus 40%-100% of the formulas that are based on the uniformity and independence assumptions.

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| Constraint relational databases use constraints to both model and query data. A constraint relation contains a nite set of generalized tuples. Each generalized tuple is represented by a conjunction of constraints on a given logical theory and, depending on the logical theory and the speci c conjunction of constraints, it may possibly represent an innite set of relational tuples. For their characteristics, constraint databases are well suited to model multidimensional and structured data, like spatial and temporal data. The de nition of an algebra for constraint relational databases is important in order to make constraint databases a practical technology. In this paper, we extend the previously de ned constraint algebra (called generalized relational algebra). First, we show that the relational model is not the only possible semantic reference model for constraint relational databases and we show how constraint relations can be interpreted under the nested relational model. Then, we introduce two distinct classes of constraint algebras, one based on the relational algebra, and one based on the nested relational algebra, and we present an algebra of the latter type. The algebra is proved equivalent to the generalized relational algebra when input relations are modi ed by introducing generalized tuple identi ers. However, it is more suitable from a user point of view. Thus, the di erence existing between such algebras is similar to the di erence existing between the relational algebra and the nested relational algebra, dealing with only one level of nesting. We also show how external functions can be added to the proposed algebra. Keywords| Constraints, generalized relations, relational algebra, nested relational algebra, external functions.

Access control is an important component of any database management system. Several access control models have been proposed for conventional databases. However, these models do not seem adequate for geographical databases, due to the peculiarities of geographical data. Previous work on access control models for geographical data mainly concerns raster maps (images). In this paper, we present a discretionary access control model for geographical maps. We assume that each map is composed of a set of features. Each feature is represented in one or more maps by spatial objects, described by means of different spatial properties: geometric properties, describing the shape, extension and location of the objects, and topological properties, describing the topological relationships existing among objects. The proposed access control model allows the security administrator to define authorizations against map objects at a very fine granularity level, taking into account the various spatial representations and the object dimension. The model also supports both positive and negative authorizations as well as different propagation rules that make access control very flexible. Categories and Subject Descriptors