No abstract

Nowadays, there exists an increased interest for the development of systems that are able to store and manipulate spatial information. In this thesis we deal with the modeling and the efficient evaluation of spatial queries in constraint database environments.We start by adopting from the relevant literature the indefinite constraint database model. This proposal can model definite, indefinite, finite and infinite spatial information. Query evaluation over indefinite constraint databases is a hard computational problem. It is therefore important to seek tractable instances of query evaluation. Assuming an arbitrary class of constraints C with some reasonable computational and closure properties we demonstrate various abstract classes of indefinite constraint databases and first-order modal queries for which query evaluation can be done efficiently.Then we try to find appropriate instantiations of the abstract class C among the subclasses of Horn disjunctive linear constraints. We show that the class of UTVPI^ constraints is the larger subclass of Horn disjunctive linear constraints with the property that variable elimination can be performed in polynomial time. In the course of our developments we also provide efficient algorithms for consistency checking and global consistency enforcement. We restate our general results with the abstract class C ranging over the above classes. Our complexity analysis shows that our tractability results identify precisely the boundary between tractable and possibly intractable cases of query evaluation.Given the high interest in spatial reasoning, in this thesis we also concentrate on cardinal direction relations. We give formal definitions for a model capturing cardinal direction relations between extended and connected regions. We extend this basic model in order to accommodate (a) disconnected regions and regions with holes and (b) points, lines and regions with emanating lines. We present the first algorithm for the consistency checking of a set of cardinal direction constraints and prove its correctness. Utilizing the above algorithm we show that the consistency checking of a set of basic (respectively arbitrary) cardinal direction constraints can be performed in polynomial time (respectively is NP-complete). Then we study the composition of two cardinal direction relations and propose an alternative technique for constraint propagation. Finally, we consider the consistency and the composition problems for the extensions of the basic model.