Indexing constraint databases by using a dual representation

Linear constraint databases are a powerful framework to model spatial and temporal data. The use of constraint databases should be supported by access data structures that make effective use of secondary storage and reduce query processing time. Such structures should be able to store both finite and infinite objects and perform both containment (ALL) and intersection (EXIST) queries. As standard indexing techniques have certain limitations in satisfying such requirements, we employ the concept of geometric duality for designing new indexing techniques. In (Bertino et al., 1997) we have used the dual transformation for polyhedra to develop a dynamic optimal indexing solution based on B⁺-trees, to detect all objects contained in or intersecting a given half-plane, when the angular coefficient belongs to a predefined set. We extend the previous solution to allow angular coefficients to take any value. We present two approximation techniques for the dual representation of spatial objects, based on B⁺-trees. The techniques handle both finite and infinite objects and process both ALL and EXIST selections in a uniform way. We show the practical applicability of the proposed techniques by an experimental comparison with respect to R⁺-trees