Approximation techniques for indexing two-dimensional constraint databases

Constraint databases have recently been proposed as a powerful framework to model and retrieve spatial 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. In this paper, we consider the indexing problem for objects represented by conjunctions of two-variable linear constraints and we analyze the problem of determining all generalized tuples whose extension intersects or is contained in the extension of a given half-plane. In an earlier paper we have shown that both selection problems can be reduced to a point location problem by using a dual transformation. If the angular coefficient of the half-plane belongs to a predefined set, we have proved that a dynamic optimal indexing solution, based on B⁺-trees, exists. In this paper we propose two approximation techniques that can be used to find the result when the angular coefficient does not belong to the predefined set. We also experimentally compare the proposed techniques with R-trees