Topological Transformation Approaches to Database Query Processing

This paper presents a novel approach that transforms the feature space into a new feature space such that a range query in the original space is mapped into an equivalent box query in the transformed space. Since box queries are axis aligned, there are several implementational advantages that can be exploited to speed up the retrieval of query results using R-Tree [9] like indexing schemes. For two dimensional data, the transformation is precise. For larger than two dimensions, we propose a space transformation scheme based on disjoint planer rotation and a new type of query, pruning box query, to get the precise results. Experimental results with large synthetic databases and some real databases show the effectiveness of the proposed transformation scheme. These experimental results have been corroborated with suitable mathematical models. In disjoint planer rotation, additional computation time is required to remove the false positives produced due to the bounding box not being precise. A second topological transformation scheme is presented based on optimized bounding box, which reduces the amount of false positives. The amount of this reduction is more with increasing dimensions. Optimized bounding box for higher dimensions is computed based on a novel approach of simultaneous local optimal projections.