On Approximate Algorithms for Distance-Based Queries using R-trees

Abstract

In modern database applications the similarity or dissimilarity of complex objects is examined by performing distance-based queries (DBQs) on data of high dimensionality. The R-tree and its variations are commonly cited multidimensional access methods that can beused for answering such queries. Although the related algorithms work well for low-dimensional data spaces, their performance degrades as the number of dimensions increases (dimensionality curse). In order to obtain acceptable response time in high-dimensional data spaces, algorithms that obtain approximate solutions can be used. Approximation techniques, like N-consider (based on the tree structure), α-allowance and e-approximate (based on distance), or Time-consider (based on time) can be applied in branch-and-bound algorithms for DBQs inorder to control the trade-off between cost and accuracy of the result. In this paper, we improve previous approximate DBQ algorithms by applying a combination of the approximation techniques in the same query algorithm (hybrid approximation scheme). We investigate the performance of these improvements for one of the most representative DBQs (the K-closest pairs query, K-CPQ) in high-dimensional data spaces, as well as the influence of the algorithmic parameters on the control of the trade-off between the response time and the accuracy of the result. The outcome of the experimental evaluation, using synthetic and real datasets, is the derivation of the outperforming DBQ approximate algorithm for large high-dimensional point datasets.