Processing Distance-Based Queries in Multidimensional Data Spaces Using R-trees

Abstract

In modern database applications the similarity, or dissimilarity of data objects is examined by performing distance-based queries (DBQs) on multidimensional data. The R-tree and its variations are commonly cited multidimensional access methods. In this paper, we investigate the performance of the most representative distance-based queries in multidimensional data spaces, where the point datasets are indexed by tree-like structures belonging to the R-tree family. In order to perform the K-nearest neighbor query (K-NNQ) and the K-closest pair query (K-CPQ), non-incremental recursive branch-and-bound algorithms are employed. The K-CPQ is shown to be a very expensive query for datasets of high cardinalities that becomes even more costly as the dimensionality increases. We also give ⇔-approximate versions of DBQ algorithms that can be performed faster than the exact ones, at the expense of introducing a distance relative error of the result. Experimentation with synthetic multidimensional point datasets, following Uniform and Gaussian distributions, reveals that the best index structure for K-NNQ is the X-tree. However, for K-CPQ, the R*-tree outperforms th e X-tree in respect to the response time and the number of disk accesses, when an LRU buffer is used. Moreover, the application of the ⇔-approximate technique on the recursive K-CPQ algorithm leads to acceptable approximations of the result quickly, although the tradeo. between cost and accuracy cannot be easily controlled by the users.

The author has been partially supported by the Spanish CICYT (project TIC 2002- 03968).