Selectivity estimators for multidimensional range queries over real attributes

Estimating the selectivity of multidimensional range queries over real valued attributes has significant applications in data exploration and database query optimization. In this paper, we consider the following problem: given a table of d attributes whose domain is the real numbers and a query that specifies a range in each dimension, find a good approximation of the number of records in the table that satisfy the query. The simplest approach to tackle this problem is to assume that the attributes are independent. More accurate estimators try to capture the joint data distribution of the attributes. In databases, such estimators include the construction of multidimensional histograms, random sampling, or the wavelet transform. In statistics, kernel estimation techniques are being used. Many traditional approaches assume that attribute values come from discrete, finite domains, where different values have high frequencies. However, for many novel applications (as in temporal, spatial, and multimedia databases) attribute values come from the infinite domain of real numbers. Consequently, each value appears very infrequently, a characteristic that affects the behavior and effectiveness of the estimator. Moreover, real-life data exhibit attribute correlations that also affect the estimator. We present a new histogram technique that is designed to approximate the density of multidimensional datasets with real attributes. Our technique defines buckets of variable size and allows the buckets to overlap. The size of the cells is based on the local density of the data. The use of overlapping buckets allows a more compact approximation of the data distribution. We also show how to generalize kernel density estimators and how to apply them to the multidimensional query approximation problem. Finally, we compare the accuracy of the proposed techniques with existing techniques using real and synthetic datasets. The experimental results show that the proposed techniques behave more accurately in high dimensionalities than previous approaches.