Self-spacial join selectivity estimation using fractal concepts

Abstract

The problem of selectivity estimation for queries of nontraditional databases is still an open issue. In this article, we examine the problem of selectivity estimation for some types of spatial queries in databases containing real data. We have shown earlier [Faloutsos and Kamel 1994] that real point sets typically have a nonuniform distribution, violating consistently the uniformity and independence assumptions. Moreover, we demonstrated that the theory of fractals can help to describe real point sets. In this article we show how the concept of fractal dimension, i.e., (noninteger) dimension, can lead to the solution for the selectivity estimation problem in spatial databases. Among the infinite family of fractal dimensions, we consider here the Hausdorff fractal dimension D 0 and the "Correlation" fractal dimension D 2 . Specifically, we show that (a) the average number of neighbors for a given point set follows a power law, with D 2 as exponent, and (b) the average number of nonempty range queries follows a power law with E Ϫ D 0 as exponent (E is the dimension of the embedding space). We present the formulas to estimate the selectivity for "biased" range queries, for self-spatial joins, and for the average number of nonempty range queries. The result of some experiments on real and synthetic point sets are shown. Our formulas achieve very low relative errors, typically about 10%, versus 40%-100% of the formulas that are based on the uniformity and independence assumptions.

A generic framework for handling uncertain data with local correlations

“…1 For the pdf representation, we can first obtain random samples from pdf(s) via sampling techniques, and then apply our proposed methodology in this paper. 2 If samples are not available, then domain-specific knowledge in real applications (e.g., [5]) can help model the data uncertainty. 3 Here, we assume that LCS(oi) excludes oi, though oi correlates with itself.…”

“…In other words, in a hypersphere centered at q with radius dist(q, Co i ), there exists only one center point Co i . Thus, we apply the power law [2], resulting in:…”

“…Cost cost f ilter is proportional to the number of possible candidate pivots within the region where LC-PNN candidates reside. By applying the power law [2], we can obtain: …”

Approximation techniques for spatial data

“…Faloutsos et al [15] and Belussi and Faloutsos [8] propose parametric methods for estimating the selectivity of ε-(self-) joins of point-sets. For self-similar data sets they achieve good approximations using power laws and fractal dimensionality.…”

Analysis of predictive spatio-temporal queries

“…Theodoridis et al [1998Theodoridis et al [ , 2000 utilize this equation for nonuniform data, by considering bucket pairs from the histograms of the join datasets (in a way similar to Figure 1). An et al [2001] maintains statistics about objects' edges and corners, while Belussi and Faloutsos [1998] and Faloutsos et al [2000] apply power laws. Sun et al [2002a] studies join selectivity restricted in a part of the data-space, and Mamoulis and Papadias [2001] addresses multi-way spatial join selectivity.…”