Abstract
Histograms and Wavelet synopsis provide useful tools in query optimization and approximate query answering. Traditional histogram construction algorithms, such as V–Optimal for relative error, use wavelet approximation schemes with deterministic or probabilistic thresholding. The deterministic scheme suggests heuristics that are not guaranteed to minimize relative error. The probabilistic scheme proposes a complicated optimization, and proceeds to provide an approximation that holds in expectation only. Expected guarantees are not sufficient for minimizing maximum error objective. The chapter also presents optimal as well as faster approximation algorithms with several relative error measures. A comprehensive analysis of time and space complexities of these algorithms with synthetic and real-life data sets analyzes the effectiveness of the algorithms in providing significantly more accurate results compared to the wavelet based methods and V–Optimal algorithm.
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