Wavelet Synopsis: Setting Unselected Coefficients to Zero Is Not Optimal
Histogram and Wavelet synopses provide useful tools in query optimization and approximate query answering. Traditional wavelet synopsis construction algorithms treat the construction algorithms as the wavelet coefficients selection problem which is called Coefficient Thresholding. However, all these algorithms just focus on the selection of best wavelet coefficients but deal with the unselected ones naively (just setting them to zero). A key problem is whether it can achieve the optimum of error when the unselected ones are set to one single value: zero. In this paper, we consider a novel Wavelet-based Synopsis construction for the known L2 error measure which can handle the unselected wavelet coefficients effectively. We provide a comprehensive theoretical analysis and demonstrate the effectiveness of these algorithms in providing more optimal error significantly through synthetic data sets.
Keywordsquery optimization data reduction wavelet synopsis error measure
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