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Maintenance of partial-sum-based histograms

This paper introduces an efficient method for the maintenance of wavelet-based histograms built on partial sums. Wavelet-based histograms can be constructed from either raw data distributions or partial sums. The two construction methods have their own merits. Previous works have only focused on the maintenance of raw-data-based histograms. However it is highly inefficient to apply directly their techniques to partial-sum-based histograms because a single data update would trigger changes of multiple partial sums, which in turn, would trigger large amounts of computation on the changes of the wavelet decomposition. We present a novel technique to compute the effects of data updates on the wavelet decomposition of partial sums. Moreover, we point out some special features of the wavelet decomposition of partial sums and adapt a probabilistic counting technique for the maintenance of partial-sum-based histograms. Experimental results show that our maintenance method is efficient and its accuracy is robust to changing data distributions.