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Histograms and Wavelet synopses provide useful tools in query optimization and approximate query answering. Traditional histogram construction algorithms, e.g., V-Optimal, use error measures which are the sums of a suitable function, e.g., square, of the error at each point. Although the best-known algorithms for solving these problems run in quadratic time, a sequence of results have given us a linear time approximation scheme for these algorithms. In recent years, there have been many emerging applications where we are interested in measuring the maximum (absolute or relative) error at a point. We show that this problem is fundamentally different from the other traditional {\rm{non}}{\hbox{-}}\ell_\infty error measures and provide an optimal algorithm that runs in linear time for a small number of buckets. We also present results which work for arbitrary weighted maximum error measures.
Histograms, algorithms.
Sudipto Guha, Kyuseok Shim, "A Note on Linear Time Algorithms for Maximum Error Histograms", IEEE Transactions on Knowledge & Data Engineering, vol. 19, no. , pp. 993-997, July 2007, doi:10.1109/TKDE.2007.1039
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