Departmental Papers (CIS)

Date of this Version

July 2007

Document Type

Journal Article


Copyright 2007 IEEE. Reprinted from IEEE Transactions on Knowledge and Data Engineering, Volume 19, Issue 7, July 2007, pages 993-997.

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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 nonl∞ 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



Date Posted: 26 July 2007

This document has been peer reviewed.