REHIST: Relative Error Histogram Construction Algorithms

Histograms and Wavelet synopses provide useful tools in query optimization and approximate query answering. Traditional histogram construction algorithms, such as V-Optimal, optimize absolute error measures for which the error in estimating a true value of 10 by 20 has the same effect of estimating a true value of 1000 by 1010. However, several researchers have recently pointed out the drawbacks of such schemes and proposed wavelet based schemes to minimize relative error measures. None of these schemes provide satisfactory guarantees – and we provide evidence that the difficulty may lie in the choice of wavelets as the representation scheme. In this paper, we consider histogram construction for the known relative error measures. We develop optimal as well as fast approximation algorithms. We provide a comprehensive theoretical analysis and demonstrate the effectiveness of these algorithms in providing significantly more accurate answers through synthetic and real life data sets.