Improved implementation and experimental evaluation of the max-error optimized wavelet synopses

This paper provides an improved implementation of an algorithm for building wavelet synopses for max-error metrics, recently introduced by Garofalakis and Kumar (GK) [4]. Given a storage space of size M , the GK algorithm finds a wavelet synopsis of size M , which minimizes the max (absolute or relative) error, measured over the data values, with respect to any other wavelet synopsis of size M . The running time of the GK algorithm is O ( NM log M ) and its space complexity is O ( NM ) . In this paper we improve the time and space complexities by a factor of M , reducing the running time to O ( N log M ) and the space requirement to O ( N ) . As in [4] no experimental results were shown, we present experimental comparison between the accuracy of the GK synopsis with other wavelet synopses, as well as experimental comparison between the running-time of the original GK algorithm with our improved implementation. We also apply the GK synopsis for rangequeries, built on the raw data as well as over the prefix-sums of the data, and compare it experimentally with other wavelet synopses, demonstrating an interesting similarity to another synopsis that can be computed in linear time.