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 flnds 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 ¡ N2M logM ¢ and its space complexity is O ¡ N2M ¢ . In this paper we improve the time and space complexities by a factor of M, reducing the running time to O ¡ N2 logM ¢ and the space requirement to O ¡ N2 ¢ . As in (4) no experimental results were shown, we present experimental comparison between the accuracy of the GK synopsis with other wavelet syn- opses, 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 range- queries, built on the raw data as well as over the preflx-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.