Efficient Haar + synopsis construction for the maximum absolute error measure

Abstract

Several wavelet synopsis construction algorithms were previously proposed based on dynamic programming for unrestricted Haar wavelet synopses as well as Haar + synopses. However, they find an optimal synopsis for every incoming value in each node of a coefficient tree, even if different incoming values share an identical optimal synopsis. To alleviate the limitation, we present novel algorithms, which keep only a minimal set of the distinct optimal synopses in each node of the tree, for the error-bounded synopsis problem. Furthermore, we propose the methods to restrict coefficient values to be considered to compute the optimal synopses in each node. In addition, by partitioning all optimal synopses in each node into a set of groups, such that every group can be represented by a compact representation, we significantly improve the performance of the proposed algorithms.