Modern analytics involve computations over enormous numbers of data records. The volume of data and the stringent response-time requirements place increasing emphasis on the efficiency of approximate query processing. A major challenge over the past years has been the construction of synopses that provide a deterministic quality guarantee, often expressed in terms of a maximum error metric. By approximating sharp discontinuities, wavelet decomposition has proved to be a very effective tool for data reduction. However, existing wavelet thresholding schemes that minimize maximum error metrics are constrained with impractical complexities for large datasets. Furthermore, they cannot efficiently handle the multi-dimensional version of the problem. In order to provide a practical solution, we develop parallel algorithms that take advantage of key-properties of the wavelet decomposition and allocate tasks to multiple workers. To that end, we present (i) a general framework for the parallelization of existing dynamic programming algorithms, (ii) a parallel version of one such DP algorithm, and (iii) two highly efficient distributed greedy algorithms that can deal with data of arbitrary dimensionality. Our extensive experiments on both real and synthetic datasets over Hadoop show that the proposed algorithms achieve linear scalability and superior running-time performance compared to their centralized counterparts.