The myriad virtues of wavelet trees

Wavelet Trees have been introduced by Grossi et al. in SODA 2003 and have been rapidly recognized as a very flexible tool for the design of compressed full-text indexes and data compression algorithms. Although several papers have investigated the properties and usefulness of this data structure in the full-text indexing scenario, its impact on data compression has not been fully explored. In this paper we provide a throughout theoretical analysis of a wide class of compression algorithms based on Wavelet Trees. Also, we propose a novel framework, called Pruned Wavelet Trees, that aims for the best combination of Wavelet Trees of properly-designed shapes and compressors either binary (like, Run-Length encoders) or non-binary (like, Huffman and Arithmetic encoders).