The myriad virtues of Wavelet Trees

  • Authors:
  • Paolo Ferragina;Raffaele Giancarlo;Giovanni Manzini

  • Affiliations:
  • Dipartimento di Informatica, Università di Pisa, Italy;Dipartimento di Matematica ed Applicazioni, Università di Palermo, Italy;Dipartimento di Informatica, Università del Piemonte Orientale, Via Bellini, 25g, 15100 Alessandria, Italy

  • Venue:
  • Information and Computation
  • Year:
  • 2009

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Abstract

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).