Abstract
Wavelet Trees have been introduced in [Grossi, Gupta and Vitter, SODA ’03] and have been rapidly recognized as a very flexible tool for the design of compressed full-text indexes and data compressors. Although several papers have investigated the beauty 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 complete theoretical analysis of a wide class of compression algorithms based on Wavelet Trees. We also show how to improve their asymptotic performance by introducing a novel framework, called Generalized Wavelet Trees, that aims for the best combination of binary compressors (like, Run-Length encoders) versus non-binary compressors (like, Huffman and Arithmetic encoders) and Wavelet Trees of properly-designed shapes. As a corollary, we prove high-order entropy bounds for the challenging combination of Burrows-Wheeler Transform and Wavelet Trees.
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References
Abel, J.: Improvements to the Burrows-Wheeler compression algorithm: After BWT stages, http://citeseer.ist.psu.edu/abel03improvements.html
Arnavut, Z., Magliveras, S.: Block sorting and compression. In: DCC: Data Compression Conference, pp. 181–190. IEEE Computer Society TCC, Los Alamitos (1997)
Burrows, M., Wheeler, D.: A block sorting lossless data compression algorithm. Technical Report 124, Digital Equipment Corporation (1994)
Ferragina, P., Giancarlo, R., Manzini, G., Sciortino, M.: Boosting textual compression in optimal linear time. Journal of the ACM 52, 688–713 (2005)
Ferragina, P., Manzini, G.: Indexing compressed text. Journal of the ACM 52(4), 552–581 (2005)
Foschini, L., Grossi, R., Gupta, A., Vitter, J.: Fast compression with a static model in high order entropy. In: DCC: Data Compression Conference, pp. 62–71. IEEE Computer Society TCC, Los Alamitos (2004)
Grossi, R., Gupta, A., Vitter, J.: High-order entropy-compressed text indexes. In: Proc. 14th Annual ACM-SIAM Symp. on Discrete Algorithms (SODA 2003), pp. 841–850 (2003)
Grossi, R., Gupta, A., Vitter, J.: When indexing equals compression: Experiments on compressing suffix arrays and applications. In: Proc. 15th Annual ACM-SIAM Symp. on Discrete Algorithms (SODA 2004), pp. 636–645 (2004)
Grossi, R., Vitter, J.: Compressed suffix arrays and suffix trees with applications to text indexing and string matching. SIAM Journal on Computing 35, 378–407 (2005)
Mäkinen, V., Navarro, G.: Succinct suffix arrays based on rul-length encoding. Nordic Journal of Computing 12(1), 40–66 (2005)
Manzini, G.: An analysis of the Burrows-Wheeler transform. Journal of the ACM 48(3), 407–430 (2001)
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© 2006 Springer-Verlag Berlin Heidelberg
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Ferragina, P., Giancarlo, R., Manzini, G. (2006). The Myriad Virtues of Wavelet Trees. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds) Automata, Languages and Programming. ICALP 2006. Lecture Notes in Computer Science, vol 4051. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11786986_49
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DOI: https://doi.org/10.1007/11786986_49
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-35904-3
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