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Wavelet Tree, Part I: A Brief History

Authors Paolo Ferragina , Raffaele Giancarlo , Giovanni Manzini , Giovanna Rosone , Rossano Venturini , Jeffrey Scott Vitter

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Subject Classification

ACM Subject Classification
  • Theory of computation → Data structures design and analysis
  • Theory of computation → Data compression
Keywords
  • Wavelet tree
  • data compression
  • text indexing
  • compressed suffix array
  • Burrows-Wheeler transform
  • rank and select

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Abstract

The Wavelet Tree data structure introduced in Grossi, Gupta, and Vitter [Grossi et al., 2003] is a space-efficient technique for rank and select queries that generalizes from binary symbols to an arbitrary multisymbol alphabet. Over the last two decades, it has become a pivotal tool in modern full-text indexing and data compression because of its properties and capabilities in compressing and indexing data, with many applications to information retrieval, genome analysis, data mining, and web search. In this paper, we survey the fascinating history and impact of Wavelet Trees; no doubt many more developments are yet to come. Our survey borrows some content from the authors' earlier works. 
This paper is divided into two parts: one (this one) giving a brief history of Wavelet Trees, including its varieties and practical implementations, dedicated to this Festschrift’s honoree Roberto Grossi; the second part deals with Wavelet Tree-based text indexing and is included in the Festschrift dedicated to Giovanni Manzini [Ferragina et al., 2025].

Cite As Get BibTex

Paolo Ferragina, Raffaele Giancarlo, Giovanni Manzini, Giovanna Rosone, Rossano Venturini, and Jeffrey Scott Vitter. Wavelet Tree, Part I: A Brief History. In From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 132, pp. 15:1-15:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/OASIcs.Grossi.15

Author Details

Paolo Ferragina
  • Department L'EMbeDS, Sant'Anna School of Advanced Studies, Pisa, Italy
  • Department of Computer Science, University of Pisa, Italy
Raffaele Giancarlo
  • Department of Mathematics and Computer Science, University of Palermo, Italy
Giovanni Manzini
  • Department of Computer Science, University of Pisa, Italy
Giovanna Rosone
  • Department of Computer Science, University of Pisa, Italy
Rossano Venturini
  • Department of Computer Science, University of Pisa, Italy
Jeffrey Scott Vitter
  • Department of Computer Science, Tulane University, New Orleans, LA, USA
  • Department of Computer and Information Science, The University of Mississippi, MS, USA

Acknowledgements

The authors would like to thank Hongwei Huo for helpful comments and figures.

References

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