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On the Compressiveness of the Burrows-Wheeler Transform

Authors Hideo Bannai , Tomohiro I , Yuto Nakashima

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ACM Subject Classification
  • Theory of computation → Data compression
  • Mathematics of computing → Combinatorics on words
Keywords
  • Data Compression
  • Bijective Burrows-Wheeler Transform
  • Fibonacci words

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Abstract

The Burrows-Wheeler transform (BWT) is a reversible transform that converts a string w into another string BWT(w). The size of the run-length encoded BWT (RLBWT) can be interpreted as a measure of repetitiveness in the class of representations called dictionary compression which are essentially representations based on copy and paste operations. In this paper, we shed new light on the compressiveness of BWT and the bijective BWT (BBWT). We first extend previous results on the relations of their run-length compressed sizes r and r_B. We also show that the so-called "clustering effect" of BWT and BBWT can be captured by measures other than empirical entropy or run-length encoding. In particular, we show that BWT and BBWT do not increase the repetitiveness of the string with respect to various measures based on dictionary compression by more than a polylogarithmic factor. Furthermore, we show that there exists an infinite family of strings that are maximally incompressible by any dictionary compression measure, but become very compressible after applying BBWT. An interesting implication of this result is that it is possible to transcend dictionary compression in some cases by simply applying BBWT before applying dictionary compression.

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Hideo Bannai, Tomohiro I, and Yuto Nakashima. On the Compressiveness of the Burrows-Wheeler Transform. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 17:1-17:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.CPM.2025.17

Author Details

Hideo Bannai
  • M&D Data Science Center, Institute of Integrated Research, Institute of Science Tokyo, Japan
Tomohiro I
  • Department of Artificial Intelligence, Kyushu Institute of Technology, Fukuoka, Japan
Yuto Nakashima
  • Department of Informatics, Kyushu University, Fukuoka, Japan

Funding

  • Bannai, Hideo: JSPS KAKENHI Grant Number JP24K02899.
  • I, Tomohiro: JSPS KAKENHI Grant Number JP22K11907 and JP24K02899, JST AIP Acceleration Research JPMJCR24U4.
  • Nakashima, Yuto: JSPS KAKENHI Grant Number JP21K17705 and JP23H04386.

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