Compression Sensitivity of the Burrows–Wheeler Transform and Its Bijective Variant

Abstract

The Burrows–Wheeler Transform (BWT) is a widely used reversible data compression method, forming the foundation of various compression algorithms and indexing structures. Prior research has analyzed the sensitivity of compression methods and repetitiveness measures to single-character edits, particularly in binary alphabets. However, the impact of such modifications on the compression efficiency of the bijective variant of BWT (BBWT) remains largely unexplored. This study extends previous work by examining the compression sensitivity of both BWT and BBWT when applied to larger alphabets, including alphabet reordering. We establish theoretical bounds on the increase in compression size due to character modifications in structured sequences such as Fibonacci words. Our devised lower bounds put the sensitivity of BBWT on the same scale as of BWT, with compression size changes exhibiting logarithmic multiplicative growth and square-root additive growth patterns depending on the edit type and the input data. These findings contribute to a deeper understanding of repetitiveness measures.

Keywords

• lossless data compression
• Burrows–Wheeler Transform (BWT)
• bijective BWT (BBWT)
• compression sensitivity
• string transformations
• Fibonacci words