2001/05/01 by Giovanni Manzini · 373 citations
Computer Science · Mathematics · #Algorithm #Algorithms and Data Compression #Block (permutation group theory) #Cellular Automata and Applications #Combinatorics #Compression (physics) #Compression ratio #Computer science #Data compression #Entropy (arrow of time) #Entropy encoding #Lossless compression #Markov chain #Mathematics #Sorting #String (physics) #Theoretical computer science #semigroups and automata theory
paper · doi:10.1145/382780.382782
published in Journal of the ACM 48(3), 407-430 (Association for Computing Machinery)
openalex publication_date 2001/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
The Burrows—Wheeler Transform (also known as Block-Sorting) is at the base of compression algorithms that are the state of the art in lossless data compression. In this paper, we analyze two algorithms that use this technique. The first one is the original algorithm described by Burrows and Wheeler, which, despite its simplicity outperforms the Gzip compressor. The second one uses an additional run-length encoding step to improve compression. We prove that the compression ratio of both algorithms can be bounded in terms of the k th order empirical entropy of the input string for any k ≥ 0. We make no assumptions on the input and we obtain bounds which hold in the worst case that is for every possible input string. All previous results for Block-Sorting algorithms were concerned with the average compression ratio and have been established assuming that the input comes from a finite-order Markov source.