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- W72506033 abstract "The best compression algorithm today for English text is based on the Burrows-Wheeler transform. This algorithm (whose common implementation is bzip2) consists of the following three essential steps: 1) Obtain the Burrows-Wheeler transform of the text, 2) Convert the transform into a sequence of integers using the move-to-front algorithm, 3) Encode the integers using arithmetic code or any order-0 encoding (possibly with run length encoding). In this paper we achieve a strong bound on the worst-case compression ratio of this algorithm, that is signiflcantly better than bounds known to date and is obtained via simple analytical techniques. Speciflcally, for any input string s, and „ > 1, the length of the compressed string is bounded by „¢jsjHk(s) + log(‡(„))¢jsj + gk where Hk is the k-th order empirical entropy, gk is a constant depending only on k and on the size of the alphabet, and ‡(„) = 1 1„ + 1 2„ + : : : is the standard zeta function. In fact we prove a stronger result: That this bound without the additive term gk holds when we replace Hk(s) by the sum of the logarithms of the integers obtain by the move-to-front encoding of the transform. This reflned bound is tight and close to the actual compression achieved in practice. To obtain this result we prove a tight result on the compressibility of integer sequences, which is of independent interest." @default.
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- W72506033 date "2005-01-01" @default.
- W72506033 modified "2023-09-27" @default.
- W72506033 title "The Burrows-Wheeler compression algorithm is even better than what you have thought" @default.
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