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Space Efficient Algorithms for the Burrows-Wheeler Backtransformation

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Abstract

The Burrows-Wheeler transformation is used for effective data compression, e.g., in the well known program bzip2. Compression and decompression are done in a block-wise fashion; larger blocks usually result in better compression rates. With the currently used algorithms for decompression, 4n bytes of auxiliary memory for processing a block of n bytes are needed, 0<n<232. This may pose a problem in embedded systems (e.g., mobile phones), where RAM is a scarce resource.

In this paper we present algorithms that reduce the memory need without sacrificing speed too much.

The main results are: Assuming an input string of n characters, 0<n<232, the reverse Burrows-Wheeler transformation can be done with 1.625 n bytes of auxiliary memory and O(n) runtime, using just a few operations per input character. Alternatively, we can use n/t bytes and 256 t n operations.

The theoretical results are backed up by experimental data showing the space-time tradeoff.

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Authors and Affiliations

  1. Siemens AG, Corporate Technology, 81730, Munich, Germany

    Ulrich Lauther

  2. Eötvös Loránd University, 1117, Budapest, Hungary

    Tamás Lukovszki

Authors
  1. Ulrich Lauther
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  2. Tamás Lukovszki
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Correspondence to Ulrich Lauther.

Additional information

A preminirary version of this paper appeared in the Proceedings of the 13th Annual European Symposium on Algorithms (ESA), LNCS, vol. 3669, pp. 293–304, 2005. This research was done while Tamás Lukovszki was with Siemens AG, Corporate Technology.

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Lauther, U., Lukovszki, T. Space Efficient Algorithms for the Burrows-Wheeler Backtransformation. Algorithmica 58, 339–351 (2010). https://doi.org/10.1007/s00453-008-9269-9

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  • DOI: https://doi.org/10.1007/s00453-008-9269-9

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