Space Efficient Algorithms for the Burrows-Wheeler Backtransformation

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 < 2 32. 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 < 2 32, 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.