Space Efficient Linear Time Computation of the Burrows and Wheeler-Transformation

Abstract

In [4] a universal data compression algorithm (BW-algorithm, for short) is described which achieves compression rates that are close to the best known rates achieved in practice. Due to its simplicity, the algorithm can be implemented with relatively low complexity. Recently [2] modified the BW-algorithm to improve the compression rate even further. For a thorough discussion on the information theoretic background of the BW-algorithm and more references, see [1]. The most time and space consuming part of the BW-algorithm is the Burrows and Wheeler-Transformation (BWT, for short), which permutes the input string in such a way that characters with a similar context are grouped together. In [4], it was observed that for an input string of length n, this transformation can be computed in O(n) time and space using suffix trees. However, suffix trees have a reputation of being very greedy for space, and therefore most researchers resorted to alternative non-linear methods for computing the BWT: The algorithm of [9] runs in O(n log n) worst case time and it requires 8n bytes of space. The algorithm of [3] is based on Quicksort. It is fast on average, but the worst case running time is O(n ²). The Benson-Sedgewick algorithm requires 4n bytes. Its running time can be improved in practice, for the cost of 4n extra bytes. Recently, [11] showed how to combine the Manber-Myers Algorithm with the Bentley-Sedgewick Algorithm, to achieve a method running in O(n log n) worst case time and using 9n bytes.