Burrows-Wheeler Transform

The Burrows-Wheeler transform is a technique used for the lossless compression of data. It is the algorithmic core of the tool bzip2 which has become a standard for the creation and distribution of compressed archives. Before the introduction of the Burrows-Wheeler transform, the field of lossless data compression was dominated by two approaches (see [2,21] for comprehensive surveys). The first approach dates back to the pioneering works of Shannon and Huffman, and it is based on the idea of using shorter codewords for the more frequent symbols. This idea has originated the techniques of Huffman and arithmetic coding and, more recently, the PPM (prediction by partial matching) family of compression algorithms. The second approach originated from the works of Lempel and Ziv and is based on the idea of adaptively building a dictionary and representing the input string as a concatenation of dictionary words. The best-known compressors based on this approach form the so-called ZIP-family; they have been the standard for several years and are available on essentially any computing platform (e.g., gzip, zip, winzip, just to cite a few). The Burrows-Wheeler transform introduced a completely new approach to lossless data compression based on the idea of transforming the input to make it easier to compress. In the authors’ words: “(this) technique [. . . ] works by applying a reversible transformation to a block of text to make redundancy in the input more accessible to simple coding schemes” [5, Sect. 7]. Not only has this technique produced some state-of-the-art compressors, but it also originated the field of compressed indexes [20] and it has been successfully extended to compress (and index) structured data such as XML files [11] and tables [22].