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The Burrows-Wheeler Transform (BWT) is an efficient invertible text transformation algorithm with the properties of tending to group identical characters together in a run, and enabling search of the text. This transformation has extensive uses particularly in lossless compression algorithms, indexing, and within bioinformatics for sequence alignment tasks. There has been recent interest in minimizing the number of identical character runs ($r$) for a transform and in finding useful alphabet orderings for the sorting step of the matrix associated with the BWT construction. This motivates the inspection of many transforms while developing algorithms. However, the full Burrows-Wheeler matrix is $O(n^2)$ space and therefore very difficult to display and inspect for large input sizes. In this paper we present a graphical user interface (GUI) for working with BWTs, which includes features for searching for matrix row prefixes, skipping over sections in the right-most column (the transform), and displaying BWTs while exploring alphabet orderings with the goal of minimizing the number of runs., Comment: 8 pages, 2 figures

The Burrows-Wheeler Transform (BWT) is a string transformation technique widely used in areas such as bioinformatics and file compression. Many applications combine a run-length encoding (RLE) with the BWT in a way which preserves the ability to query the compressed data efficiently. However, these methods may not take full advantage of the compressibility of the BWT as they do not modify the alphabet ordering for the sorting step embedded in computing the BWT. Indeed, any such alteration of the alphabet ordering can have a considerable impact on the output of the BWT, in particular on the number of runs. For an alphabet $\Sigma$ containing $\sigma$ characters, the space of all alphabet orderings is of size $\sigma!$. While for small alphabets an exhaustive investigation is possible, finding the optimal ordering for larger alphabets is not feasible. Therefore, there is a need for a more informed search strategy than brute-force sampling the entire space, which motivates a new heuristic approach. In this paper, we explore the non-trivial cases for the problem of minimizing the size of a run-length encoded BWT (RLBWT) via selecting a new ordering for the alphabet. We show that random sampling of the space of alphabet orderings usually gives sub-optimal orderings for compression and that a local search strategy can provide a large improvement in relatively few steps. We also inspect a selection of initial alphabet orderings, including ASCII, letter appearance, and letter frequency. While this alphabet ordering problem is computationally hard we demonstrate gain in compressibility., Comment: 32 pages, 8 figures