Backwards Search in Context Bound Text Transformations

The Burrows-Wheeler Transform (BWT) is the basis for many of the most effective compression and self-indexing methods used today. A key to the versatility of the BWT is the ability to search for patterns directly in the transformed text. A backwards search for a pattern P can be performed on a transformed text by iteratively determining the range of suffixes that match P. The search can be further enhanced by constructing a wavelet tree over the output of the BWT in order to emulate a suffix array. In this paper, we investigate new algorithms for search derived from a variation of the BWT whereby rotations are only sorted to a depth k, commonly referred to as a context bound transform. Interestingly, this BWT variant can be used to mimic a k-gram index, which are used in a variety of applications that need to efficiently return occurrences in text position order. In this paper, we present the first backwards search algorithms on the k-BWT, and show how to construct a self-index containing many of the attractive properties of a k-gram index.