XBWT Tricks

The eXtended Burrows-Wheeler Transform (XBWT) is a data transformation introduced in [Ferragina et al., FOCS 2005] to com- pactly represent a labeled tree and simultaneously support navigation and path-search operations over its label structure. A natural application of the XBWT is to store a dictionary of strings. A recent extensive experimental study [Martı́nez-Prieto et al., Informa- tion Systems, 2016] shows that, among the available string dictionary implementations, the XBWT is attractive because of its good tradeoff between small space usage, speed, and support for substring searches. In this paper we further investigate the use of the XBWT for storing a string dictionary. Our first contribution is to show how to add suffix links (aka failure links) to a XBWT string dictionary. For a XBWT dictionary with n internal nodes our suffix links can be traversed in constant time and only take 2n + o(n) bits of space. Our second contribution are practical construction algorithms for the XBWT, including the additional data structure supporting the traver- sal of suffix links. Our algorithms build on the many well engineered algorithms for Suffix Array and BWT construction and offer different tradeoffs between running time and working space.