Geometric BWT: Compressed Text Indexing via Sparse Suffixes and Range Searching

We introduce a new variant of the popular Burrows-Wheeler transform (BWT), called Geometric Burrows-Wheeler Transform (GBWT), which converts a text into a set of points in 2-dimensional geometry. We also introduce a reverse transform, called Points2Text, which converts a set of points into text. Using these two transforms, we show strong equivalence between data structural problems in geometric range searching and text pattern matching. This allows us to apply the lower bounds known in the field of orthogonal range searching to the problems in compressed text indexing. In addition, we give the first succinct (compact) index for I/O-efficient pattern matching in external memory, and show how this index can be further improved to achieve higher-order entropy compressed space.