Lightweight algorithms for constructing and inverting the BWT of string collections

Recent progress in the field of DNA sequencing motivates us to consider the problem of computing the Burrows–Wheeler transform (BWT) of a collection of strings. A human genome sequencing experiment might yield a billion or more sequences, each 100 characters in length. Such a dataset can now be generated in just a few days on a single sequencing machine. Many algorithms and data structures for compression and indexing of text have the BWT at their heart, and it would be of great interest to explore their applications to sequence collections such as these. However, computing the BWT for 100 billion characters or more of data remains a computational challenge. In this work we address this obstacle by presenting a methodology for computing the BWT of a string collection in a lightweight fashion. A first implementation of our algorithm needs O ( m log m ) bits of memory to process m strings, while a second variant makes additional use of external memory to achieve RAM usage that is constant with respect to m and negligible in size for a small alphabet such as DNA. The algorithms work on any number of strings and any size. We evaluate our algorithms on collections of up to 1 billion strings and compare their performance to other approaches on smaller datasets. We take further steps toward making the BWT a practical tool for processing string collections on this scale. First, we give two algorithms for recovering the strings in a collection from its BWT. Second, we show that if sequences are added to or removed from the collection, then the BWT of the original collection can be efficiently updated to obtain the BWT of the revised collection.