Refining the $r$-index

TL;DR

This paper improves the $r$-index data structure for genomic databases, enabling efficient updates, construction, and matching, thereby enhancing DNA analysis speed and practicality.

Contribution

It strengthens the Toehold Lemma, introduces an efficient update method for the $r$-index, and develops an online LZ77 construction algorithm, with practical validation.

Findings

Efficient $r$-index updates after adding new genomes.

Practical online LZ77 construction from run-length BWT.

Enhanced $r$-index for rapid matching statistics computation.

Abstract

Gagie, Navarro and Prezza's $r$-index (SODA, 2018) promises to speed up DNA alignment and variation calling by allowing us to index entire genomic databases, provided certain obstacles can be overcome. In this paper we first strengthen and simplify Policriti and Prezza's Toehold Lemma (DCC '16; Algorithmica, 2017), which inspired the $r$-index and plays an important role in its implementation. We then show how to update the $r$-index efficiently after adding a new genome to the database, which is likely to be vital in practice. As a by-product of this result, we obtain an online version of Policriti and Prezza's algorithm for constructing the LZ77 parse from a run-length compressed Burrows-Wheeler Transform. Our experiments demonstrate the practicality of all three of these results. Finally, we show how to augment the $r$-index such that, given a new genome and fast random access to the database, we can quickly compute the matching statistics and maximal exact matches of the new genome with respect to the database.