r*-indexing

TL;DR

This paper introduces a space-efficient indexing method for texts based on the r*-index, enabling fast pattern matching and occurrence reporting using space proportional to the combined complexity measures of runs in the BWT and LZ77 phrases.

Contribution

The authors present a novel indexing structure that combines run-length and LZ77 measures to achieve efficient pattern search within compressed space.

Findings

Index size is $O(r^* ext{log}(n/r^*) + z ext{log} n)$ bits.

Pattern occurrences can be reported in $O(m ext{log} n + occ ext{log}^ ext{ε} n)$ time.

Supports locating the leftmost and rightmost pattern occurrences efficiently.

Abstract

Let $T [1..n]$ be a text over an alphabet of size $\sigma \in \mathrm{polylog} (n)$, let $r^*$ be the sum of the numbers of runs in the Burrows-Wheeler Transforms of $T$ and its reverse, and let $z$ be the number of phrases in the LZ77 parse of $T$. We show how to store $T$ in $O (r^* \log (n / r^*) + z \log n)$ bits such that, given a pattern $P [1..m]$, we can report the locations of the $\mathrm{occ}$ occurrences of $P$ in $T$ in $O (m \log n + \mathrm{occ} \log^\epsilon n)$ time. We can also report the position of the leftmost and rightmost occurrences of $P$ in $T$ in the same space and $O (m \log^\epsilon n)$ time.