RLZ-r and LZ-End-r: Enhancing Move-r

TL;DR

This paper enhances the r-index and Move-r data structures for string pattern matching by integrating compressed suffix arrays using Relative Lempel-Ziv and LZ-End schemes, significantly improving locate query speed and offering new space-performance trade-offs.

Contribution

It introduces the use of compressed suffix arrays with two schemes to improve locate query efficiency in r-index and Move-r, providing practical trade-offs between index size and query speed.

Findings

Locate queries are significantly faster with the new methods.

Different compression schemes offer distinct trade-offs.

Performance improvements are notable for patterns with many occurrences.

Abstract

In pattern matching on strings, a locate query asks for an enumeration of all the occurrences of a given pattern in a given text. The r-index [Gagie et al., 2018] is a recently presented compressed self index that stores the text and auxiliary information in compressed space. With some modifications, locate queries can be answered in optimal time [Nishimoto & Tabei, 2021], which has recently been proven relevant in practice in the form of Move-r [Bertram et al., 2024]. However, there remains the practical bottleneck of evaluating function $\Phi$ for every occurrence to report. This motivates enhancing the index by a compressed representation of the suffix array featuring efficient random access, trading off space for faster answering of locate queries [Puglisi & Zhukova, 2021]. In this work, we build upon this idea considering two suitable compression schemes: Relative Lempel-Ziv [Kuruppu et al., 2010], improving the work by Puglisi and Zhukova, and LZ-End [Kreft & Navarro, 2010], introducing a different trade-off where compression is better than for Relative Lempel-Ziv at the cost of slower access times. We enhance both the r-index and Move-r by the compressed suffix arrays and evaluate locate query performance in an experiment. We show that locate queries can be sped up considerably in both the r-index and Move-r, especially if the queried pattern has many occurrences. The choice between two different compression schemes offers new trade-offs regarding index size versus query performance.