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

Patrick Dinklage; Johannes Fischer; Lukas Nalbach; Jan Zumbrink

Home/Archive/arXiv

arXiv · 2507.17300

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

Patrick Dinklage·Johannes Fischer·Lukas Nalbach·Jan Zumbrink

View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

cs.DS

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Patrick Dinklage, Johannes Fischer, Lukas Nalbach, Jan Zumbrink. 2025-07-23. RLZ-r and LZ-End-r: Enhancing Move-r. https://arxiv.org/abs/2507.17300

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Quasi-Monte Carlo Beyond Hardy-Krause II: $(1 + \varepsilon)n$ Samples Suffice

Numerical integration studies how well one can estimate the integral of a function $f$ over $[0,1)^d$ using $n$ sample points. The two classical methods, Monte Carlo (MC) and quasi-Monte Carlo (QMC), have complementary strengths and weaknesses, and a fundamental question is to design an approach that combines the benefits of both. Recently, building on the transference principle in discrepancy theory, Bansal and Jiang~\cite{BJ25a} gave a randomized QMC method that bridges MC and QMC guarantees using only i.i.d.\ samples. Their method also goes beyond the classical Koksma--Hlawka inequality: it achieves integration error $\widetilde{O}_d(\sigma_{\mathsf{SO}}(f)/n)$, where the smoothed-out variation $\sigma_{\mathsf{SO}}(f)$ can be substantially smaller than the Hardy--Krause variation that governs the classical bound. However, their algorithm requires $n^2$ i.i.d.\ samples as input, and this quadratic blowup is inherent to any method based on the transference principle. In this work, we bypass the quadratic blowup: for any constant $\varepsilon > 0$, we show that $(1+\varepsilon)n$ i.i.d.\ samples suffice to both obtain the beyond-Hardy--Krause guarantee of~\cite{BJ25a}, resolving an open problem posed there, and to produce low-discrepancy point sequences. Our algorithms are variants of the online Haar-thinning method of Dwivedi, Feldheim, Gurel-Gurevich, and Ramdas~\cite{DFG+19}.

cs.DS↗

arXiv2026

A deterministic $(1+\varepsilon)^n$ approximation for the permanent of a nonnegative matrix

For every fixed $0<\varepsilon\le1$, we give a deterministic strongly polynomial algorithm that, given a nonnegative matrix $A\in\mathbb{R}_{\ge0}^{n\times n}$, returns $Q$ satisfying $\operatorname{per} A\le Q\le(1+\varepsilon)^n\operatorname{per} A$.

cs.DS↗

arXiv2026

Single-Exponential Algorithms and a Polynomial Kernel for Strong Connectivity Augmentation

Strong Connectivity Augmentation (SCA) asks whether a directed acyclic graph can be made strongly connected by adding at most $k$ prescribed links whose total weight is within a given budget. Klinkby, Misra, and Saurabh (SODA 2021) gave an $O^*(2^{O(k\log k)})$-time algorithm and asked whether the problem admits a single-exponential parameterized algorithm and a polynomial kernel. We answer both questions affirmatively: SCA can be solved in $O^*(9^k)$ time and admits a polynomial kernel with $O(k^4)$ vertices and $O(k^{16})$ bits. For unweighted SCA, we obtain $O^*(4^k)$ time and a kernel with $O(k^3)$ vertices. Our algorithms are based on a particularly simple reduction to Strongly Connected Spanning Subgraph with two edge costs.

cs.DS↗