Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2002.09041

Compressed Data Structures for Binary Relations in Practice

Carlos Quijada-Fuentes·Miguel R. Penabad·Susana Ladra·Gilberto Gutiérrez
View original source ↗Read source document ↗Export metadata ↓

Abstract

Binary relations are commonly used in Computer Science for modeling data. In addition to classical representations using matrices or lists, some compressed data structures have recently been proposed to represent binary relations in compact space, such as the $k^2$-tree and the Binary Relation Wavelet Tree (BRWT). Knowing their storage needs, supported operations and time performance is key for enabling an appropriate choice of data representation given a domain or application, its data distribution and typical operations that are computed over the data. In this work, we present an empirical comparison among several compressed representations for binary relations. We analyze their space usage and the speed of their operations using different (synthetic and real) data distributions. We include both neighborhood and set operations, also proposing algorithms for set operations for the BRWT, which were not presented before in the literature. We conclude that there is not a clear choice that outperforms the rest, but we give some recommendations of usage of each compact representation depending on the data distribution and types of operations performed over the data. We also include a scalability study of the data representations.

Explore related subjects

cs.DS

Keep this discovery

BibTeXRIS

Carlos Quijada-Fuentes, Miguel R. Penabad, Susana Ladra, Gilberto Gutiérrez. 2020-02-20. Compressed Data Structures for Binary Relations in Practice. https://doi.org/10.1109/access.2020.2970983

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

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↗