Robust Learning-Augmented Dictionaries

Ali Zeynali; Shahin Kamali; Mohammad Hajiesmaili

Home/Archive/arXiv

arXiv · 2402.09687

Robust Learning-Augmented Dictionaries

Ali Zeynali·Shahin Kamali·Mohammad Hajiesmaili

View original source ↗Read source document ↗Export metadata ↓

Abstract

We present the first learning-augmented data structure for implementing dictionaries with optimal consistency and robustness. Our data structure, named RobustSL, is a skip list augmented by predictions of access frequencies of elements in a data sequence. With proper predictions, RobustSL has optimal consistency (achieves static optimality). At the same time, it maintains a logarithmic running time for each operation, ensuring optimal robustness, even if predictions are generated adversarially. Therefore, RobustSL has all the advantages of the recent learning-augmented data structures of Lin, Luo, and Woodruff (ICML 2022) and Cao et al. (arXiv 2023), while providing robustness guarantees that are absent in the previous work. Numerical experiments show that RobustSL outperforms alternative data structures using both synthetic and real datasets.

Explore related subjects

cs.DS cs.LG

Keep this discovery

BibTeX RIS

Ali Zeynali, Shahin Kamali, Mohammad Hajiesmaili. 2024-02-15. Robust Learning-Augmented Dictionaries. https://arxiv.org/abs/2402.09687

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↗