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PAC Learning with Bandit Feedback: Sharp Sample Complexity in the Realizable Setting Algorithms with Polynomially-Improved Approximation Factors for the $2 \rightarrow q$ Norm, and Applications A computational phase transition for learning-to-sample from Ising models Covering vertices by sequential stars Fermi-Dirac machines as quantizations of neurons A Comprehensive Evaluation of Vertex Elimination Algorithms for Algorithmic Differentiation A Tight Bound on Localization of Electrical Flows Optimal Dimension-Free Sampling for Regularized Classification Reducing the Randomness in Partition Oracles for Bounded Degree Minor-Free Graphs Beyond the Half-Approximation: Fair and Efficient Online Class Matching Efficient Uniform Sampling of Surjections via their Profiles Tractable Maximization of Budgeted Phylogenetic Diversity on Networks Utilizing Node Scanwidth Fairness in Aggregation: Optimal Top-$k$ and Improved Full Ranking Learning-Augmented Online Scheduling with Parsimonious Preemption Entropy Equivalence Testing Lumberjack: Better Differentially Private Random Forests through Heavy Hitter Detection in Trees The Secretary Problem with a Stochastic Precursor Polynomial-Time Robust Multiclass Linear Classification under Gaussian Marginals Efficient Banzhaf-Based Data Valuation for $k$-Nearest Neighbors Classification Block-Sphere Vector Quantization An Approximation Algorithm for Graph Label Selection Iterative Chow Filtering for Learning with Distribution Shift Complexity of Non-Log-Concave Sampling in Fisher Information Stochastic Matching via Local Sparsification Finite Sample Bounds for Learning with Score Matching What is Learnable in Valiant's Theory of the Learnable? Provable Quantization with Randomized Hadamard Transform Min-Max Optimization Requires Exponentially Many Queries Fast and Compact Graph Cuts for the Boykov-Kolmogorov Algorithm A proximal gradient algorithm for composite log-concave sampling
Relative Error Streaming Quantiles with Seamless Mergeabi...
Tomáš Domes, Pavel Veselý · 2025-11-22 · via cs.DS updates on arXiv.org

Quantile summaries provide a scalable way to estimate the distribution of individual attributes in large datasets that are often distributed across multiple machines or generated by sensor networks. ReqSketch (arXiv:2004.01668) is currently the most space-efficient summary with two key properties: relative error guarantees, offering increasingly higher accuracy towards the distribution's tails, and mergeability, allowing distributed or parallel processing of datasets. Due to these features and its simple algorithm design, ReqSketch has been adopted in practice, via implementation in the Apache DataSketches library. However, the proof of mergeability in ReqSketch is overly complicated, requiring an intricate charging argument and complex variance analysis. In this paper, we provide a refined version of ReqSketch, by developing so-called adaptive compactors. This enables a significantly simplified proof of relative error guarantees in the most general mergeability setting, while retaining the original space bound, update time, and algorithmic simplicity. Moreover, the adaptivity of our sketch, together with the proof technique, yields near-optimal space bounds in specific scenarios - particularly when merging sketches of comparable size.