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cs.DS updates on arXiv.org

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
Frequent Elements with Witnesses in Data Streams
Christian Konrad · 2019-11-20 · via cs.DS updates on arXiv.org

Detecting frequent elements is among the oldest and most-studied problems in the area of data streams. Given a stream of $m$ data items in $\{1, 2, \dots, n\}$, the objective is to output items that appear at least $d$ times, for some threshold parameter $d$, and provably optimal algorithms are known today. However, in many applications, knowing only the frequent elements themselves is not enough: For example, an Internet router may not only need to know the most frequent destination IP addresses of forwarded packages, but also the timestamps of when these packages appeared or any other meta-data that "arrived" with the packages, e.g., their source IP addresses. In this paper, we introduce the witness version of the frequent elements problem: Given a desired approximation guarantee $α\ge 1$ and a desired frequency $d \le Δ$, where $Δ$ is the frequency of the most frequent item, the objective is to report an item together with at least $d / α$ timestamps of when the item appeared in the stream (or any other meta-data that arrived with the items). We give provably optimal algorithms for both the insertion-only and insertion-deletion stream settings: In insertion-only streams, we show that space $\tilde{O}(n + d \cdot n^{\frac{1}α})$ is necessary and sufficient for every integral $1 \le α\le \log n$. In insertion-deletion streams, we show that space $\tilde{O}(\frac{n \cdot d}{α^2})$ is necessary and sufficient, for every $α\le \sqrt{n}$.