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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
HRNN: A Hybrid Graph Index for Approximate Reverse k-Near...
Wenxuan Xia, Mingyu Yang, Wentao Li, Wei Wang · 2026-06-02 · via cs.DS updates on arXiv.org

Reverse k-nearest neighbor (RkNN) search returns all data points that regard a query vector as one of their k-nearest neighbors (kNNs). Existing RkNN methods typically follow a filter-and-verification framework: vectors near the query vector are first collected as candidates and then verified against their kNN-radius (i.e., the distance to their k-th nearest neighbor). However, existing methods face two key limitations in high-dimensional spaces. First, nearby vectors often do not belong to the query's true RkNN set, resulting in excessive candidate expansion overhead. Second, existing methods compute kNN-radius online during verification, incurring substantial query-processing cost. To address these limitations, we propose HRNN, a hybrid graph index for approximate RkNN search. (1) Rather than directly treating nearby vectors as RkNN candidates, HRNN uses them as proxy points based on the assumption that a query's RkNN results can often be discovered through the RkNN results of its nearby vectors. (2) To reduce verification cost, HRNN materializes high-fidelity kNN-radius offline, eliminating expensive online reconstruction while preserving accuracy. HRNN combines a navigation graph, a ranked KNN graph, and reverse-neighbor lists into a hybrid index that supports efficient proxy retrieval, candidate generation, and kNN-radius access. We also develop efficient index construction and append-only maintenance algorithms. Extensive experiments show that HRNN consistently outperforms existing methods, achieving up to one order of magnitude higher throughput. Moreover, HRNN scales to datasets containing up to 10 million high-dimensional vectors while supporting efficient dynamic index maintenance.