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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
iRangeGraph: Improvising Range-dedicated Graphs for Range...
Yuexuan Xu, Jianyang Gao, Yutong Gou, Cheng Long, Christian S. J · 2024-09-04 · via cs.DS updates on arXiv.org

Range-filtering approximate nearest neighbor (RFANN) search is attracting increasing attention in academia and industry. Given a set of data objects, each being a pair of a high-dimensional vector and a numeric value, an RFANN query with a vector and a numeric range as parameters returns the data object whose numeric value is in the query range and whose vector is nearest to the query vector. To process this query, a recent study proposes to build $O(n^2)$ dedicated graph-based indexes for all possible query ranges to enable efficient processing on a database of $n$ objects. As storing all these indexes is prohibitively expensive, the study constructs compressed indexes instead, which reduces the memory consumption considerably. However, this incurs suboptimal performance because the compression is lossy. In this study, instead of materializing a compressed index for every possible query range in preparation for querying, we materialize graph-based indexes, called elemental graphs, for a moderate number of ranges. We then provide an effective and efficient algorithm that during querying can construct an index for any query range using the elemental graphs. We prove that the time needed to construct such an index is low. We also cover an experimental study on real-world datasets that provides evidence that the materialized elemental graphs only consume moderate space and that the proposed method is capable of superior and stable query performance across different query workloads.