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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
glass: ordered set data structure for client-side order b...
Viktor Krapivensky · 2025-06-17 · via cs.DS updates on arXiv.org

The "ordered set" abstract data type with operations "insert", "erase", "find", "min", "max", "next" and "prev" is ubiquitous in computer science. It is usually implemented with red-black trees, $B$-trees, or $B^+$-trees. We present our implementation of ordered set based on a trie. It only supports integer keys (as opposed to keys of any strict weakly ordered type) and is optimized for market data, namely for what we call sequential locality. The following is the list of what we believe to be novelties: * Cached path to exploit sequential locality, and fast truncation thereof on erase operation; * A hash table (or, rather, a cache table) with hard O(1) time guarantees on any operation to speed up key lookup (up to a pre-leaf node); * Hardware-accelerated "find next/previous set bit" operations with BMI2 instruction set extension on x86-64; * Order book-specific features: the preemption principle and the tree restructure operation that prevent the tree from consuming too much memory. We achieve the following speedups over C++'s standard std::map container: 6x-20x on modifying operations, 30x on lookup operations, 9x-15x on real market data, and a more modest 2x-3x speedup on iteration. In this paper, we discuss our implementation.