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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
Array Layouts for Comparison-Based Searching
Paul-Virak Khuong, Pat Morin · 2015-09-17 · via cs.DS updates on arXiv.org

We attempt to determine the best order and search algorithm to store $n$ comparable data items in an array, $A$, of length $n$ so that we can, for any query value, $x$, quickly find the smallest value in $A$ that is greater than or equal to $x$. In particular, we consider the important case where there are many such queries to the same array, $A$, which resides entirely in RAM. In addition to the obvious sorted order/binary search combination we consider the Eytzinger (BFS) layout normally used for heaps, an implicit B-tree layout that generalizes the Eytzinger layout, and the van Emde Boas layout commonly used in the cache-oblivious algorithms literature. After extensive testing and tuning on a wide variety of modern hardware, we arrive at the conclusion that, for small values of $n$, sorted order, combined with a good implementation of binary search is best. For larger values of $n$, we arrive at the surprising conclusion that the Eytzinger layout is usually the fastest. The latter conclusion is unexpected and goes counter to earlier experimental work by Brodal, Fagerberg, and Jacob (SODA~2003), who concluded that both the B-tree and van Emde Boas layouts were faster than the Eytzinger layout for large values of $n$. Our fastest C++ implementations, when compiled, use conditional moves to avoid branch mispredictions and prefetching to reduce cache latency.