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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
Dynamic External Hashing: The Limit of Buffering
Zhewei Wei, Ke Yi, Qin Zhang · 2008-11-19 · via cs.DS updates on arXiv.org

Hash tables are one of the most fundamental data structures in computer science, in both theory and practice. They are especially useful in external memory, where their query performance approaches the ideal cost of just one disk access. Knuth gave an elegant analysis showing that with some simple collision resolution strategies such as linear probing or chaining, the expected average number of disk I/Os of a lookup is merely $1+1/2^{Ω(b)}$, where each I/O can read a disk block containing $b$ items. Inserting a new item into the hash table also costs $1+1/2^{Ω(b)}$ I/Os, which is again almost the best one can do if the hash table is entirely stored on disk. However, this assumption is unrealistic since any algorithm operating on an external hash table must have some internal memory (at least $Ω(1)$ blocks) to work with. The availability of a small internal memory buffer can dramatically reduce the amortized insertion cost to $o(1)$ I/Os for many external memory data structures. In this paper we study the inherent query-insertion tradeoff of external hash tables in the presence of a memory buffer. In particular, we show that for any constant $c>1$, if the query cost is targeted at $1+O(1/b^{c})$ I/Os, then it is not possible to support insertions in less than $1-O(1/b^{\frac{c-1}{4}})$ I/Os amortized, which means that the memory buffer is essentially useless. While if the query cost is relaxed to $1+O(1/b^{c})$ I/Os for any constant $c<1$, there is a simple dynamic hash table with $o(1)$ insertion cost. These results also answer the open question recently posed by Jensen and Pagh.