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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
Optimal Hashing in External Memory
Alex Conway, Martin Farach-Colton, Philip Shilane · 2018-05-24 · via cs.DS updates on arXiv.org

Hash tables are a ubiquitous class of dictionary data structures. However, standard hash table implementations do not translate well into the external memory model, because they do not incorporate locality for insertions. Iacono and Patracsu established an update/query tradeoff curve for external hash tables: a hash table that performs insertions in $O(λ/B)$ amortized IOs requires $Ω(\log_λN)$ expected IOs for queries, where $N$ is the number of items that can be stored in the data structure, $B$ is the size of a memory transfer, $M$ is the size of memory, and $λ$ is a tuning parameter. They provide a hashing data structure that meets this curve for $λ$ that is $Ω(\log\log M + \log_M N)$. Their data structure, which we call an \defn{IP hash table}, is complicated and, to the best of our knowledge, has not been implemented. In this paper, we present a new and much simpler optimal external memory hash table, the \defn{Bundle of Arrays Hash Table} (BOA). BOAs are based on size-tiered LSMs, a well-studied data structure, and are almost as easy to implement. The BOA is optimal for a narrower range of $λ$. However, the simplicity of BOAs allows them to be readily modified to achieve the following results: \begin{itemize} \item A new external memory data structure, the \defn{Bundle of Trees Hash Table} (BOT), that matches the performance of the IP hash table, while retaining some of the simplicity of the BOAs. \item The \defn{cache-oblivious Bundle of Trees Hash Table} (COBOT), the first cache-oblivious hash table. This data structure matches the optimality of BOTs and IP hash tables over the same range of $λ$. \end{itemize}